TSTP Solution File: RNG086+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG086+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.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 13:57:46 EDT 2023
% Result : Theorem 19.19s 3.36s
% Output : Proof 19.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG086+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n013.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 01:57:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.69/1.12 Prover 1: Preprocessing ...
% 2.69/1.12 Prover 4: Preprocessing ...
% 2.69/1.16 Prover 0: Preprocessing ...
% 2.69/1.16 Prover 3: Preprocessing ...
% 2.69/1.16 Prover 5: Preprocessing ...
% 2.69/1.16 Prover 6: Preprocessing ...
% 2.69/1.16 Prover 2: Preprocessing ...
% 7.60/1.82 Prover 1: Constructing countermodel ...
% 7.60/1.82 Prover 3: Constructing countermodel ...
% 7.60/1.83 Prover 6: Proving ...
% 8.23/1.88 Prover 5: Proving ...
% 8.43/1.92 Prover 4: Constructing countermodel ...
% 8.43/1.95 Prover 2: Proving ...
% 9.77/2.11 Prover 0: Proving ...
% 12.07/2.50 Prover 3: gave up
% 12.71/2.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.71/2.56 Prover 7: Preprocessing ...
% 14.34/2.73 Prover 7: Constructing countermodel ...
% 14.34/2.76 Prover 1: gave up
% 14.34/2.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.06/2.83 Prover 8: Preprocessing ...
% 15.68/3.00 Prover 8: Warning: ignoring some quantifiers
% 15.68/3.01 Prover 8: Constructing countermodel ...
% 18.82/3.36 Prover 7: Found proof (size 15)
% 18.82/3.36 Prover 7: proved (850ms)
% 18.82/3.36 Prover 2: stopped
% 18.82/3.36 Prover 5: stopped
% 18.82/3.36 Prover 0: stopped
% 18.82/3.36 Prover 8: stopped
% 18.82/3.36 Prover 6: stopped
% 18.82/3.36 Prover 4: stopped
% 18.82/3.36
% 19.19/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.19/3.36
% 19.19/3.37 % SZS output start Proof for theBenchmark
% 19.19/3.37 Assumptions after simplification:
% 19.19/3.37 ---------------------------------
% 19.19/3.37
% 19.19/3.37 (mDefIdeal)
% 19.19/3.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1)
% 19.19/3.40 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~
% 19.19/3.40 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i]
% 19.19/3.40 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~
% 19.19/3.40 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) |
% 19.19/3.40 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 19.19/3.40 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) |
% 19.19/3.40 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 19.19/3.40 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2,
% 19.19/3.40 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 19.19/3.40 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 19.19/3.40 aElementOf0(v5, v0)))))
% 19.19/3.40
% 19.19/3.40 (mDefSSum)
% 19.19/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.19/3.41 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) |
% 19.19/3.41 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 19.19/3.41 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) |
% 19.19/3.41 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 19.19/3.41 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 19.19/3.41 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 19.19/3.41 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3)
% 19.19/3.41 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) |
% 19.19/3.41 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) &
% 19.19/3.41 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6,
% 19.19/3.41 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.19/3.41 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 19.19/3.41 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) |
% 19.19/3.41 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 19.19/3.41 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] :
% 19.19/3.41 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 19.19/3.41 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 19.19/3.41
% 19.19/3.41 (m__)
% 19.19/3.41 $i(xx) & $i(xJ) & $i(xI) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) =
% 19.19/3.41 xx) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0,
% 19.19/3.41 xI))
% 19.19/3.41
% 19.19/3.41 (m__870)
% 19.19/3.41 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI)
% 19.19/3.41
% 19.19/3.41 (m__901)
% 19.19/3.41 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) =
% 19.19/3.41 v0 & $i(v0) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz))
% 19.19/3.41
% 19.19/3.41 Further assumptions not needed in the proof:
% 19.19/3.41 --------------------------------------------
% 19.19/3.41 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefSInt, mEOfElem,
% 19.19/3.41 mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort,
% 19.19/3.41 mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr
% 19.19/3.41
% 19.19/3.41 Those formulas are unsatisfiable:
% 19.19/3.41 ---------------------------------
% 19.19/3.41
% 19.19/3.41 Begin of proof
% 19.19/3.41 |
% 19.19/3.41 | ALPHA: (mDefSSum) implies:
% 19.19/3.42 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 19.19/3.42 | (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 19.19/3.42 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ?
