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