TSTP Solution File: SET874+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.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 15:26:52 EDT 2023
% Result : Theorem 5.27s 1.45s
% Output : Proof 6.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n024.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 : Sat Aug 26 15:49:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/0.97 Prover 1: Preprocessing ...
% 2.13/0.97 Prover 4: Preprocessing ...
% 2.40/1.03 Prover 3: Preprocessing ...
% 2.40/1.03 Prover 0: Preprocessing ...
% 2.40/1.03 Prover 6: Preprocessing ...
% 2.40/1.03 Prover 2: Preprocessing ...
% 2.40/1.03 Prover 5: Preprocessing ...
% 3.53/1.23 Prover 1: Warning: ignoring some quantifiers
% 3.53/1.23 Prover 3: Warning: ignoring some quantifiers
% 3.53/1.25 Prover 5: Proving ...
% 4.19/1.25 Prover 3: Constructing countermodel ...
% 4.19/1.25 Prover 6: Proving ...
% 4.19/1.25 Prover 1: Constructing countermodel ...
% 4.19/1.27 Prover 4: Warning: ignoring some quantifiers
% 4.19/1.28 Prover 4: Constructing countermodel ...
% 4.19/1.29 Prover 0: Proving ...
% 4.19/1.30 Prover 2: Proving ...
% 5.27/1.45 Prover 0: proved (820ms)
% 5.27/1.45
% 5.27/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.27/1.45
% 5.27/1.45 Prover 3: proved (817ms)
% 5.27/1.45
% 5.27/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.27/1.45
% 5.27/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.27/1.45 Prover 6: stopped
% 5.27/1.45 Prover 5: stopped
% 5.27/1.45 Prover 2: proved (824ms)
% 5.27/1.45
% 5.27/1.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.27/1.46
% 5.27/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.27/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.27/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.27/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.27/1.47 Prover 4: Found proof (size 16)
% 5.27/1.47 Prover 4: proved (835ms)
% 5.27/1.48 Prover 1: stopped
% 5.27/1.48 Prover 8: Preprocessing ...
% 5.27/1.49 Prover 10: Preprocessing ...
% 5.27/1.49 Prover 11: Preprocessing ...
% 5.27/1.49 Prover 13: Preprocessing ...
% 5.27/1.49 Prover 7: Preprocessing ...
% 5.95/1.50 Prover 10: stopped
% 5.95/1.51 Prover 7: stopped
% 5.95/1.51 Prover 13: stopped
% 5.95/1.51 Prover 11: stopped
% 5.95/1.53 Prover 8: Warning: ignoring some quantifiers
% 5.95/1.54 Prover 8: Constructing countermodel ...
% 5.95/1.54 Prover 8: stopped
% 5.95/1.54
% 5.95/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.95/1.54
% 5.95/1.54 % SZS output start Proof for theBenchmark
% 5.95/1.55 Assumptions after simplification:
% 5.95/1.55 ---------------------------------
% 5.95/1.55
% 5.95/1.55 (commutativity_k2_tarski)
% 5.95/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 5.95/1.58 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 5.95/1.58 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 5.95/1.58 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 5.95/1.58
% 5.95/1.58 (d2_tarski)
% 5.95/1.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 5.95/1.58 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 5.95/1.58 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.95/1.58 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) =
% 5.95/1.58 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 5.95/1.58 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~
% 5.95/1.58 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : !
% 5.95/1.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) =
% 5.95/1.58 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] :
% 5.95/1.58 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) &
% 5.95/1.58 (v5 = 0 | v4 = v2 | v4 = v1)))
% 5.95/1.58
% 5.95/1.58 (l23_zfmisc_1)
% 5.95/1.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 5.95/1.59 (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0)
% 5.95/1.59 | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1:
% 5.95/1.59 $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 6.44/1.59 (singleton(v0) = v2 & set_union2(v2, v1) = v1 & $i(v2)))
% 6.44/1.59
% 6.44/1.59 (t14_zfmisc_1)
