TSTP Solution File: NUM537+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM537+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 11:48:28 EDT 2023
% Result : Theorem 18.39s 3.36s
% Output : Proof 21.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM537+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 10:53:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.87/1.12 Prover 1: Preprocessing ...
% 2.87/1.12 Prover 4: Preprocessing ...
% 2.91/1.16 Prover 0: Preprocessing ...
% 2.91/1.16 Prover 3: Preprocessing ...
% 2.91/1.16 Prover 2: Preprocessing ...
% 2.91/1.16 Prover 5: Preprocessing ...
% 2.91/1.16 Prover 6: Preprocessing ...
% 6.81/1.70 Prover 5: Constructing countermodel ...
% 6.81/1.72 Prover 1: Constructing countermodel ...
% 7.07/1.74 Prover 3: Constructing countermodel ...
% 7.07/1.75 Prover 2: Proving ...
% 7.07/1.75 Prover 6: Proving ...
% 8.09/1.98 Prover 4: Constructing countermodel ...
% 8.09/2.01 Prover 0: Proving ...
% 18.39/3.36 Prover 0: proved (2703ms)
% 18.39/3.36
% 18.39/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.39/3.36
% 18.39/3.36 Prover 3: stopped
% 18.39/3.36 Prover 5: stopped
% 18.39/3.38 Prover 2: stopped
% 18.39/3.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.39/3.38 Prover 6: stopped
% 19.30/3.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 19.30/3.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.30/3.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.30/3.40 Prover 7: Preprocessing ...
% 19.30/3.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.30/3.44 Prover 11: Preprocessing ...
% 19.30/3.44 Prover 13: Preprocessing ...
% 19.30/3.44 Prover 8: Preprocessing ...
% 19.30/3.47 Prover 10: Preprocessing ...
% 20.22/3.52 Prover 10: Constructing countermodel ...
% 20.22/3.52 Prover 7: Constructing countermodel ...
% 20.22/3.52 Prover 13: Constructing countermodel ...
% 20.84/3.64 Prover 8: Warning: ignoring some quantifiers
% 20.84/3.64 Prover 8: Constructing countermodel ...
% 20.84/3.65 Prover 10: Found proof (size 22)
% 20.84/3.65 Prover 10: proved (263ms)
% 20.84/3.65 Prover 13: stopped
% 20.84/3.65 Prover 7: stopped
% 20.84/3.65 Prover 8: stopped
% 20.84/3.65 Prover 4: stopped
% 20.84/3.65 Prover 1: stopped
% 21.38/3.70 Prover 11: Constructing countermodel ...
% 21.38/3.71 Prover 11: stopped
% 21.38/3.71
% 21.38/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.38/3.71
% 21.38/3.71 % SZS output start Proof for theBenchmark
% 21.38/3.71 Assumptions after simplification:
% 21.38/3.71 ---------------------------------
% 21.38/3.71
% 21.38/3.71 (mEOfElem)
% 21.38/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 21.38/3.72 ~ aSet0(v0) | aElement0(v1))
% 21.38/3.72
% 21.38/3.72 (m__)
% 21.38/3.74 $i(xS) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v0, xx)
% 21.38/3.74 = v1 & sdtpldt0(xS, xx) = v0 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) &
% 21.38/3.74 aSet0(v0) & ~ aElementOf0(xx, v1) & ! [v3: $i] : (v3 = xx | ~ $i(v3) | ~
% 21.38/3.74 aElementOf0(v3, v0) | ~ aElement0(v3) | aElementOf0(v3, v1)) & ! [v3:
% 21.38/3.74 $i] : (v3 = xx | ~ $i(v3) | ~ aElementOf0(v3, v0) | aElementOf0(v3, xS))
% 21.38/3.74 & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v1) | aElementOf0(v3, v0)) &
% 21.38/3.74 ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v1) | aElement0(v3)) & ! [v3:
% 21.38/3.74 $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aElement0(v3)) & ! [v3: $i] :
