TSTP Solution File: RNG091+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG091+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 : n003.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 13:57:48 EDT 2023
% Result : Theorem 23.98s 3.98s
% Output : Proof 24.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG091+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n003.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 : Sun Aug 27 03:04:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.40/1.11 Prover 1: Preprocessing ...
% 2.40/1.11 Prover 4: Preprocessing ...
% 3.10/1.15 Prover 5: Preprocessing ...
% 3.10/1.15 Prover 2: Preprocessing ...
% 3.10/1.15 Prover 6: Preprocessing ...
% 3.10/1.15 Prover 3: Preprocessing ...
% 3.10/1.15 Prover 0: Preprocessing ...
% 7.49/1.73 Prover 1: Constructing countermodel ...
% 7.49/1.75 Prover 6: Proving ...
% 7.49/1.75 Prover 3: Constructing countermodel ...
% 8.19/1.89 Prover 5: Proving ...
% 8.78/1.92 Prover 2: Proving ...
% 8.78/1.95 Prover 4: Constructing countermodel ...
% 9.48/2.01 Prover 0: Proving ...
% 17.16/3.07 Prover 3: gave up
% 17.16/3.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.93/3.12 Prover 7: Preprocessing ...
% 19.47/3.40 Prover 7: Constructing countermodel ...
% 23.98/3.97 Prover 7: Found proof (size 54)
% 23.98/3.97 Prover 7: proved (904ms)
% 23.98/3.97 Prover 2: stopped
% 23.98/3.97 Prover 5: stopped
% 23.98/3.97 Prover 4: stopped
% 23.98/3.97 Prover 1: stopped
% 23.98/3.97 Prover 6: stopped
% 23.98/3.98 Prover 0: stopped
% 23.98/3.98
% 23.98/3.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.98/3.98
% 23.98/3.99 % SZS output start Proof for theBenchmark
% 23.98/3.99 Assumptions after simplification:
% 23.98/3.99 ---------------------------------
% 23.98/3.99
% 23.98/3.99 (mDefIdeal)
% 24.62/4.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1)
% 24.62/4.02 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~
% 24.62/4.02 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i]
% 24.62/4.02 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~
% 24.62/4.02 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) |
% 24.62/4.02 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 24.62/4.02 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) |
% 24.62/4.02 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 24.62/4.02 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2,
% 24.62/4.02 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) |
% 24.62/4.02 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~
% 24.62/4.02 aElementOf0(v5, v0)))))
% 24.62/4.02
% 24.62/4.02 (mDefSSum)
% 24.62/4.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.62/4.03 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) |
% 24.62/4.03 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 24.62/4.03 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) |
% 24.62/4.03 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 24.62/4.03 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 24.62/4.03 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ?
% 24.62/4.03 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3)
% 24.62/4.03 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) |
% 24.62/4.03 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) &
% 24.62/4.03 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6,
% 24.62/4.03 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.62/4.03 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 24.62/4.03 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) |
% 24.62/4.03 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 24.62/4.03 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] :
% 24.62/4.03 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.62/4.03 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 24.62/4.03
% 24.62/4.03 (m__)
% 24.62/4.03 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : ?
