TSTP Solution File: SEU152+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU152+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n025.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  : 300s
% DateTime : Thu Aug 31 17:42:49 EDT 2023

% Result   : Theorem 10.90s 2.19s
% Output   : Proof 13.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU152+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n025.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  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 17:20:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.27/1.13  Prover 4: Preprocessing ...
% 3.27/1.13  Prover 1: Preprocessing ...
% 3.51/1.17  Prover 0: Preprocessing ...
% 3.51/1.17  Prover 3: Preprocessing ...
% 3.51/1.17  Prover 2: Preprocessing ...
% 3.51/1.17  Prover 6: Preprocessing ...
% 3.51/1.17  Prover 5: Preprocessing ...
% 8.56/1.87  Prover 5: Proving ...
% 8.56/1.88  Prover 1: Warning: ignoring some quantifiers
% 9.09/1.92  Prover 6: Proving ...
% 9.09/1.96  Prover 1: Constructing countermodel ...
% 9.09/1.97  Prover 3: Warning: ignoring some quantifiers
% 9.09/1.99  Prover 4: Warning: ignoring some quantifiers
% 9.09/2.00  Prover 3: Constructing countermodel ...
% 9.09/2.02  Prover 2: Proving ...
% 9.87/2.09  Prover 4: Constructing countermodel ...
% 10.90/2.19  Prover 3: proved (1564ms)
% 10.90/2.19  
% 10.90/2.19  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.90/2.19  
% 10.90/2.19  Prover 2: stopped
% 10.90/2.19  Prover 6: stopped
% 10.90/2.19  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.90/2.20  Prover 5: stopped
% 10.90/2.21  Prover 0: Proving ...
% 10.90/2.21  Prover 0: stopped
% 10.90/2.21  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.90/2.21  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.90/2.21  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.90/2.21  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.85/2.33  Prover 13: Preprocessing ...
% 11.85/2.33  Prover 7: Preprocessing ...
% 11.85/2.33  Prover 11: Preprocessing ...
% 11.85/2.34  Prover 8: Preprocessing ...
% 11.85/2.34  Prover 1: Found proof (size 21)
% 11.85/2.34  Prover 1: proved (1722ms)
% 11.85/2.34  Prover 10: Preprocessing ...
% 11.85/2.35  Prover 4: stopped
% 12.21/2.38  Prover 7: stopped
% 12.21/2.39  Prover 10: stopped
% 12.21/2.39  Prover 11: stopped
% 12.21/2.40  Prover 13: stopped
% 12.73/2.47  Prover 8: Warning: ignoring some quantifiers
% 12.89/2.49  Prover 8: Constructing countermodel ...
% 12.89/2.50  Prover 8: stopped
% 12.89/2.50  
% 12.89/2.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.89/2.50  
% 12.89/2.50  % SZS output start Proof for theBenchmark
% 12.89/2.51  Assumptions after simplification:
% 12.89/2.51  ---------------------------------
% 12.89/2.51  
% 12.89/2.51    (l23_zfmisc_1)
% 12.89/2.53     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = v1) &
% 12.89/2.53      singleton(v0) = v2 & set_union2(v2, v1) = v3 & in(v0, v1) = 0 & $i(v3) &
% 12.89/2.53      $i(v2) & $i(v1) & $i(v0))
% 12.89/2.53  
% 12.89/2.53    (l2_zfmisc_1)
% 13.11/2.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 13.11/2.53      (singleton(v0) = v2) |  ~ (subset(v2, v1) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 13.11/2.53      [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) &  ! [v0: $i] :  ! [v1: $i] : 
% 13.11/2.53    ! [v2: $i] : ( ~ (singleton(v0) = v2) |  ~ (subset(v2, v1) = 0) |  ~ $i(v1) | 
% 13.11/2.53      ~ $i(v0) | in(v0, v1) = 0)
% 13.11/2.53  
% 13.11/2.53    (t12_xboole_1)
% 13.11/2.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (set_union2(v0, v1) =
% 13.11/2.53        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & subset(v0, v1)
% 13.11/2.53        = v3))
% 13.11/2.53  
% 13.11/2.53    (function-axioms)
% 13.11/2.54     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 13.11/2.54    [v3: $i] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 13.11/2.54    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 13.11/2.54      (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0:
% 13.11/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 13.11/2.54    : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0:
% 13.11/2.54      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 13.11/2.54      (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  !
