TSTP Solution File: SEU152+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU152+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 4.30s 1.34s
% Output : Proof 5.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU152+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n017.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 : 300
% 0.13/0.35 % DateTime : Wed Aug 23 19:45:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.17/1.03 Prover 4: Preprocessing ...
% 2.17/1.03 Prover 1: Preprocessing ...
% 2.17/1.07 Prover 0: Preprocessing ...
% 2.17/1.07 Prover 5: Preprocessing ...
% 2.17/1.07 Prover 2: Preprocessing ...
% 2.17/1.07 Prover 6: Preprocessing ...
% 2.17/1.07 Prover 3: Preprocessing ...
% 3.15/1.19 Prover 1: Warning: ignoring some quantifiers
% 3.15/1.20 Prover 3: Warning: ignoring some quantifiers
% 3.15/1.21 Prover 6: Proving ...
% 3.44/1.21 Prover 3: Constructing countermodel ...
% 3.44/1.21 Prover 1: Constructing countermodel ...
% 3.44/1.21 Prover 2: Proving ...
% 3.44/1.21 Prover 5: Proving ...
% 3.44/1.23 Prover 4: Constructing countermodel ...
% 3.64/1.24 Prover 0: Proving ...
% 3.64/1.32 Prover 3: gave up
% 4.30/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.30/1.33 Prover 1: gave up
% 4.30/1.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.30/1.33 Prover 6: gave up
% 4.30/1.33 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.30/1.33 Prover 5: proved (691ms)
% 4.30/1.33
% 4.30/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.34
% 4.30/1.35 Prover 2: proved (702ms)
% 4.30/1.35
% 4.30/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.35
% 4.30/1.35 Prover 7: Preprocessing ...
% 4.30/1.35 Prover 0: proved (704ms)
% 4.30/1.35
% 4.30/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.35
% 4.30/1.36 Prover 9: Preprocessing ...
% 4.30/1.36 Prover 8: Preprocessing ...
% 4.30/1.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.30/1.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.30/1.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.30/1.37 Prover 7: Warning: ignoring some quantifiers
% 4.30/1.37 Prover 11: Preprocessing ...
% 4.30/1.37 Prover 10: Preprocessing ...
% 4.30/1.38 Prover 13: Preprocessing ...
% 4.30/1.39 Prover 8: Warning: ignoring some quantifiers
% 4.30/1.39 Prover 7: Constructing countermodel ...
% 4.30/1.40 Prover 8: Constructing countermodel ...
% 4.30/1.41 Prover 4: Found proof (size 19)
% 4.30/1.41 Prover 4: proved (764ms)
% 4.30/1.41 Prover 8: stopped
% 4.30/1.42 Prover 13: stopped
% 4.30/1.42 Prover 7: stopped
% 4.30/1.42 Prover 10: Warning: ignoring some quantifiers
% 4.30/1.42 Prover 10: Constructing countermodel ...
% 4.30/1.43 Prover 9: Warning: ignoring some quantifiers
% 4.30/1.43 Prover 10: stopped
% 4.30/1.43 Prover 9: Constructing countermodel ...
% 4.30/1.43 Prover 11: Constructing countermodel ...
% 4.30/1.43 Prover 9: stopped
% 4.30/1.44 Prover 11: stopped
% 4.30/1.44
% 4.30/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.44
% 4.30/1.44 % SZS output start Proof for theBenchmark
% 4.30/1.44 Assumptions after simplification:
% 4.30/1.44 ---------------------------------
% 4.30/1.44
% 4.30/1.44 (l23_zfmisc_1)
% 4.30/1.47 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) &
% 4.30/1.47 singleton(v0) = v2 & set_union2(v2, v1) = v3 & in(v0, v1) = 0 & $i(v3) &
% 4.30/1.47 $i(v2) & $i(v1) & $i(v0))
% 4.30/1.47
% 4.30/1.47 (l2_zfmisc_1)
% 4.30/1.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.30/1.48 (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 4.30/1.48 [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] :
% 4.30/1.48 ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 4.30/1.48 $i] : ? [v4: int] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) =
% 4.30/1.48 v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 4.30/1.48 (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 4.30/1.48 in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~
% 4.30/1.48 $i(v1) | ~ $i(v0) | ? [v2: $i] : (singleton(v0) = v2 & subset(v2, v1) = 0
% 4.30/1.48 & $i(v2)))
% 4.30/1.48
% 4.30/1.48 (t12_xboole_1)
% 4.30/1.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (set_union2(v0, v1) =
% 4.30/1.48 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0, v1)
% 4.30/1.48 = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1)
% 4.30/1.48 | ~ $i(v0) | set_union2(v0, v1) = v1)
% 4.30/1.48
% 4.30/1.49 (function-axioms)