% 21.38/3.74 ( ~ $i(v3) | ~ aElementOf0(v3, xS) | ~ aElement0(v3) | aElementOf0(v3,
% 21.38/3.74 v0)) & ( ~ aElement0(xx) | aElementOf0(xx, v0)) & ((aElementOf0(v2, v1)
% 21.38/3.74 & ~ aSubsetOf0(v1, xS) & ~ aElementOf0(v2, xS)) | (aElementOf0(v2, xS)
% 21.38/3.74 & ~ aSubsetOf0(xS, v1) & ~ aElementOf0(v2, v1))))
% 21.38/3.74
% 21.38/3.74 (m__679)
% 21.38/3.74 $i(xS) & $i(xx) & aElement0(xx) & aSet0(xS)
% 21.38/3.74
% 21.38/3.74 (m__679_02)
% 21.38/3.74 $i(xS) & $i(xx) & ~ aElementOf0(xx, xS)
% 21.38/3.74
% 21.38/3.74 Further assumptions not needed in the proof:
% 21.38/3.74 --------------------------------------------
% 21.38/3.74 mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons, mDefDiff, mDefEmp,
% 21.38/3.74 mDefSub, mElmSort, mEmpFin, mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl,
% 21.38/3.74 mSubTrans
% 21.38/3.74
% 21.38/3.74 Those formulas are unsatisfiable:
% 21.38/3.74 ---------------------------------
% 21.38/3.74
% 21.38/3.74 Begin of proof
% 21.38/3.75 |
% 21.38/3.75 | ALPHA: (m__679) implies:
% 21.38/3.75 | (1) aSet0(xS)
% 21.38/3.75 |
% 21.38/3.75 | ALPHA: (m__679_02) implies:
% 21.38/3.75 | (2) ~ aElementOf0(xx, xS)
% 21.38/3.75 |
% 21.38/3.75 | ALPHA: (m__) implies:
% 21.38/3.75 | (3) $i(xS)
% 21.38/3.75 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v0, xx) = v1 &
% 21.38/3.75 | sdtpldt0(xS, xx) = v0 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) &
% 21.38/3.75 | aSet0(v0) & ~ aElementOf0(xx, v1) & ! [v3: $i] : (v3 = xx | ~
% 21.38/3.75 | $i(v3) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) |
% 21.38/3.75 | aElementOf0(v3, v1)) & ! [v3: $i] : (v3 = xx | ~ $i(v3) | ~
% 21.38/3.75 | aElementOf0(v3, v0) | aElementOf0(v3, xS)) & ! [v3: $i] : ( ~
% 21.38/3.75 | $i(v3) | ~ aElementOf0(v3, v1) | aElementOf0(v3, v0)) & ! [v3:
% 21.38/3.75 | $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v1) | aElement0(v3)) & !
% 21.38/3.75 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aElement0(v3)) & !
% 21.38/3.75 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, xS) | ~ aElement0(v3) |
% 21.38/3.75 | aElementOf0(v3, v0)) & ( ~ aElement0(xx) | aElementOf0(xx, v0)) &
% 21.38/3.75 | ((aElementOf0(v2, v1) & ~ aSubsetOf0(v1, xS) & ~ aElementOf0(v2,
% 21.38/3.75 | xS)) | (aElementOf0(v2, xS) & ~ aSubsetOf0(xS, v1) & ~
% 21.38/3.75 | aElementOf0(v2, v1))))
% 21.38/3.75 |
% 21.38/3.75 | DELTA: instantiating (4) with fresh symbols all_15_0, all_15_1, all_15_2
% 21.38/3.75 | gives:
% 21.38/3.76 | (5) sdtmndt0(all_15_2, xx) = all_15_1 & sdtpldt0(xS, xx) = all_15_2 &
% 21.38/3.76 | $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & aSet0(all_15_1) &
% 21.38/3.76 | aSet0(all_15_2) & ~ aElementOf0(xx, all_15_1) & ! [v0: $i] : (v0 = xx
% 21.38/3.76 | | ~ $i(v0) | ~ aElementOf0(v0, all_15_2) | ~ aElement0(v0) |
% 21.38/3.76 | aElementOf0(v0, all_15_1)) & ! [v0: $i] : (v0 = xx | ~ $i(v0) | ~
% 21.38/3.76 | aElementOf0(v0, all_15_2) | aElementOf0(v0, xS)) & ! [v0: $i] : ( ~
% 21.38/3.76 | $i(v0) | ~ aElementOf0(v0, all_15_1) | aElementOf0(v0, all_15_2)) &
% 21.38/3.76 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_15_1) | aElement0(v0))
% 21.38/3.76 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_15_2) |
% 21.38/3.76 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) |
% 21.38/3.76 | ~ aElement0(v0) | aElementOf0(v0, all_15_2)) & ( ~ aElement0(xx) |
% 21.38/3.76 | aElementOf0(xx, all_15_2)) & ((aElementOf0(all_15_0, all_15_1) & ~
% 21.38/3.76 | aSubsetOf0(all_15_1, xS) & ~ aElementOf0(all_15_0, xS)) |