% 13.11/2.54    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 13.11/2.54      (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0: $i] :  !
% 13.11/2.54    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unordered_pair(v3, v2) =
% 13.11/2.54        v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 13.11/2.54    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 13.11/2.54      (proper_subset(v3, v2) = v1) |  ~ (proper_subset(v3, v2) = v0)) &  ! [v0:
% 13.11/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 13.11/2.54    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 13.11/2.54      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 13.11/2.54      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 13.11/2.54    [v2: $i] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  !
% 13.11/2.54    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~
% 13.11/2.54      (singleton(v2) = v0))
% 13.11/2.54  
% 13.11/2.54  Further assumptions not needed in the proof:
% 13.11/2.54  --------------------------------------------
% 13.11/2.54  antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 13.11/2.54  commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski,
% 13.11/2.54  d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d3_tarski, d3_xboole_0,
% 13.11/2.54  d4_xboole_0, d7_xboole_0, d8_xboole_0, dt_k1_tarski, dt_k1_xboole_0,
% 13.11/2.54  dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0,
% 13.11/2.54  fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 13.17/2.54  idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l32_xboole_1,
% 13.17/2.54  l3_zfmisc_1, l4_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 13.17/2.54  symmetry_r1_xboole_0, t10_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole,
% 13.17/2.54  t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski,
% 13.17/2.54  t2_xboole_1, t33_xboole_1, t36_xboole_1, t37_xboole_1, t39_xboole_1, t3_boole,
% 13.17/2.54  t3_xboole_0, t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1, t4_boole,
% 13.17/2.54  t4_xboole_0, t60_xboole_1, t63_xboole_1, t69_enumset1, t6_boole, t6_zfmisc_1,
% 13.17/2.54  t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1,
% 13.17/2.54  t9_zfmisc_1
% 13.17/2.54  
% 13.17/2.54  Those formulas are unsatisfiable:
% 13.17/2.54  ---------------------------------
% 13.17/2.54  
% 13.17/2.54  Begin of proof
% 13.17/2.54  | 
% 13.17/2.54  | ALPHA: (l2_zfmisc_1) implies:
% 13.17/2.54  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 13.17/2.55  |          (singleton(v0) = v2) |  ~ (subset(v2, v1) = v3) |  ~ $i(v1) |  ~
% 13.17/2.55  |          $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 13.17/2.55  | 
% 13.17/2.55  | ALPHA: (function-axioms) implies:
% 13.17/2.55  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 13.17/2.55  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 13.17/2.55  | 
% 13.17/2.55  | DELTA: instantiating (l23_zfmisc_1) with fresh symbols all_77_0, all_77_1,
% 13.17/2.55  |        all_77_2, all_77_3 gives:
% 13.17/2.55  |   (3)   ~ (all_77_0 = all_77_2) & singleton(all_77_3) = all_77_1 &
% 13.17/2.55  |        set_union2(all_77_1, all_77_2) = all_77_0 & in(all_77_3, all_77_2) = 0
% 13.17/2.55  |        & $i(all_77_0) & $i(all_77_1) & $i(all_77_2) & $i(all_77_3)
% 13.17/2.55  | 
% 13.17/2.55  | ALPHA: (3) implies:
% 13.17/2.55  |   (4)   ~ (all_77_0 = all_77_2)
% 13.17/2.55  |   (5)  $i(all_77_3)
% 13.17/2.55  |   (6)  $i(all_77_2)
% 13.17/2.55  |   (7)  $i(all_77_1)
% 13.17/2.55  |   (8)  in(all_77_3, all_77_2) = 0
% 13.17/2.55  |   (9)  set_union2(all_77_1, all_77_2) = all_77_0
% 13.17/2.55  |   (10)  singleton(all_77_3) = all_77_1
% 13.17/2.55  | 
% 13.17/2.55  | GROUND_INST: instantiating (t12_xboole_1) with all_77_1, all_77_2, all_77_0,
% 13.17/2.55  |              simplifying with (6), (7), (9) gives:
% 13.17/2.55  |   (11)  all_77_0 = all_77_2 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_77_1,
% 13.17/2.55  |             all_77_2) = v0)
% 13.17/2.55  | 
% 13.17/2.55  | BETA: splitting (11) gives:
% 13.17/2.55  | 
% 13.17/2.55  | Case 1:
% 13.17/2.55  | | 
% 13.17/2.55  | |   (12)  all_77_0 = all_77_2
% 13.17/2.55  | | 
% 13.17/2.55  | | REDUCE: (4), (12) imply:
% 13.17/2.55  | |   (13)  $false
% 13.17/2.55  | | 
% 13.17/2.55  | | CLOSE: (13) is inconsistent.