% 24.62/4.03 [v2: $i] : (sdtpldt1(xI, xJ) = v1 & $i(v1) & ((sdtasdt0(xz, xx) = v2 & $i(v2)
% 24.62/4.03 & ~ aElementOf0(v2, v1)) | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~
% 24.62/4.03 aElementOf0(v0, v1))))
% 24.62/4.03
% 24.62/4.03 (m__1021)
% 24.62/4.03 $i(xl) & $i(xk) & $i(xz) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] :
% 24.62/4.03 (sdtasdt0(xz, xl) = v1 & sdtasdt0(xz, xk) = v0 & $i(v1) & $i(v0) &
% 24.62/4.03 aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 24.62/4.03
% 24.62/4.03 (m__1061)
% 24.62/4.03 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1:
% 24.62/4.03 $i] : ? [v2: $i] : (sdtpldt0(v1, v2) = v0 & sdtpldt0(xl, xn) = v2 &
% 24.62/4.03 sdtpldt0(xk, xm) = v1 & sdtpldt0(xx, xy) = v0 & $i(v2) & $i(v1) & $i(v0))
% 24.62/4.03
% 24.62/4.03 (m__1098)
% 24.62/4.03 $i(xl) & $i(xk) & $i(xz) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 24.62/4.03 (sdtasdt0(xz, xl) = v2 & sdtasdt0(xz, xk) = v1 & sdtasdt0(xz, xx) = v0 &
% 24.62/4.03 sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 24.62/4.03
% 24.62/4.03 (m__870)
% 24.62/4.03 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI)
% 24.62/4.03
% 24.62/4.03 (m__901)
% 24.62/4.04 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) =
% 24.62/4.04 v0 & $i(v0) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz))
% 24.62/4.04
% 24.62/4.04 (m__994)
% 24.62/4.04 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1:
% 24.62/4.04 $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) = v0 & $i(v1) & $i(v0) &
% 24.62/4.04 aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 24.62/4.04
% 24.62/4.04 (function-axioms)
% 24.62/4.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.62/4.04 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 24.62/4.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 24.62/4.04 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.62/4.04 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 24.62/4.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.62/4.04 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 24.62/4.04 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) =
% 24.62/4.04 v0))
% 24.62/4.04
% 24.62/4.04 Further assumptions not needed in the proof:
% 24.62/4.04 --------------------------------------------
% 24.62/4.04 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefSInt, mEOfElem,
% 24.62/4.04 mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort,
% 24.62/4.04 mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__934, m__967
% 24.62/4.04
% 24.62/4.04 Those formulas are unsatisfiable:
% 24.62/4.04 ---------------------------------
% 24.62/4.04
% 24.62/4.04 Begin of proof
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (mDefSSum) implies:
% 24.62/4.04 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 24.62/4.04 | ! [v5: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) |
% 24.62/4.04 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 24.62/4.04 | | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~
% 24.62/4.04 | aSet0(v0) | aElementOf0(v3, v2))
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (mDefIdeal) implies:
% 24.62/4.04 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0))
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (m__870) implies:
% 24.62/4.04 | (3) aIdeal0(xI)
% 24.62/4.04 | (4) aIdeal0(xJ)
