TSTP Solution File: LCL666+1.001 by Princess---170717

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---170717
% Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess-casc +printProof -timeout=%d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 13:40:59 EDT 2022

% Result   : Theorem 1.93s 1.16s
% Output   : Proof 2.92s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14  % Command  : princess-casc +printProof -timeout=%d %s
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul  4 22:05:57 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.49/0.62  ________       _____
% 0.49/0.62  ___  __ \_________(_)________________________________
% 0.49/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.49/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.49/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.49/0.62  
% 0.49/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.49/0.62  (CASC 2017-07-17)
% 0.49/0.62  
% 0.49/0.62  (c) Philipp Rümmer, 2009-2017
% 0.49/0.62  (contributions by Peter Backeman, Peter Baumgartner,
% 0.49/0.62                    Angelo Brillout, Aleksandar Zeljic)
% 0.49/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.62  Bug reports to ph_r@gmx.net
% 0.49/0.62  
% 0.49/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.49/0.62  
% 0.49/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.65  Prover 0: Options:  +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off
% 1.37/0.96  Prover 0: Preprocessing ...
% 1.71/1.09  Prover 0: Constructing countermodel ...
% 1.93/1.16  Prover 0: proved (508ms)
% 1.93/1.16  
% 1.93/1.16  VALID
% 1.93/1.16  % SZS status Theorem for theBenchmark
% 1.93/1.16  
% 1.93/1.16  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off
% 2.05/1.19  Prover 1: Preprocessing ...
% 2.28/1.24  Prover 1: Constructing countermodel ...
% 2.32/1.28  Prover 1: gave up
% 2.32/1.28  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off
% 2.32/1.29  Prover 4: Preprocessing ...
% 2.49/1.33  Prover 4: Constructing countermodel ...
% 2.58/1.40  Prover 4: Found proof (size 18)
% 2.58/1.40  Prover 4: proved (118ms)
% 2.58/1.40  
% 2.58/1.40  
% 2.58/1.42  % SZS output start Proof for theBenchmark
% 2.58/1.42  Assumptions after simplification:
% 2.58/1.42  ---------------------------------
% 2.58/1.42  
% 2.58/1.42    (main)
% 2.79/1.46     ? [v0: $int] : (p201(v0) = 0 & p101(v0) = 0 &  ! [v1: $int] : ( ~ (p201(v1) =
% 2.79/1.46          0) |  ? [v2: $int] :  ? [v3: $int] : (p101(v1) = v3 & r1(v0, v1) = v2 &
% 2.79/1.46          ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v1: $int] : ( ~ (p101(v1) = 0) |  ?
% 2.79/1.46        [v2: $int] :  ? [v3: $int] : (p201(v1) = v3 & r1(v0, v1) = v2 & ( ~ (v3 =
% 2.79/1.46              0) |  ~ (v2 = 0)))) &  ! [v1: $int] : ( ~ (r1(v0, v1) = 0) |  ? [v2:
% 2.79/1.46          $int] :  ? [v3: $int] : (p201(v1) = v2 & p101(v1) = v3 & ( ~ (v3 = 0) | 
% 2.79/1.46            ~ (v2 = 0)))))
% 2.79/1.46  
% 2.79/1.46    (reflexivity)
% 2.79/1.46     ! [v0: $int] :  ! [v1: $int] : (v1 = 0 |  ~ (r1(v0, v0) = v1))
% 2.79/1.46  
% 2.79/1.46    (axioms)
% 2.79/1.46     ! [v0: $int] :  ! [v1: $int] :  ! [v2: $int] :  ! [v3: $int] : (v1 = v0 |  ~
% 2.79/1.46      (r1(v3, v2) = v1) |  ~ (r1(v3, v2) = v0)) &  ! [v0: $int] :  ! [v1: $int] : 
% 2.79/1.46    ! [v2: $int] : (v1 = v0 |  ~ (p201(v2) = v1) |  ~ (p201(v2) = v0)) &  ! [v0:
% 2.79/1.46      $int] :  ! [v1: $int] :  ! [v2: $int] : (v1 = v0 |  ~ (p101(v2) = v1) |  ~
% 2.79/1.46      (p101(v2) = v0))
% 2.79/1.46  
% 2.79/1.46  Those formulas are unsatisfiable:
% 2.79/1.46  ---------------------------------
% 2.79/1.46  
% 2.79/1.46  Begin of proof
% 2.79/1.46  | 
% 2.79/1.47  | ALPHA: (axioms) implies:
% 2.79/1.47  |   (1)   ! [v0: $int] :  ! [v1: $int] :  ! [v2: $int] : (v1 = v0 |  ~ (p201(v2)
% 2.79/1.47  |            = v1) |  ~ (p201(v2) = v0))
% 2.79/1.47  |   (2)   ! [v0: $int] :  ! [v1: $int] :  ! [v2: $int] :  ! [v3: $int] : (v1 =
% 2.79/1.47  |          v0 |  ~ (r1(v3, v2) = v1) |  ~ (r1(v3, v2) = v0))
% 2.79/1.47  | 
% 2.79/1.47  | DELTA: instantiating (main) with fresh symbol all_2_0 gives:
% 2.79/1.47  |   (3)  p201(all_2_0) = 0 & p101(all_2_0) = 0 &  ! [v0: $int] : ( ~ (p201(v0) =
% 2.79/1.47  |            0) |  ? [v1: $int] :  ? [v2: $int] : (p101(v0) = v2 & r1(all_2_0,
% 2.79/1.47  |              v0) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0)))) &  ! [v0: $int] : ( ~
% 2.79/1.47  |          (p101(v0) = 0) |  ? [v1: $int] :  ? [v2: $int] : (p201(v0) = v2 &
% 2.79/1.47  |            r1(all_2_0, v0) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0)))) &  ! [v0:
% 2.79/1.47  |          $int] : ( ~ (r1(all_2_0, v0) = 0) |  ? [v1: $int] :  ? [v2: $int] :
% 2.79/1.47  |          (p201(v0) = v1 & p101(v0) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0))))
% 2.79/1.47  | 
% 2.79/1.47  | ALPHA: (3) implies:
% 2.79/1.47  |   (4)  p101(all_2_0) = 0
% 2.79/1.47  |   (5)  p201(all_2_0) = 0
% 2.79/1.47  |   (6)   ! [v0: $int] : ( ~ (p101(v0) = 0) |  ? [v1: $int] :  ? [v2: $int] :
% 2.79/1.47  |          (p201(v0) = v2 & r1(all_2_0, v0) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0))))
% 2.92/1.48  |   (7)   ! [v0: $int] : ( ~ (p201(v0) = 0) |  ? [v1: $int] :  ? [v2: $int] :
% 2.92/1.48  |          (p101(v0) = v2 & r1(all_2_0, v0) = v1 & ( ~ (v2 = 0) |  ~ (v1 = 0))))
% 2.92/1.48  | 
% 2.92/1.48  | GROUND_INST: instantiating (7) with all_2_0, simplifying with (5) gives:
% 2.92/1.48  |   (8)   ? [v0: $int] :  ? [v1: $int] : (p101(all_2_0) = v1 & r1(all_2_0,
% 2.92/1.48  |            all_2_0) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 2.92/1.48  | 
% 2.92/1.48  | GROUND_INST: instantiating (6) with all_2_0, simplifying with (4) gives:
% 2.92/1.48  |   (9)   ? [v0: $int] :  ? [v1: $int] : (p201(all_2_0) = v1 & r1(all_2_0,
% 2.92/1.48  |            all_2_0) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 2.92/1.48  | 
% 2.92/1.48  | DELTA: instantiating (9) with fresh symbols all_10_0, all_10_1 gives:
% 2.92/1.48  |   (10)  p201(all_2_0) = all_10_0 & r1(all_2_0, all_2_0) = all_10_1 & ( ~
% 2.92/1.48  |           (all_10_0 = 0) |  ~ (all_10_1 = 0))
% 2.92/1.48  | 
% 2.92/1.48  | ALPHA: (10) implies:
% 2.92/1.48  |   (11)  r1(all_2_0, all_2_0) = all_10_1
% 2.92/1.48  |   (12)  p201(all_2_0) = all_10_0
% 2.92/1.48  |   (13)   ~ (all_10_0 = 0) |  ~ (all_10_1 = 0)
% 2.92/1.48  | 
% 2.92/1.48  | DELTA: instantiating (8) with fresh symbols all_12_0, all_12_1 gives:
% 2.92/1.48  |   (14)  p101(all_2_0) = all_12_0 & r1(all_2_0, all_2_0) = all_12_1 & ( ~
% 2.92/1.48  |           (all_12_0 = 0) |  ~ (all_12_1 = 0))
% 2.92/1.48  | 
% 2.92/1.48  | ALPHA: (14) implies:
% 2.92/1.48  |   (15)  r1(all_2_0, all_2_0) = all_12_1
% 2.92/1.48  | 
% 2.92/1.48  | GROUND_INST: instantiating (1) with 0, all_10_0, all_2_0, simplifying with
% 2.92/1.48  |              (5), (12) gives:
% 2.92/1.48  |   (16)  all_10_0 = 0
% 2.92/1.48  | 
% 2.92/1.48  | GROUND_INST: instantiating (reflexivity) with all_2_0, all_12_1, simplifying
% 2.92/1.48  |              with (15) gives:
% 2.92/1.48  |   (17)  all_12_1 = 0
% 2.92/1.48  | 
% 2.92/1.48  | GROUND_INST: instantiating (2) with all_12_1, all_10_1, all_2_0, all_2_0,
% 2.92/1.48  |              simplifying with (11), (15) gives:
% 2.92/1.48  |   (18)  all_12_1 = all_10_1
% 2.92/1.48  | 
% 2.92/1.48  | COMBINE_EQS: (17), (18) imply:
% 2.92/1.48  |   (19)  all_10_1 = 0
% 2.92/1.48  | 
% 2.92/1.48  | BETA: splitting (13) gives:
% 2.92/1.48  | 
% 2.92/1.48  | Case 1:
% 2.92/1.48  | | 
% 2.92/1.48  | |   (20)   ~ (all_10_0 = 0)
% 2.92/1.48  | | 
% 2.92/1.48  | | REDUCE: (16), (20) imply:
% 2.92/1.48  | |   (21)   ~ (0 = 0)
% 2.92/1.48  | | 
% 2.92/1.48  | | CLOSE: (21) is inconsistent.
% 2.92/1.48  | | 
% 2.92/1.48  | Case 2:
% 2.92/1.48  | | 
% 2.92/1.48  | |   (22)   ~ (all_10_1 = 0)
% 2.92/1.48  | | 
% 2.92/1.49  | | REDUCE: (19), (22) imply:
% 2.92/1.49  | |   (23)   ~ (0 = 0)
% 2.92/1.49  | | 
% 2.92/1.49  | | CLOSE: (23) is inconsistent.
% 2.92/1.49  | | 
% 2.92/1.49  | End of split
% 2.92/1.49  | 
% 2.92/1.49  End of proof
% 2.92/1.49  % SZS output end Proof for theBenchmark
% 2.92/1.49  
% 2.92/1.49  855ms
%------------------------------------------------------------------------------