TSTP Solution File: SYN367+1 by Princess---170717

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Princess---170717
% Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess-casc +printProof -timeout=%d %s

% Computer : n029.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 : Thu Jul 21 11:10:33 EDT 2022

% Result   : Theorem 1.44s 1.02s
% Output   : Proof 2.56s
% Verified :
% SZS Type : -

%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12  % Command  : princess-casc +printProof -timeout=%d %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 14:59:47 EDT 2022
% 0.12/0.33  % CPUTime  :
% 0.18/0.57  ________       _____
% 0.18/0.57  ___  __ \_________(_)________________________________
% 0.18/0.57  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.57  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.57  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.57
% 0.18/0.57  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.57  (CASC 2017-07-17)
% 0.18/0.57
% 0.18/0.57  (c) Philipp RÃ¼mmer, 2009-2017
% 0.18/0.57  (contributions by Peter Backeman, Peter Baumgartner,
% 0.18/0.57                    Angelo Brillout, Aleksandar Zeljic)
% 0.18/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57  Bug reports to ph_r@gmx.net
% 0.18/0.57
% 0.18/0.57
% 0.61/0.60  Prover 0: Options:  +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off
% 1.14/0.86  Prover 0: Preprocessing ...
% 1.44/0.95  Prover 0: Constructing countermodel ...
% 1.44/1.02  Prover 0: proved (415ms)
% 1.44/1.02
% 1.44/1.02  VALID
% 1.44/1.02  % SZS status Theorem for theBenchmark
% 1.44/1.02
% 1.44/1.02  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off
% 1.73/1.04  Prover 1: Preprocessing ...
% 1.73/1.08  Prover 1: Constructing countermodel ...
% 1.96/1.16  Prover 1: gave up
% 1.96/1.16  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off
% 1.96/1.17  Prover 4: Preprocessing ...
% 2.21/1.20  Prover 4: Constructing countermodel ...
% 2.37/1.24  Prover 4: Found proof (size 10)
% 2.37/1.24  Prover 4: proved (77ms)
% 2.37/1.24
% 2.37/1.24
% 2.37/1.25  % SZS output start Proof for theBenchmark
% 2.37/1.25  Assumptions after simplification:
% 2.37/1.25  ---------------------------------
% 2.37/1.25
% 2.37/1.25    (x2118)
% 2.56/1.31     ? [v0: \$int] :  ? [v1: \$int] :  ? [v2: \$int] :  ? [v3: \$int] : ( ~ (v3 = 0) &
% 2.56/1.31       ~ (v1 = 0) & big_r(v0) = v1 & big_q(v2) = v3 &  ! [v4: \$int] :  ! [v5:
% 2.56/1.31        \$int] : (v5 = 0 |  ~ (big_r(v4) = v5) | big_q(v4) = 0) &  ! [v4: \$int] :
% 2.56/1.31      ! [v5: \$int] : (v5 = 0 |  ~ (big_r(v4) = v5) | p) &  ! [v4: \$int] :  ! [v5:
% 2.56/1.31        \$int] : (v5 = 0 |  ~ (big_q(v4) = v5) |  ~ p) &  ! [v4: \$int] :  ! [v5:
% 2.56/1.31        \$int] : (v5 = 0 |  ~ (big_q(v4) = v5) | big_r(v4) = 0) &  ! [v4: \$int] :