% 13.17/2.55  | | 
% 13.17/2.55  | Case 2:
% 13.17/2.55  | | 
% 13.17/2.55  | |   (14)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_77_1, all_77_2) = v0)
% 13.17/2.55  | | 
% 13.17/2.55  | | DELTA: instantiating (14) with fresh symbol all_114_0 gives:
% 13.17/2.55  | |   (15)   ~ (all_114_0 = 0) & subset(all_77_1, all_77_2) = all_114_0
% 13.17/2.55  | | 
% 13.17/2.55  | | ALPHA: (15) implies:
% 13.17/2.55  | |   (16)   ~ (all_114_0 = 0)
% 13.17/2.55  | |   (17)  subset(all_77_1, all_77_2) = all_114_0
% 13.17/2.55  | | 
% 13.17/2.55  | | GROUND_INST: instantiating (1) with all_77_3, all_77_2, all_77_1, all_114_0,
% 13.17/2.55  | |              simplifying with (5), (6), (10), (17) gives:
% 13.17/2.56  | |   (18)  all_114_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_77_3, all_77_2)
% 13.17/2.56  | |           = v0)
% 13.17/2.56  | | 
% 13.17/2.56  | | BETA: splitting (18) gives:
% 13.17/2.56  | | 
% 13.17/2.56  | | Case 1:
% 13.17/2.56  | | | 
% 13.17/2.56  | | |   (19)  all_114_0 = 0
% 13.17/2.56  | | | 
% 13.17/2.56  | | | REDUCE: (16), (19) imply:
% 13.17/2.56  | | |   (20)  $false
% 13.17/2.56  | | | 
% 13.17/2.56  | | | CLOSE: (20) is inconsistent.
% 13.17/2.56  | | | 
% 13.17/2.56  | | Case 2:
% 13.17/2.56  | | | 
% 13.17/2.56  | | |   (21)   ? [v0: int] : ( ~ (v0 = 0) & in(all_77_3, all_77_2) = v0)
% 13.17/2.56  | | | 
% 13.17/2.56  | | | DELTA: instantiating (21) with fresh symbol all_138_0 gives:
% 13.17/2.56  | | |   (22)   ~ (all_138_0 = 0) & in(all_77_3, all_77_2) = all_138_0
% 13.17/2.56  | | | 
% 13.17/2.56  | | | ALPHA: (22) implies:
% 13.17/2.56  | | |   (23)   ~ (all_138_0 = 0)
% 13.17/2.56  | | |   (24)  in(all_77_3, all_77_2) = all_138_0
% 13.17/2.56  | | | 
% 13.17/2.56  | | | GROUND_INST: instantiating (2) with 0, all_138_0, all_77_2, all_77_3,
% 13.17/2.56  | | |              simplifying with (8), (24) gives:
% 13.17/2.56  | | |   (25)  all_138_0 = 0
% 13.17/2.56  | | | 
% 13.17/2.56  | | | REDUCE: (23), (25) imply:
% 13.17/2.56  | | |   (26)  $false
% 13.17/2.56  | | | 
% 13.17/2.56  | | | CLOSE: (26) is inconsistent.
% 13.17/2.56  | | | 
% 13.17/2.56  | | End of split
% 13.17/2.56  | | 
% 13.17/2.56  | End of split
% 13.17/2.56  | 
% 13.17/2.56  End of proof
% 13.17/2.56  % SZS output end Proof for theBenchmark
% 13.17/2.56  
% 13.17/2.56  1955ms
%------------------------------------------------------------------------------