% 19.19/3.42 | [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 19.19/3.42 | aElementOf0(v5, v1) & aElementOf0(v4, v0)))
% 19.19/3.42 |
% 19.19/3.42 | ALPHA: (mDefIdeal) implies:
% 19.19/3.42 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0))
% 19.19/3.42 |
% 19.19/3.42 | ALPHA: (m__870) implies:
% 19.19/3.42 | (3) aIdeal0(xI)
% 19.19/3.42 | (4) aIdeal0(xJ)
% 19.19/3.42 |
% 19.19/3.42 | ALPHA: (m__901) implies:
% 19.19/3.42 | (5) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & aElementOf0(xy, v0) &
% 19.19/3.42 | aElementOf0(xx, v0) & aElement0(xz))
% 19.19/3.42 |
% 19.19/3.42 | ALPHA: (m__) implies:
% 19.19/3.42 | (6) $i(xI)
% 19.19/3.42 | (7) $i(xJ)
% 19.19/3.42 | (8) $i(xx)
% 19.19/3.42 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) = xx) | ~ $i(v1) |
% 19.19/3.42 | ~ $i(v0) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, xI))
% 19.19/3.42 |
% 19.19/3.42 | DELTA: instantiating (5) with fresh symbol all_23_0 gives:
% 19.19/3.42 | (10) sdtpldt1(xI, xJ) = all_23_0 & $i(all_23_0) & aElementOf0(xy, all_23_0)
% 19.19/3.42 | & aElementOf0(xx, all_23_0) & aElement0(xz)
% 19.19/3.42 |
% 19.19/3.42 | ALPHA: (10) implies:
% 19.19/3.42 | (11) aElementOf0(xx, all_23_0)
% 19.19/3.42 | (12) $i(all_23_0)
% 19.19/3.42 | (13) sdtpldt1(xI, xJ) = all_23_0
% 19.19/3.42 |
% 19.19/3.42 | GROUND_INST: instantiating (2) with xI, simplifying with (3), (6) gives:
% 19.19/3.42 | (14) aSet0(xI)
% 19.19/3.42 |
% 19.19/3.42 | GROUND_INST: instantiating (2) with xJ, simplifying with (4), (7) gives:
% 19.19/3.42 | (15) aSet0(xJ)
% 19.19/3.42 |
% 19.19/3.42 | GROUND_INST: instantiating (1) with xI, xJ, all_23_0, xx, simplifying with
% 19.19/3.42 | (6), (7), (8), (11), (12), (13), (14), (15) gives:
% 19.19/3.42 | (16) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, v1) = xx & $i(v1) & $i(v0) &
% 19.19/3.42 | aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 19.19/3.42 |
% 19.19/3.42 | DELTA: instantiating (16) with fresh symbols all_44_0, all_44_1 gives:
% 19.19/3.42 | (17) sdtpldt0(all_44_1, all_44_0) = xx & $i(all_44_0) & $i(all_44_1) &
% 19.19/3.42 | aElementOf0(all_44_0, xJ) & aElementOf0(all_44_1, xI)
% 19.19/3.42 |
% 19.19/3.42 | ALPHA: (17) implies:
% 19.19/3.42 | (18) aElementOf0(all_44_1, xI)
% 19.19/3.42 | (19) aElementOf0(all_44_0, xJ)
% 19.19/3.42 | (20) $i(all_44_1)
% 19.19/3.42 | (21) $i(all_44_0)
% 19.19/3.42 | (22) sdtpldt0(all_44_1, all_44_0) = xx
% 19.19/3.42 |
% 19.19/3.42 | GROUND_INST: instantiating (9) with all_44_1, all_44_0, simplifying with (18),
% 19.19/3.42 | (19), (20), (21), (22) gives:
% 19.19/3.42 | (23) $false
% 19.19/3.43 |
% 19.19/3.43 | CLOSE: (23) is inconsistent.
% 19.19/3.43 |
% 19.19/3.43 End of proof
% 19.19/3.43 % SZS output end Proof for theBenchmark
% 19.19/3.43
% 19.19/3.43 2811ms
%------------------------------------------------------------------------------