% 2.56/1.31      ! [v5: \$int] : ( ~ (big_r(v4) = v5) |  ~ p | big_q(v4) = 0) &  ! [v4: \$int]
% 2.56/1.31      :  ! [v5: \$int] : ( ~ (big_q(v4) = v5) | big_r(v4) = 0 | p))
% 2.56/1.31
% 2.56/1.31  Those formulas are unsatisfiable:
% 2.56/1.31  ---------------------------------
% 2.56/1.31
% 2.56/1.31  Begin of proof
% 2.56/1.32  |
% 2.56/1.32  | DELTA: instantiating (x2118) with fresh symbols all_1_0, all_1_1, all_1_2,
% 2.56/1.32  |        all_1_3 gives:
% 2.56/1.32  |   (1)   ~ (all_1_0 = 0) &  ~ (all_1_2 = 0) & big_r(all_1_3) = all_1_2 &
% 2.56/1.32  |        big_q(all_1_1) = all_1_0 &  ! [v0: \$int] :  ! [v1: \$int] : (v1 = 0 |  ~
% 2.56/1.32  |          (big_r(v0) = v1) | big_q(v0) = 0) &  ! [v0: \$int] :  ! [v1: \$int] :
% 2.56/1.32  |        (v1 = 0 |  ~ (big_r(v0) = v1) | p) &  ! [v0: \$int] :  ! [v1: \$int] :
% 2.56/1.32  |        (v1 = 0 |  ~ (big_q(v0) = v1) |  ~ p) &  ! [v0: \$int] :  ! [v1: \$int] :
% 2.56/1.32  |        (v1 = 0 |  ~ (big_q(v0) = v1) | big_r(v0) = 0) &  ! [v0: \$int] :  !
% 2.56/1.32  |        [v1: \$int] : ( ~ (big_r(v0) = v1) |  ~ p | big_q(v0) = 0) &  ! [v0:
% 2.56/1.32  |          \$int] :  ! [v1: \$int] : ( ~ (big_q(v0) = v1) | big_r(v0) = 0 | p)
% 2.56/1.32  |
% 2.56/1.32  | ALPHA: (1) implies:
% 2.56/1.33  |   (2)   ~ (all_1_2 = 0)
% 2.56/1.33  |   (3)   ~ (all_1_0 = 0)
% 2.56/1.33  |   (4)  big_q(all_1_1) = all_1_0
% 2.56/1.33  |   (5)  big_r(all_1_3) = all_1_2
% 2.56/1.33  |   (6)   ! [v0: \$int] :  ! [v1: \$int] : (v1 = 0 |  ~ (big_q(v0) = v1) |  ~ p)
% 2.56/1.33  |   (7)   ! [v0: \$int] :  ! [v1: \$int] : (v1 = 0 |  ~ (big_r(v0) = v1) | p)
% 2.56/1.33  |
% 2.56/1.33  | GROUND_INST: instantiating (7) with all_1_3, all_1_2, simplifying with (5)
% 2.56/1.33  |              gives:
% 2.56/1.33  |   (8)  all_1_2 = 0 | p
% 2.56/1.33  |
% 2.56/1.33  | BETA: splitting (8) gives:
% 2.56/1.33  |
% 2.56/1.33  | Case 1:
% 2.56/1.33  | |
% 2.56/1.33  | |   (9)  p
% 2.56/1.33  | |
% 2.56/1.33  | | GROUND_INST: instantiating (6) with all_1_1, all_1_0, simplifying with (4),
% 2.56/1.33  | |              (9) gives:
% 2.56/1.33  | |   (10)  all_1_0 = 0
% 2.56/1.33  | |
% 2.56/1.33  | | REDUCE: (3), (10) imply:
% 2.56/1.33  | |   (11)   ~ (0 = 0)
% 2.56/1.33  | |
% 2.56/1.33  | | CLOSE: (11) is inconsistent.
% 2.56/1.33  | |
% 2.56/1.33  | Case 2:
% 2.56/1.33  | |
% 2.56/1.33  | |   (12)  all_1_2 = 0
% 2.56/1.33  | |
% 2.56/1.33  | | REDUCE: (2), (12) imply:
% 2.56/1.33  | |   (13)   ~ (0 = 0)
% 2.56/1.33  | |
% 2.56/1.33  | | CLOSE: (13) is inconsistent.
% 2.56/1.33  | |
% 2.56/1.33  | End of split
% 2.56/1.33  |
% 2.56/1.33  End of proof
% 2.56/1.33  % SZS output end Proof for theBenchmark
% 2.56/1.33
% 2.56/1.33  751ms
%------------------------------------------------------------------------------
```