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (m__901) implies:
% 24.62/4.04 | (5) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & aElementOf0(xy, v0) &
% 24.62/4.04 | aElementOf0(xx, v0) & aElement0(xz))
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (m__994) implies:
% 24.62/4.04 | (6) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) =
% 24.62/4.04 | v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (m__1021) implies:
% 24.62/4.04 | (7) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xz, xl) = v1 & sdtasdt0(xz, xk) =
% 24.62/4.04 | v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (m__1061) implies:
% 24.62/4.04 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v2) = v0 &
% 24.62/4.04 | sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = v1 & sdtpldt0(xx, xy) = v0
% 24.62/4.04 | & $i(v2) & $i(v1) & $i(v0))
% 24.62/4.04 |
% 24.62/4.04 | ALPHA: (m__1098) implies:
% 24.62/4.05 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xz, xl) = v2 &
% 24.62/4.05 | sdtasdt0(xz, xk) = v1 & sdtasdt0(xz, xx) = v0 & sdtpldt0(v1, v2) = v0
% 24.62/4.05 | & $i(v2) & $i(v1) & $i(v0))
% 24.62/4.05 |
% 24.62/4.05 | ALPHA: (m__) implies:
% 24.62/4.05 | (10) $i(xI)
% 24.62/4.05 | (11) $i(xJ)
% 24.62/4.05 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtpldt1(xI, xJ) = v1 &
% 24.62/4.05 | $i(v1) & ((sdtasdt0(xz, xx) = v2 & $i(v2) & ~ aElementOf0(v2, v1))
% 24.62/4.05 | | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~ aElementOf0(v0, v1))))
% 24.62/4.05 |
% 24.62/4.05 | ALPHA: (function-axioms) implies:
% 24.62/4.05 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.62/4.05 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 24.62/4.05 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.62/4.05 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 24.62/4.05 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.62/4.05 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0))
% 24.62/4.05 |
% 24.62/4.05 | DELTA: instantiating (5) with fresh symbol all_22_0 gives:
% 24.62/4.05 | (16) sdtpldt1(xI, xJ) = all_22_0 & $i(all_22_0) & aElementOf0(xy, all_22_0)
% 24.62/4.05 | & aElementOf0(xx, all_22_0) & aElement0(xz)
% 24.62/4.05 |
% 24.62/4.05 | ALPHA: (16) implies:
% 24.62/4.05 | (17) sdtpldt1(xI, xJ) = all_22_0
% 24.62/4.05 |
% 24.62/4.05 | DELTA: instantiating (6) with fresh symbols all_24_0, all_24_1 gives:
% 24.62/4.05 | (18) sdtpldt0(xl, xn) = all_24_0 & sdtpldt0(xk, xm) = all_24_1 &
% 24.62/4.05 | $i(all_24_0) & $i(all_24_1) & aElementOf0(all_24_0, xJ) &
% 24.62/4.05 | aElementOf0(all_24_1, xI)
% 24.62/4.05 |
% 24.62/4.05 | ALPHA: (18) implies:
% 24.62/4.05 | (19) aElementOf0(all_24_1, xI)
% 24.62/4.05 | (20) aElementOf0(all_24_0, xJ)
% 24.62/4.05 | (21) sdtpldt0(xk, xm) = all_24_1
% 24.62/4.05 | (22) sdtpldt0(xl, xn) = all_24_0
% 24.62/4.05 |
% 24.62/4.05 | DELTA: instantiating (7) with fresh symbols all_26_0, all_26_1 gives:
% 24.62/4.05 | (23) sdtasdt0(xz, xl) = all_26_0 & sdtasdt0(xz, xk) = all_26_1 &
% 24.62/4.05 | $i(all_26_0) & $i(all_26_1) & aElementOf0(all_26_0, xJ) &
% 24.62/4.05 | aElementOf0(all_26_1, xI)
% 24.62/4.05 |
% 24.62/4.05 | ALPHA: (23) implies:
% 24.62/4.05 | (24) aElementOf0(all_26_1, xI)
% 24.62/4.05 | (25) aElementOf0(all_26_0, xJ)
% 24.62/4.05 | (26) sdtasdt0(xz, xk) = all_26_1
% 24.62/4.05 | (27) sdtasdt0(xz, xl) = all_26_0