% 6.44/1.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 6.44/1.59 = v3) & singleton(v0) = v2 & set_union2(v2, v3) = v4 & unordered_pair(v0,
% 6.44/1.59 v1) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.44/1.59
% 6.44/1.59 Further assumptions not needed in the proof:
% 6.44/1.59 --------------------------------------------
% 6.44/1.59 antisymmetry_r2_hidden, commutativity_k2_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 6.44/1.59 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0
% 6.44/1.59
% 6.44/1.59 Those formulas are unsatisfiable:
% 6.44/1.59 ---------------------------------
% 6.44/1.59
% 6.44/1.59 Begin of proof
% 6.44/1.59 |
% 6.44/1.59 | ALPHA: (commutativity_k2_tarski) implies:
% 6.44/1.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 6.44/1.59 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 6.44/1.59 | $i(v2)))
% 6.44/1.59 |
% 6.44/1.59 | ALPHA: (d2_tarski) implies:
% 6.44/1.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.44/1.60 | (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3) | ~ $i(v2) | ~
% 6.44/1.60 | $i(v1) | ~ $i(v0))
% 6.44/1.60 |
% 6.44/1.60 | ALPHA: (l23_zfmisc_1) implies:
% 6.44/1.60 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 6.44/1.60 | (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ $i(v1) | ~
% 6.44/1.60 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 6.44/1.60 |
% 6.44/1.60 | DELTA: instantiating (t14_zfmisc_1) with fresh symbols all_15_0, all_15_1,
% 6.44/1.60 | all_15_2, all_15_3, all_15_4 gives:
% 6.44/1.60 | (4) ~ (all_15_0 = all_15_1) & singleton(all_15_4) = all_15_2 &
% 6.44/1.60 | set_union2(all_15_2, all_15_1) = all_15_0 & unordered_pair(all_15_4,
% 6.44/1.60 | all_15_3) = all_15_1 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) &
% 6.44/1.60 | $i(all_15_3) & $i(all_15_4)
% 6.44/1.60 |
% 6.44/1.60 | ALPHA: (4) implies:
% 6.44/1.60 | (5) ~ (all_15_0 = all_15_1)
% 6.44/1.60 | (6) $i(all_15_4)
% 6.44/1.60 | (7) $i(all_15_3)
% 6.44/1.60 | (8) unordered_pair(all_15_4, all_15_3) = all_15_1
% 6.44/1.60 | (9) set_union2(all_15_2, all_15_1) = all_15_0
% 6.44/1.60 | (10) singleton(all_15_4) = all_15_2
% 6.44/1.60 |
% 6.44/1.61 | GROUND_INST: instantiating (1) with all_15_3, all_15_4, all_15_1, simplifying
% 6.44/1.61 | with (6), (7), (8) gives:
% 6.44/1.61 | (11) unordered_pair(all_15_3, all_15_4) = all_15_1 & $i(all_15_1)
% 6.44/1.61 |
% 6.44/1.61 | ALPHA: (11) implies:
% 6.44/1.61 | (12) $i(all_15_1)
% 6.44/1.61 | (13) unordered_pair(all_15_3, all_15_4) = all_15_1
% 6.44/1.61 |
% 6.44/1.61 | GROUND_INST: instantiating (3) with all_15_4, all_15_1, all_15_2, all_15_0,
% 6.44/1.61 | simplifying with (6), (9), (10), (12) gives:
% 6.44/1.61 | (14) all_15_0 = all_15_1 | ? [v0: int] : ( ~ (v0 = 0) & in(all_15_4,
% 6.44/1.61 | all_15_1) = v0)
% 6.44/1.61 |
% 6.44/1.61 | BETA: splitting (14) gives:
% 6.44/1.61 |
% 6.44/1.61 | Case 1:
% 6.44/1.61 | |
% 6.44/1.61 | | (15) all_15_0 = all_15_1
% 6.44/1.61 | |
% 6.44/1.61 | | REDUCE: (5), (15) imply:
% 6.44/1.61 | | (16) $false
% 6.44/1.61 | |
% 6.44/1.61 | | CLOSE: (16) is inconsistent.
% 6.44/1.61 | |
% 6.44/1.61 | Case 2:
% 6.44/1.61 | |
% 6.44/1.61 | | (17) ? [v0: int] : ( ~ (v0 = 0) & in(all_15_4, all_15_1) = v0)
% 6.44/1.61 | |
% 6.44/1.61 | | DELTA: instantiating (17) with fresh symbol all_33_0 gives:
% 6.44/1.61 | | (18) ~ (all_33_0 = 0) & in(all_15_4, all_15_1) = all_33_0
% 6.44/1.61 | |
% 6.44/1.61 | | ALPHA: (18) implies:
% 6.44/1.61 | | (19) ~ (all_33_0 = 0)
% 6.44/1.61 | | (20) in(all_15_4, all_15_1) = all_33_0
% 6.44/1.61 | |
% 6.44/1.61 | | GROUND_INST: instantiating (2) with all_15_3, all_15_4, all_15_1, all_33_0,
% 6.44/1.61 | | simplifying with (6), (7), (12), (13), (20) gives:
% 6.44/1.61 | | (21) all_33_0 = 0
% 6.44/1.61 | |
% 6.44/1.61 | | REDUCE: (19), (21) imply:
% 6.44/1.61 | | (22) $false
% 6.44/1.61 | |
% 6.44/1.61 | | CLOSE: (22) is inconsistent.
% 6.44/1.61 | |
% 6.44/1.61 | End of split
% 6.44/1.61 |
% 6.44/1.61 End of proof
% 6.44/1.61 % SZS output end Proof for theBenchmark
% 6.44/1.61
% 6.44/1.61 1002ms
%------------------------------------------------------------------------------