% 4.30/1.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.30/1.49 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 4.30/1.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 4.30/1.49 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 4.30/1.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.30/1.49 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 4.30/1.49 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 4.30/1.49 (singleton(v2) = v0))
% 4.30/1.49
% 4.30/1.49 Further assumptions not needed in the proof:
% 4.30/1.49 --------------------------------------------
% 5.24/1.49 antisymmetry_r2_hidden, commutativity_k2_xboole_0, dt_k1_tarski, dt_k2_xboole_0,
% 5.24/1.49 idempotence_k2_xboole_0, reflexivity_r1_tarski
% 5.24/1.49
% 5.24/1.49 Those formulas are unsatisfiable:
% 5.24/1.49 ---------------------------------
% 5.24/1.49
% 5.24/1.49 Begin of proof
% 5.24/1.49 |
% 5.24/1.49 | ALPHA: (l2_zfmisc_1) implies:
% 5.24/1.50 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~
% 5.24/1.50 | $i(v0) | ? [v2: $i] : (singleton(v0) = v2 & subset(v2, v1) = 0 &
% 5.24/1.50 | $i(v2)))
% 5.24/1.50 |
% 5.24/1.50 | ALPHA: (t12_xboole_1) implies:
% 5.24/1.50 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (set_union2(v0,
% 5.24/1.50 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 5.24/1.50 | subset(v0, v1) = v3))
% 5.24/1.50 |
% 5.24/1.50 | ALPHA: (function-axioms) implies:
% 5.24/1.50 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 5.24/1.50 | = v1) | ~ (singleton(v2) = v0))
% 5.24/1.50 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.24/1.50 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 5.24/1.50 | = v0))
% 5.24/1.50 |
% 5.24/1.50 | DELTA: instantiating (l23_zfmisc_1) with fresh symbols all_9_0, all_9_1,
% 5.24/1.50 | all_9_2, all_9_3 gives:
% 5.24/1.50 | (5) ~ (all_9_0 = all_9_2) & singleton(all_9_3) = all_9_1 &
% 5.24/1.50 | set_union2(all_9_1, all_9_2) = all_9_0 & in(all_9_3, all_9_2) = 0 &
% 5.24/1.50 | $i(all_9_0) & $i(all_9_1) & $i(all_9_2) & $i(all_9_3)
% 5.24/1.50 |
% 5.24/1.50 | ALPHA: (5) implies:
% 5.24/1.50 | (6) ~ (all_9_0 = all_9_2)
% 5.24/1.50 | (7) $i(all_9_3)
% 5.24/1.50 | (8) $i(all_9_2)
% 5.24/1.51 | (9) $i(all_9_1)
% 5.24/1.51 | (10) in(all_9_3, all_9_2) = 0
% 5.24/1.51 | (11) set_union2(all_9_1, all_9_2) = all_9_0
% 5.24/1.51 | (12) singleton(all_9_3) = all_9_1
% 5.24/1.51 |
% 5.24/1.51 | GROUND_INST: instantiating (1) with all_9_3, all_9_2, simplifying with (7),
% 5.24/1.51 | (8), (10) gives:
% 5.24/1.51 | (13) ? [v0: $i] : (singleton(all_9_3) = v0 & subset(v0, all_9_2) = 0 &
% 5.24/1.51 | $i(v0))
% 5.24/1.51 |
% 5.24/1.51 | GROUND_INST: instantiating (2) with all_9_1, all_9_2, all_9_0, simplifying
% 5.24/1.51 | with (8), (9), (11) gives:
% 5.24/1.51 | (14) all_9_0 = all_9_2 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1,
% 5.24/1.51 | all_9_2) = v0)
% 5.24/1.51 |
% 5.24/1.51 | DELTA: instantiating (13) with fresh symbol all_19_0 gives:
% 5.24/1.51 | (15) singleton(all_9_3) = all_19_0 & subset(all_19_0, all_9_2) = 0 &
% 5.24/1.51 | $i(all_19_0)
% 5.24/1.51 |
% 5.24/1.51 | ALPHA: (15) implies:
% 5.24/1.51 | (16) subset(all_19_0, all_9_2) = 0
% 5.24/1.51 | (17) singleton(all_9_3) = all_19_0
% 5.24/1.51 |
% 5.24/1.51 | BETA: splitting (14) gives:
% 5.24/1.51 |
% 5.24/1.51 | Case 1:
% 5.24/1.51 | |
% 5.24/1.51 | | (18) all_9_0 = all_9_2
% 5.24/1.51 | |
% 5.24/1.51 | | REDUCE: (6), (18) imply:
% 5.24/1.51 | | (19) $false
% 5.24/1.51 | |
% 5.24/1.51 | | CLOSE: (19) is inconsistent.
% 5.24/1.51 | |
% 5.24/1.51 | Case 2:
% 5.24/1.51 | |
% 5.24/1.51 | | (20) ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1, all_9_2) = v0)
% 5.24/1.51 | |
% 5.24/1.51 | | DELTA: instantiating (20) with fresh symbol all_25_0 gives:
% 5.24/1.51 | | (21) ~ (all_25_0 = 0) & subset(all_9_1, all_9_2) = all_25_0
% 5.24/1.51 | |
% 5.24/1.51 | | ALPHA: (21) implies:
% 5.24/1.52 | | (22) ~ (all_25_0 = 0)
% 5.24/1.52 | | (23) subset(all_9_1, all_9_2) = all_25_0
% 5.24/1.52 | |
% 5.24/1.52 | | GROUND_INST: instantiating (3) with all_9_1, all_19_0, all_9_3, simplifying
% 5.24/1.52 | | with (12), (17) gives:
% 5.24/1.52 | | (24) all_19_0 = all_9_1
% 5.24/1.52 | |
% 5.24/1.52 | | REDUCE: (16), (24) imply:
% 5.24/1.52 | | (25) subset(all_9_1, all_9_2) = 0
% 5.24/1.52 | |
% 5.24/1.52 | | GROUND_INST: instantiating (4) with all_25_0, 0, all_9_2, all_9_1,
% 5.24/1.52 | | simplifying with (23), (25) gives:
% 5.24/1.52 | | (26) all_25_0 = 0
% 5.24/1.52 | |
% 5.24/1.52 | | REDUCE: (22), (26) imply:
% 5.24/1.52 | | (27) $false
% 5.24/1.52 | |
% 5.24/1.52 | | CLOSE: (27) is inconsistent.
% 5.24/1.52 | |
% 5.24/1.52 | End of split
% 5.24/1.52 |
% 5.24/1.52 End of proof
% 5.24/1.52 % SZS output end Proof for theBenchmark
% 5.24/1.52
% 5.24/1.52 896ms
%------------------------------------------------------------------------------