% 21.38/3.76 | (aElementOf0(all_15_0, xS) & ~ aSubsetOf0(xS, all_15_1) & ~
% 21.38/3.76 | aElementOf0(all_15_0, all_15_1)))
% 21.38/3.76 |
% 21.38/3.76 | ALPHA: (5) implies:
% 21.38/3.76 | (6) ~ aElementOf0(xx, all_15_1)
% 21.38/3.76 | (7) $i(all_15_0)
% 21.38/3.76 | (8) (aElementOf0(all_15_0, all_15_1) & ~ aSubsetOf0(all_15_1, xS) & ~
% 21.38/3.76 | aElementOf0(all_15_0, xS)) | (aElementOf0(all_15_0, xS) & ~
% 21.38/3.76 | aSubsetOf0(xS, all_15_1) & ~ aElementOf0(all_15_0, all_15_1))
% 21.38/3.76 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | ~ aElement0(v0) |
% 21.38/3.76 | aElementOf0(v0, all_15_2))
% 21.38/3.76 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_15_1) |
% 21.38/3.76 | aElementOf0(v0, all_15_2))
% 21.38/3.76 | (11) ! [v0: $i] : (v0 = xx | ~ $i(v0) | ~ aElementOf0(v0, all_15_2) |
% 21.38/3.76 | aElementOf0(v0, xS))
% 21.38/3.76 | (12) ! [v0: $i] : (v0 = xx | ~ $i(v0) | ~ aElementOf0(v0, all_15_2) | ~
% 21.38/3.76 | aElement0(v0) | aElementOf0(v0, all_15_1))
% 21.38/3.76 |
% 21.38/3.76 | BETA: splitting (8) gives:
% 21.38/3.76 |
% 21.38/3.76 | Case 1:
% 21.38/3.76 | |
% 21.38/3.76 | | (13) aElementOf0(all_15_0, all_15_1) & ~ aSubsetOf0(all_15_1, xS) & ~
% 21.38/3.76 | | aElementOf0(all_15_0, xS)
% 21.38/3.76 | |
% 21.38/3.76 | | ALPHA: (13) implies:
% 21.38/3.76 | | (14) ~ aElementOf0(all_15_0, xS)
% 21.38/3.76 | | (15) aElementOf0(all_15_0, all_15_1)
% 21.38/3.76 | |
% 21.38/3.76 | | GROUND_INST: instantiating (10) with all_15_0, simplifying with (7), (15)
% 21.38/3.76 | | gives:
% 21.38/3.76 | | (16) aElementOf0(all_15_0, all_15_2)
% 21.38/3.76 | |
% 21.38/3.76 | | GROUND_INST: instantiating (11) with all_15_0, simplifying with (7), (14),
% 21.38/3.76 | | (16) gives:
% 21.38/3.76 | | (17) all_15_0 = xx
% 21.38/3.76 | |
% 21.38/3.76 | | REDUCE: (15), (17) imply:
% 21.38/3.76 | | (18) aElementOf0(xx, all_15_1)
% 21.38/3.76 | |
% 21.38/3.76 | | PRED_UNIFY: (6), (18) imply:
% 21.38/3.76 | | (19) $false
% 21.38/3.76 | |
% 21.38/3.76 | | CLOSE: (19) is inconsistent.
% 21.38/3.76 | |
% 21.38/3.76 | Case 2:
% 21.38/3.76 | |
% 21.38/3.76 | | (20) aElementOf0(all_15_0, xS) & ~ aSubsetOf0(xS, all_15_1) & ~
% 21.38/3.76 | | aElementOf0(all_15_0, all_15_1)
% 21.38/3.77 | |
% 21.38/3.77 | | ALPHA: (20) implies:
% 21.38/3.77 | | (21) ~ aElementOf0(all_15_0, all_15_1)
% 21.38/3.77 | | (22) aElementOf0(all_15_0, xS)
% 21.38/3.77 | |
% 21.38/3.77 | | GROUND_INST: instantiating (mEOfElem) with xS, all_15_0, simplifying with
% 21.38/3.77 | | (1), (3), (7), (22) gives:
% 21.38/3.77 | | (23) aElement0(all_15_0)
% 21.38/3.77 | |
% 21.38/3.77 | | GROUND_INST: instantiating (9) with all_15_0, simplifying with (7), (22),
% 21.38/3.77 | | (23) gives:
% 21.38/3.77 | | (24) aElementOf0(all_15_0, all_15_2)
% 21.38/3.77 | |
% 21.38/3.77 | | GROUND_INST: instantiating (12) with all_15_0, simplifying with (7), (21),
% 21.38/3.77 | | (23), (24) gives:
% 21.38/3.77 | | (25) all_15_0 = xx
% 21.38/3.77 | |
% 21.38/3.77 | | REDUCE: (22), (25) imply:
% 21.38/3.77 | | (26) aElementOf0(xx, xS)
% 21.38/3.77 | |
% 21.38/3.77 | | PRED_UNIFY: (2), (26) imply:
% 21.38/3.77 | | (27) $false
% 21.38/3.77 | |
% 21.38/3.77 | | CLOSE: (27) is inconsistent.
% 21.38/3.77 | |
% 21.38/3.77 | End of split
% 21.38/3.77 |
% 21.38/3.77 End of proof
% 21.38/3.77 % SZS output end Proof for theBenchmark
% 21.38/3.77
% 21.38/3.77 3145ms
%------------------------------------------------------------------------------