% 24.62/4.05 |
% 24.62/4.05 | DELTA: instantiating (8) with fresh symbols all_28_0, all_28_1, all_28_2
% 24.62/4.05 | gives:
% 24.62/4.05 | (28) sdtpldt0(all_28_1, all_28_0) = all_28_2 & sdtpldt0(xl, xn) = all_28_0
% 24.62/4.05 | & sdtpldt0(xk, xm) = all_28_1 & sdtpldt0(xx, xy) = all_28_2 &
% 24.62/4.05 | $i(all_28_0) & $i(all_28_1) & $i(all_28_2)
% 24.62/4.05 |
% 24.62/4.05 | ALPHA: (28) implies:
% 24.62/4.05 | (29) $i(all_28_2)
% 24.62/4.05 | (30) $i(all_28_1)
% 24.62/4.05 | (31) $i(all_28_0)
% 24.62/4.05 | (32) sdtpldt0(xx, xy) = all_28_2
% 24.62/4.05 | (33) sdtpldt0(xk, xm) = all_28_1
% 24.62/4.05 | (34) sdtpldt0(xl, xn) = all_28_0
% 24.62/4.05 | (35) sdtpldt0(all_28_1, all_28_0) = all_28_2
% 24.62/4.05 |
% 24.62/4.05 | DELTA: instantiating (9) with fresh symbols all_30_0, all_30_1, all_30_2
% 24.62/4.05 | gives:
% 24.62/4.05 | (36) sdtasdt0(xz, xl) = all_30_0 & sdtasdt0(xz, xk) = all_30_1 &
% 24.62/4.05 | sdtasdt0(xz, xx) = all_30_2 & sdtpldt0(all_30_1, all_30_0) = all_30_2
% 24.62/4.05 | & $i(all_30_0) & $i(all_30_1) & $i(all_30_2)
% 24.62/4.05 |
% 24.62/4.05 | ALPHA: (36) implies:
% 24.62/4.05 | (37) $i(all_30_2)
% 24.62/4.05 | (38) $i(all_30_1)
% 24.62/4.05 | (39) $i(all_30_0)
% 24.62/4.05 | (40) sdtpldt0(all_30_1, all_30_0) = all_30_2
% 24.62/4.05 | (41) sdtasdt0(xz, xx) = all_30_2
% 24.62/4.05 | (42) sdtasdt0(xz, xk) = all_30_1
% 24.62/4.06 | (43) sdtasdt0(xz, xl) = all_30_0
% 24.62/4.06 |
% 24.62/4.06 | DELTA: instantiating (12) with fresh symbols all_32_0, all_32_1, all_32_2
% 24.62/4.06 | gives:
% 24.62/4.06 | (44) sdtpldt1(xI, xJ) = all_32_1 & $i(all_32_1) & ((sdtasdt0(xz, xx) =
% 24.62/4.06 | all_32_0 & $i(all_32_0) & ~ aElementOf0(all_32_0, all_32_1)) |
% 24.62/4.06 | (sdtpldt0(xx, xy) = all_32_2 & $i(all_32_2) & ~
% 24.62/4.06 | aElementOf0(all_32_2, all_32_1)))
% 24.62/4.06 |
% 24.62/4.06 | ALPHA: (44) implies:
% 24.62/4.06 | (45) $i(all_32_1)
% 24.62/4.06 | (46) sdtpldt1(xI, xJ) = all_32_1
% 24.62/4.06 | (47) (sdtasdt0(xz, xx) = all_32_0 & $i(all_32_0) & ~ aElementOf0(all_32_0,
% 24.62/4.06 | all_32_1)) | (sdtpldt0(xx, xy) = all_32_2 & $i(all_32_2) & ~
% 24.62/4.06 | aElementOf0(all_32_2, all_32_1))
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (13) with all_24_1, all_28_1, xm, xk, simplifying
% 24.62/4.06 | with (21), (33) gives:
% 24.62/4.06 | (48) all_28_1 = all_24_1
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (13) with all_24_0, all_28_0, xn, xl, simplifying
% 24.62/4.06 | with (22), (34) gives:
% 24.62/4.06 | (49) all_28_0 = all_24_0
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (14) with all_26_1, all_30_1, xk, xz, simplifying
% 24.62/4.06 | with (26), (42) gives:
% 24.62/4.06 | (50) all_30_1 = all_26_1
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (14) with all_26_0, all_30_0, xl, xz, simplifying
% 24.62/4.06 | with (27), (43) gives:
% 24.62/4.06 | (51) all_30_0 = all_26_0
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (15) with all_22_0, all_32_1, xJ, xI, simplifying
% 24.62/4.06 | with (17), (46) gives:
% 24.62/4.06 | (52) all_32_1 = all_22_0
% 24.62/4.06 |
% 24.62/4.06 | REDUCE: (40), (50), (51) imply:
% 24.62/4.06 | (53) sdtpldt0(all_26_1, all_26_0) = all_30_2
% 24.62/4.06 |
% 24.62/4.06 | REDUCE: (35), (48), (49) imply:
% 24.62/4.06 | (54) sdtpldt0(all_24_1, all_24_0) = all_28_2
% 24.62/4.06 |
% 24.62/4.06 | REDUCE: (45), (52) imply:
% 24.62/4.06 | (55) $i(all_22_0)
% 24.62/4.06 |
% 24.62/4.06 | REDUCE: (39), (51) imply:
% 24.62/4.06 | (56) $i(all_26_0)
% 24.62/4.06 |
% 24.62/4.06 | REDUCE: (38), (50) imply:
% 24.62/4.06 | (57) $i(all_26_1)
% 24.62/4.06 |
% 24.62/4.06 | REDUCE: (31), (49) imply:
% 24.62/4.06 | (58) $i(all_24_0)
% 24.62/4.06 |
% 24.62/4.06 | REDUCE: (30), (48) imply:
% 24.62/4.06 | (59) $i(all_24_1)
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (2) with xI, simplifying with (3), (10) gives:
% 24.62/4.06 | (60) aSet0(xI)
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (2) with xJ, simplifying with (4), (11) gives:
% 24.62/4.06 | (61) aSet0(xJ)
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (1) with xI, xJ, all_22_0, all_30_2, all_26_1,
% 24.62/4.06 | all_26_0, simplifying with (10), (11), (17), (24), (25), (37),
% 24.62/4.06 | (53), (55), (56), (57), (60), (61) gives:
% 24.62/4.06 | (62) aElementOf0(all_30_2, all_22_0)
% 24.62/4.06 |
% 24.62/4.06 | GROUND_INST: instantiating (1) with xI, xJ, all_22_0, all_28_2, all_24_1,
% 24.62/4.06 | all_24_0, simplifying with (10), (11), (17), (19), (20), (29),
% 24.62/4.06 | (54), (55), (58), (59), (60), (61) gives:
% 24.62/4.06 | (63) aElementOf0(all_28_2, all_22_0)
% 24.62/4.06 |
% 24.62/4.06 | BETA: splitting (47) gives:
% 24.62/4.06 |
% 24.62/4.06 | Case 1:
% 24.62/4.06 | |
% 24.62/4.07 | | (64) sdtasdt0(xz, xx) = all_32_0 & $i(all_32_0) & ~
% 24.62/4.07 | | aElementOf0(all_32_0, all_32_1)
% 24.62/4.07 | |
% 24.62/4.07 | | ALPHA: (64) implies:
% 24.62/4.07 | | (65) ~ aElementOf0(all_32_0, all_32_1)
% 24.62/4.07 | | (66) sdtasdt0(xz, xx) = all_32_0
% 24.62/4.07 | |
% 24.62/4.07 | | REDUCE: (52), (65) imply:
% 24.62/4.07 | | (67) ~ aElementOf0(all_32_0, all_22_0)
% 24.62/4.07 | |
% 24.62/4.07 | | GROUND_INST: instantiating (14) with all_30_2, all_32_0, xx, xz, simplifying
% 24.62/4.07 | | with (41), (66) gives:
% 24.62/4.07 | | (68) all_32_0 = all_30_2
% 24.62/4.07 | |
% 24.62/4.07 | | PRED_UNIFY: (62), (67) imply:
% 24.62/4.07 | | (69) ~ (all_32_0 = all_30_2)
% 24.62/4.07 | |
% 24.62/4.07 | | REDUCE: (68), (69) imply:
% 24.62/4.07 | | (70) $false
% 24.62/4.07 | |
% 24.62/4.07 | | CLOSE: (70) is inconsistent.
% 24.62/4.07 | |
% 24.62/4.07 | Case 2:
% 24.62/4.07 | |
% 24.62/4.07 | | (71) sdtpldt0(xx, xy) = all_32_2 & $i(all_32_2) & ~
% 24.62/4.07 | | aElementOf0(all_32_2, all_32_1)
% 24.62/4.07 | |
% 24.62/4.07 | | ALPHA: (71) implies:
% 24.62/4.07 | | (72) ~ aElementOf0(all_32_2, all_32_1)
% 24.62/4.07 | | (73) sdtpldt0(xx, xy) = all_32_2
% 24.62/4.07 | |
% 24.62/4.07 | | REDUCE: (52), (72) imply:
% 24.62/4.07 | | (74) ~ aElementOf0(all_32_2, all_22_0)
% 24.62/4.07 | |
% 24.62/4.07 | | GROUND_INST: instantiating (13) with all_28_2, all_32_2, xy, xx, simplifying
% 24.62/4.07 | | with (32), (73) gives:
% 24.62/4.07 | | (75) all_32_2 = all_28_2
% 24.62/4.07 | |
% 24.62/4.07 | | PRED_UNIFY: (63), (74) imply:
% 24.62/4.07 | | (76) ~ (all_32_2 = all_28_2)
% 24.62/4.07 | |
% 24.62/4.07 | | REDUCE: (75), (76) imply:
% 24.62/4.07 | | (77) $false
% 24.62/4.07 | |
% 24.62/4.07 | | CLOSE: (77) is inconsistent.
% 24.62/4.07 | |
% 24.62/4.07 | End of split
% 24.62/4.07 |
% 24.62/4.07 End of proof
% 24.62/4.07 % SZS output end Proof for theBenchmark
% 24.62/4.07
% 24.62/4.07 3451ms
%------------------------------------------------------------------------------