TSTP Solution File: RNG088+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG088+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 : n005.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 13:57:47 EDT 2023
% Result : Theorem 10.37s 2.17s
% Output : Proof 14.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG088+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n005.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 : Sun Aug 27 01:45:41 EDT 2023
% 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 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 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 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 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
% 3.20/1.13 Prover 4: Preprocessing ...
% 3.20/1.13 Prover 1: Preprocessing ...
% 3.24/1.16 Prover 5: Preprocessing ...
% 3.24/1.16 Prover 2: Preprocessing ...
% 3.24/1.16 Prover 3: Preprocessing ...
% 3.24/1.16 Prover 0: Preprocessing ...
% 3.24/1.17 Prover 6: Preprocessing ...
% 7.70/1.79 Prover 1: Constructing countermodel ...
% 8.21/1.83 Prover 5: Proving ...
% 8.21/1.83 Prover 3: Constructing countermodel ...
% 8.27/1.84 Prover 6: Proving ...
% 9.11/1.98 Prover 4: Constructing countermodel ...
% 9.11/1.98 Prover 2: Proving ...
% 9.11/1.99 Prover 0: Proving ...
% 10.37/2.17 Prover 3: proved (1521ms)
% 10.37/2.17
% 10.37/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.37/2.17
% 10.37/2.17 Prover 2: stopped
% 10.37/2.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.37/2.17 Prover 5: stopped
% 10.37/2.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.37/2.18 Prover 0: stopped
% 10.37/2.18 Prover 6: stopped
% 10.37/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.37/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.37/2.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.84/2.23 Prover 11: Preprocessing ...
% 10.84/2.24 Prover 7: Preprocessing ...
% 10.84/2.24 Prover 10: Preprocessing ...
% 10.84/2.24 Prover 13: Preprocessing ...
% 10.84/2.24 Prover 8: Preprocessing ...
% 11.95/2.37 Prover 10: Constructing countermodel ...
% 11.95/2.40 Prover 7: Constructing countermodel ...
% 11.95/2.41 Prover 8: Warning: ignoring some quantifiers
% 11.95/2.42 Prover 8: Constructing countermodel ...
% 11.95/2.43 Prover 13: Warning: ignoring some quantifiers
% 12.59/2.46 Prover 13: Constructing countermodel ...
% 13.04/2.52 Prover 11: Constructing countermodel ...
% 14.09/2.68 Prover 10: Found proof (size 12)
% 14.09/2.68 Prover 10: proved (508ms)
% 14.09/2.69 Prover 7: stopped
% 14.09/2.69 Prover 13: stopped
% 14.09/2.69 Prover 11: stopped
% 14.09/2.69 Prover 8: stopped
% 14.09/2.69 Prover 4: stopped
% 14.09/2.69 Prover 1: stopped
% 14.09/2.69
% 14.09/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.09/2.69
% 14.09/2.69 % SZS output start Proof for theBenchmark
% 14.09/2.69 Assumptions after simplification:
% 14.09/2.69 ---------------------------------
% 14.09/2.69
% 14.09/2.69 (m__)
% 14.54/2.72 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1:
% 14.54/2.72 $i] : ((sdtpldt0(xl, xn) = v1 & $i(v1) & ~ aElementOf0(v1, xJ)) |
% 14.54/2.72 (sdtpldt0(xk, xm) = v0 & $i(v0) & ~ aElementOf0(v0, xI)))
% 14.54/2.72
% 14.54/2.72 (m__870)
% 14.54/2.72 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) & aSet0(xJ) & aSet0(xI) & ! [v0:
% 14.54/2.72 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) |
% 14.54/2.72 ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ))
% 14.54/2.72 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~
% 14.54/2.72 $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) |
% 14.54/2.72 aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.54/2.72 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) |
% 14.54/2.72 ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ)) & ! [v0: $i] : ! [v1: $i] :
