TSTP Solution File: SEU163+1 by Princess---170717

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Princess---170717
% Problem  : SEU163+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess-casc +printProof -timeout=%d %s

% Computer : n028.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 : Tue Jul 19 13:22:42 EDT 2022

% Result   : Theorem 1.99s 1.18s
% Output   : Proof 2.71s
% Verified :
% SZS Type : -

%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU163+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command  : princess-casc +printProof -timeout=%d %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 19 00:49:59 EDT 2022
% 0.13/0.34  % CPUTime  :
% 0.65/0.64  ________       _____
% 0.65/0.64  ___  __ \_________(_)________________________________
% 0.65/0.64  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.65/0.64  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.65/0.64  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.65/0.64
% 0.65/0.64  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.65/0.64  (CASC 2017-07-17)
% 0.65/0.64
% 0.65/0.64  (c) Philipp RÃ¼mmer, 2009-2017
% 0.65/0.64  (contributions by Peter Backeman, Peter Baumgartner,
% 0.65/0.64                    Angelo Brillout, Aleksandar Zeljic)
% 0.65/0.64  Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.64  Bug reports to ph_r@gmx.net
% 0.65/0.64
% 0.65/0.64
% 0.65/0.67  Prover 0: Options:  +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off
% 1.34/0.97  Prover 0: Preprocessing ...
% 1.72/1.10  Prover 0: Proving ...
% 1.99/1.18  Prover 0: proved (510ms)
% 1.99/1.18
% 1.99/1.18  VALID
% 1.99/1.18  % SZS status Theorem for theBenchmark
% 1.99/1.18
% 1.99/1.18  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off
% 1.99/1.21  Prover 1: Preprocessing ...
% 2.30/1.27  Prover 1: Constructing countermodel ...
% 2.48/1.35  Prover 1: Found proof (size 12)
% 2.48/1.35  Prover 1: proved (164ms)
% 2.48/1.35
% 2.48/1.35
% 2.48/1.35  % SZS output start Proof for theBenchmark
% 2.48/1.36  Assumptions after simplification:
% 2.48/1.36  ---------------------------------
% 2.48/1.36
% 2.48/1.36    (l50_zfmisc_1)
% 2.56/1.41     ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] : (v3 = 0 |  ~
% 2.56/1.41      (union(v1) = v2) |  ~ (subset(v0, v2) = v3) |  ? [v4: \$int] : ( ~ (v4 = 0) &
% 2.56/1.41        in(v0, v1) = v4))
% 2.56/1.41
% 2.56/1.41    (t92_zfmisc_1)
% 2.56/1.42     ? [v0: \$int] :  ? [v1: \$int] :  ? [v2: \$int] :  ? [v3: \$int] : ( ~ (v3 = 0) &
% 2.56/1.42      union(v1) = v2 & in(v0, v1) = 0 & subset(v0, v2) = v3)
% 2.56/1.42
% 2.56/1.42    (axioms)
% 2.56/1.42     ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] : (v1 = v0 |  ~
% 2.56/1.42      (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0: \$int] :  ! [v1: \$int] :
% 2.56/1.42    ! [v2: \$int] :  ! [v3: \$int] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~
% 2.56/1.42      (subset(v3, v2) = v0)) &  ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] : (v1
% 2.56/1.42      = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0))
% 2.56/1.42
% 2.56/1.42  Further assumptions not needed in the proof:
% 2.56/1.42  --------------------------------------------
% 2.56/1.42  antisymmetry_r2_hidden, dt_k3_tarski, reflexivity_r1_tarski
% 2.56/1.42
% 2.56/1.42  Those formulas are unsatisfiable:
% 2.56/1.42  ---------------------------------
% 2.56/1.42
% 2.56/1.42  Begin of proof
% 2.56/1.42  |
% 2.56/1.42  | ALPHA: (axioms) implies:
% 2.56/1.43  |   (1)   ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] : (v1 =
% 2.56/1.43  |          v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 2.56/1.43  |
% 2.56/1.43  | DELTA: instantiating (t92_zfmisc_1) with fresh symbols all_4_0, all_4_1,
% 2.56/1.43  |        all_4_2, all_4_3 gives:
% 2.71/1.43  |   (2)   ~ (all_4_0 = 0) & union(all_4_2) = all_4_1 & in(all_4_3, all_4_2) = 0
% 2.71/1.43  |        & subset(all_4_3, all_4_1) = all_4_0
% 2.71/1.43  |
% 2.71/1.43  | ALPHA: (2) implies:
% 2.71/1.43  |   (3)   ~ (all_4_0 = 0)
% 2.71/1.43  |   (4)  subset(all_4_3, all_4_1) = all_4_0
% 2.71/1.43  |   (5)  in(all_4_3, all_4_2) = 0
% 2.71/1.43  |   (6)  union(all_4_2) = all_4_1
% 2.71/1.43  |
% 2.71/1.43  | GROUND_INST: instantiating (l50_zfmisc_1) with all_4_3, all_4_2, all_4_1,
% 2.71/1.43  |              all_4_0, simplifying with (4), (6) gives:
% 2.71/1.43  |   (7)  all_4_0 = 0 |  ? [v0: \$int] : ( ~ (v0 = 0) & in(all_4_3, all_4_2) = v0)
% 2.71/1.43  |
% 2.71/1.43  | BETA: splitting (7) gives:
% 2.71/1.43  |
% 2.71/1.43  | Case 1:
% 2.71/1.43  | |
% 2.71/1.43  | |   (8)  all_4_0 = 0
% 2.71/1.43  | |
% 2.71/1.43  | | REDUCE: (3), (8) imply:
% 2.71/1.43  | |   (9)   ~ (0 = 0)
% 2.71/1.44  | |
% 2.71/1.44  | | CLOSE: (9) is inconsistent.
% 2.71/1.44  | |
% 2.71/1.44  | Case 2:
% 2.71/1.44  | |
% 2.71/1.44  | |   (10)   ? [v0: \$int] : ( ~ (v0 = 0) & in(all_4_3, all_4_2) = v0)
% 2.71/1.44  | |
% 2.71/1.44  | | DELTA: instantiating (10) with fresh symbol all_17_0 gives:
% 2.71/1.44  | |   (11)   ~ (all_17_0 = 0) & in(all_4_3, all_4_2) = all_17_0
% 2.71/1.44  | |
% 2.71/1.44  | | ALPHA: (11) implies:
% 2.71/1.44  | |   (12)   ~ (all_17_0 = 0)
% 2.71/1.44  | |   (13)  in(all_4_3, all_4_2) = all_17_0
% 2.71/1.44  | |
% 2.71/1.44  | | GROUND_INST: instantiating (1) with 0, all_17_0, all_4_2, all_4_3,
% 2.71/1.44  | |              simplifying with (5), (13) gives:
% 2.71/1.44  | |   (14)  all_17_0 = 0
% 2.71/1.44  | |
% 2.71/1.44  | | REDUCE: (12), (14) imply:
% 2.71/1.44  | |   (15)   ~ (0 = 0)
% 2.71/1.44  | |
% 2.71/1.44  | | CLOSE: (15) is inconsistent.
% 2.71/1.44  | |
% 2.71/1.44  | End of split
% 2.71/1.44  |
% 2.71/1.44  End of proof
% 2.71/1.44  % SZS output end Proof for theBenchmark
% 2.71/1.44
% 2.71/1.44  787ms
%------------------------------------------------------------------------------
```