% 14.54/2.72 ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 14.54/2.72 aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI))
% 14.54/2.72
% 14.54/2.72 (m__934)
% 14.54/2.72 sdtpldt0(xk, xl) = xx & $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI) &
% 14.54/2.72 aElementOf0(xl, xJ) & aElementOf0(xk, xI)
% 14.54/2.72
% 14.54/2.72 (m__967)
% 14.68/2.72 sdtpldt0(xm, xn) = xy & $i(xn) & $i(xm) & $i(xy) & $i(xJ) & $i(xI) &
% 14.68/2.73 aElementOf0(xn, xJ) & aElementOf0(xm, xI)
% 14.68/2.73
% 14.68/2.73 Further assumptions not needed in the proof:
% 14.68/2.73 --------------------------------------------
% 14.68/2.73 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt,
% 14.68/2.73 mDefSSum, mEOfElem, mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero,
% 14.68/2.73 mSetEq, mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr,
% 14.68/2.73 m__901
% 14.68/2.73
% 14.68/2.73 Those formulas are unsatisfiable:
% 14.68/2.73 ---------------------------------
% 14.68/2.73
% 14.68/2.73 Begin of proof
% 14.69/2.73 |
% 14.69/2.73 | ALPHA: (m__870) implies:
% 14.69/2.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 14.69/2.73 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0,
% 14.69/2.73 | xI) | aElementOf0(v2, xI))
% 14.69/2.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 14.69/2.73 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0,
% 14.69/2.73 | xJ) | aElementOf0(v2, xJ))
% 14.69/2.73 |
% 14.69/2.73 | ALPHA: (m__934) implies:
% 14.69/2.73 | (3) aElementOf0(xk, xI)
% 14.69/2.73 | (4) aElementOf0(xl, xJ)
% 14.69/2.73 |
% 14.69/2.73 | ALPHA: (m__967) implies:
% 14.69/2.73 | (5) aElementOf0(xm, xI)
% 14.69/2.73 | (6) aElementOf0(xn, xJ)
% 14.69/2.73 |
% 14.69/2.73 | ALPHA: (m__) implies:
% 14.69/2.73 | (7) $i(xk)
% 14.69/2.73 | (8) $i(xl)
% 14.69/2.73 | (9) $i(xm)
% 14.69/2.73 | (10) $i(xn)
% 14.69/2.73 | (11) ? [v0: $i] : ? [v1: $i] : ((sdtpldt0(xl, xn) = v1 & $i(v1) & ~
% 14.69/2.73 | aElementOf0(v1, xJ)) | (sdtpldt0(xk, xm) = v0 & $i(v0) & ~
% 14.69/2.73 | aElementOf0(v0, xI)))
% 14.69/2.73 |
% 14.69/2.73 | DELTA: instantiating (11) with fresh symbols all_23_0, all_23_1 gives:
% 14.69/2.73 | (12) (sdtpldt0(xl, xn) = all_23_0 & $i(all_23_0) & ~ aElementOf0(all_23_0,
% 14.69/2.73 | xJ)) | (sdtpldt0(xk, xm) = all_23_1 & $i(all_23_1) & ~
% 14.69/2.73 | aElementOf0(all_23_1, xI))
% 14.69/2.73 |
% 14.69/2.73 | BETA: splitting (12) gives:
% 14.69/2.73 |
% 14.69/2.73 | Case 1:
% 14.69/2.73 | |
% 14.69/2.73 | | (13) sdtpldt0(xl, xn) = all_23_0 & $i(all_23_0) & ~
% 14.69/2.73 | | aElementOf0(all_23_0, xJ)
% 14.69/2.73 | |
% 14.69/2.73 | | ALPHA: (13) implies:
% 14.69/2.74 | | (14) ~ aElementOf0(all_23_0, xJ)
% 14.69/2.74 | | (15) sdtpldt0(xl, xn) = all_23_0
% 14.69/2.74 | |
% 14.69/2.74 | | GROUND_INST: instantiating (2) with xl, xn, all_23_0, simplifying with (4),
% 14.69/2.74 | | (6), (8), (10), (14), (15) gives:
% 14.69/2.74 | | (16) $false
% 14.69/2.74 | |
% 14.69/2.74 | | CLOSE: (16) is inconsistent.
% 14.69/2.74 | |
% 14.69/2.74 | Case 2:
% 14.69/2.74 | |
% 14.69/2.74 | | (17) sdtpldt0(xk, xm) = all_23_1 & $i(all_23_1) & ~
% 14.69/2.74 | | aElementOf0(all_23_1, xI)
% 14.69/2.74 | |
% 14.69/2.74 | | ALPHA: (17) implies:
% 14.69/2.74 | | (18) ~ aElementOf0(all_23_1, xI)
% 14.69/2.74 | | (19) sdtpldt0(xk, xm) = all_23_1
% 14.69/2.74 | |
% 14.69/2.74 | | GROUND_INST: instantiating (1) with xk, xm, all_23_1, simplifying with (3),
% 14.69/2.74 | | (5), (7), (9), (18), (19) gives:
% 14.69/2.74 | | (20) $false
% 14.69/2.74 | |
% 14.69/2.74 | | CLOSE: (20) is inconsistent.
% 14.69/2.74 | |
% 14.69/2.74 | End of split
% 14.69/2.74 |
% 14.69/2.74 End of proof
% 14.69/2.74 % SZS output end Proof for theBenchmark
% 14.69/2.74
% 14.69/2.74 2114ms
%------------------------------------------------------------------------------