TSTP Solution File: NUM429+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM429+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 : n025.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 11:47:41 EDT 2023
% Result : Theorem 36.91s 5.90s
% Output : Proof 37.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM429+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 11:02:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.90/1.17 Prover 4: Preprocessing ...
% 2.90/1.17 Prover 1: Preprocessing ...
% 3.33/1.22 Prover 2: Preprocessing ...
% 3.33/1.22 Prover 0: Preprocessing ...
% 3.33/1.22 Prover 5: Preprocessing ...
% 3.33/1.22 Prover 3: Preprocessing ...
% 3.33/1.22 Prover 6: Preprocessing ...
% 6.04/1.64 Prover 1: Constructing countermodel ...
% 6.37/1.67 Prover 3: Constructing countermodel ...
% 6.37/1.70 Prover 6: Proving ...
% 7.09/1.82 Prover 4: Constructing countermodel ...
% 7.67/1.86 Prover 5: Constructing countermodel ...
% 7.67/1.90 Prover 2: Proving ...
% 8.14/1.94 Prover 0: Proving ...
% 8.46/2.03 Prover 3: gave up
% 9.00/2.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.27/2.09 Prover 7: Preprocessing ...
% 9.27/2.21 Prover 1: gave up
% 9.27/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.27/2.25 Prover 8: Preprocessing ...
% 10.84/2.30 Prover 7: Constructing countermodel ...
% 10.84/2.36 Prover 8: Warning: ignoring some quantifiers
% 11.37/2.39 Prover 8: Constructing countermodel ...
% 14.37/2.79 Prover 8: gave up
% 14.60/2.80 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 14.60/2.85 Prover 9: Preprocessing ...
% 16.55/3.11 Prover 9: Constructing countermodel ...
% 36.91/5.90 Prover 7: Found proof (size 32)
% 36.91/5.90 Prover 7: proved (3859ms)
% 36.91/5.90 Prover 5: stopped
% 36.91/5.90 Prover 9: stopped
% 36.91/5.90 Prover 0: stopped
% 36.91/5.90 Prover 2: stopped
% 36.91/5.90 Prover 4: stopped
% 36.91/5.90 Prover 6: stopped
% 36.91/5.90
% 36.91/5.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.91/5.90
% 36.91/5.91 % SZS output start Proof for theBenchmark
% 36.91/5.91 Assumptions after simplification:
% 36.91/5.91 ---------------------------------
% 36.91/5.91
% 36.91/5.91 (mAddComm)
% 37.47/5.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~
% 37.47/5.93 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v0, v1)
% 37.47/5.93 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 37.47/5.93 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~
% 37.47/5.93 aInteger0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 37.47/5.93
% 37.47/5.93 (mDivisor)
% 37.47/5.94 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 37.47/5.94 (sdtasdt0(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 37.47/5.94 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) &
% 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1, v0) |
% 37.47/5.94 ~ aInteger0(v0) | aInteger0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 37.47/5.94 ~ $i(v0) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0) | ? [v2: $i] :
% 37.47/5.94 (sdtasdt0(v1, v2) = v0 & $i(v2) & aInteger0(v2))) & ! [v0: $i] : ( ~ $i(v0)
% 37.47/5.94 | ~ aDivisorOf0(sz00, v0) | ~ aInteger0(v0))
% 37.47/5.94
% 37.47/5.94 (mEquMod)
% 37.47/5.94 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 37.47/5.94 : (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) |
% 37.47/5.94 ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) | ~
% 37.47/5.94 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v2, v4)) &
% 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 =
% 37.47/5.94 sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~
% 37.47/5.94 $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v2, v4) | ~ aInteger0(v2) | ~
% 37.47/5.94 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v1, v2))
% 37.47/5.94
% 37.47/5.94 (mIntNeg)
% 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 37.47/5.94 aInteger0(v0) | aInteger0(v1))
% 37.47/5.94
% 37.47/5.94 (mIntPlus)
% 37.47/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 37.47/5.94 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2))
% 37.47/5.94
% 37.47/5.94 (mMulMinOne)
% 37.47/5.94 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 37.47/5.94 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 37.47/5.94 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 37.47/5.94 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 37.47/5.94 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 37.47/5.94 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 37.47/5.94 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2))))
% 37.47/5.94
% 37.47/5.94 (m__)
% 37.47/5.94 $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1
% 37.47/5.94 & smndt0(xb) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) =
% 37.47/5.94 v1) | ~ $i(v2) | ~ aInteger0(v2)))
% 37.47/5.94
% 37.47/5.94 (m__818)
% 37.47/5.95 ~ (xq = sz00) & $i(xc) & $i(xq) & $i(xb) & $i(xa) & $i(sz00) & aInteger0(xc)
% 37.47/5.95 & aInteger0(xq) & aInteger0(xb) & aInteger0(xa)
% 37.47/5.95
% 37.47/5.95 (m__853)
% 37.47/5.95 $i(xc) & $i(xq) & $i(xb) & $i(xa) & sdteqdtlpzmzozddtrp0(xb, xc, xq) &
% 37.47/5.95 sdteqdtlpzmzozddtrp0(xa, xb, xq)
% 37.47/5.95
% 37.47/5.95 Further assumptions not needed in the proof:
% 37.47/5.95 --------------------------------------------
% 37.47/5.95 mAddAsso, mAddNeg, mAddZero, mDistrib, mEquModRef, mEquModSym, mIntMult,
% 37.47/5.95 mIntOne, mIntZero, mIntegers, mMulAsso, mMulComm, mMulOne, mMulZero, mZeroDiv
% 37.47/5.95
% 37.47/5.95 Those formulas are unsatisfiable:
% 37.47/5.95 ---------------------------------
% 37.47/5.95
% 37.47/5.95 Begin of proof
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (mAddComm) implies:
% 37.47/5.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) |
% 37.47/5.95 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 37.47/5.95 | (sdtpldt0(v0, v1) = v2 & $i(v2)))
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (mMulMinOne) implies:
% 37.47/5.95 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 37.47/5.95 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 37.47/5.95 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] :
% 37.47/5.95 | ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~
% 37.47/5.95 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2)))
% 37.47/5.95 | & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~
% 37.47/5.95 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 &
% 37.47/5.95 | $i(v2))))
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (mDivisor) implies:
% 37.47/5.95 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1,
% 37.47/5.95 | v0) | ~ aInteger0(v0) | ? [v2: $i] : (sdtasdt0(v1, v2) = v0 &
% 37.47/5.95 | $i(v2) & aInteger0(v2)))
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (mEquMod) implies:
% 37.47/5.95 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 37.47/5.95 | (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~
% 37.47/5.95 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2)
% 37.47/5.95 | | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 37.47/5.95 | aDivisorOf0(v2, v4))
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (m__818) implies:
% 37.47/5.95 | (5) ~ (xq = sz00)
% 37.47/5.95 | (6) aInteger0(xa)
% 37.47/5.95 | (7) aInteger0(xb)
% 37.47/5.95 | (8) aInteger0(xq)
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (m__853) implies:
% 37.47/5.95 | (9) sdteqdtlpzmzozddtrp0(xa, xb, xq)
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (m__) implies:
% 37.47/5.95 | (10) $i(xa)
% 37.47/5.95 | (11) $i(xb)
% 37.47/5.95 | (12) $i(xq)
% 37.47/5.95 | (13) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1 & smndt0(xb) = v0 &
% 37.47/5.95 | $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) = v1) | ~
% 37.47/5.95 | $i(v2) | ~ aInteger0(v2)))
% 37.47/5.95 |
% 37.47/5.95 | DELTA: instantiating (13) with fresh symbols all_21_0, all_21_1 gives:
% 37.47/5.95 | (14) sdtpldt0(xa, all_21_1) = all_21_0 & smndt0(xb) = all_21_1 &
% 37.47/5.95 | $i(all_21_0) & $i(all_21_1) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) =
% 37.47/5.95 | all_21_0) | ~ $i(v0) | ~ aInteger0(v0))
% 37.47/5.95 |
% 37.47/5.95 | ALPHA: (14) implies:
% 37.47/5.95 | (15) smndt0(xb) = all_21_1
% 37.47/5.96 | (16) sdtpldt0(xa, all_21_1) = all_21_0
% 37.47/5.96 | (17) ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_21_0) | ~ $i(v0) | ~
% 37.47/5.96 | aInteger0(v0))
% 37.47/5.96 |
% 37.47/5.96 | DELTA: instantiating (2) with fresh symbol all_24_0 gives:
% 37.47/5.96 | (18) smndt0(sz10) = all_24_0 & $i(all_24_0) & ! [v0: $i] : ! [v1: $i] : (
% 37.47/5.96 | ~ (sdtasdt0(v0, all_24_0) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 37.47/5.96 | (sdtasdt0(all_24_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0:
% 37.47/5.96 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_24_0, v0) = v1) | ~ $i(v0) |
% 37.47/5.96 | ~ aInteger0(v0) | (sdtasdt0(v0, all_24_0) = v1 & smndt0(v0) = v1 &
% 37.47/5.96 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~
% 37.47/5.96 | $i(v0) | ~ aInteger0(v0) | (sdtasdt0(v0, all_24_0) = v1 &
% 37.47/5.96 | sdtasdt0(all_24_0, v0) = v1 & $i(v1)))
% 37.47/5.96 |
% 37.47/5.96 | ALPHA: (18) implies:
% 37.47/5.96 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 37.47/5.96 | aInteger0(v0) | (sdtasdt0(v0, all_24_0) = v1 & sdtasdt0(all_24_0,
% 37.47/5.96 | v0) = v1 & $i(v1)))
% 37.47/5.96 |
% 37.47/5.96 | GROUND_INST: instantiating (mIntNeg) with xb, all_21_1, simplifying with (7),
% 37.47/5.96 | (11), (15) gives:
% 37.47/5.96 | (20) aInteger0(all_21_1)
% 37.47/5.96 |
% 37.47/5.96 | GROUND_INST: instantiating (19) with xb, all_21_1, simplifying with (7), (11),
% 37.47/5.96 | (15) gives:
% 37.47/5.96 | (21) sdtasdt0(all_24_0, xb) = all_21_1 & sdtasdt0(xb, all_24_0) = all_21_1
% 37.47/5.96 | & $i(all_21_1)
% 37.47/5.96 |
% 37.47/5.96 | ALPHA: (21) implies:
% 37.47/5.96 | (22) $i(all_21_1)
% 37.47/5.96 |
% 37.47/5.96 | GROUND_INST: instantiating (4) with xa, xb, xq, all_21_1, all_21_0,
% 37.47/5.96 | simplifying with (6), (7), (8), (9), (10), (11), (12), (15), (16)
% 37.47/5.96 | gives:
% 37.47/5.96 | (23) xq = sz00 | aDivisorOf0(xq, all_21_0)
% 37.47/5.96 |
% 37.47/5.96 | BETA: splitting (23) gives:
% 37.47/5.96 |
% 37.47/5.96 | Case 1:
% 37.47/5.96 | |
% 37.47/5.96 | | (24) aDivisorOf0(xq, all_21_0)
% 37.47/5.96 | |
% 37.47/5.96 | | GROUND_INST: instantiating (1) with all_21_1, xa, all_21_0, simplifying with
% 37.47/5.96 | | (6), (10), (16), (20), (22) gives:
% 37.47/5.96 | | (25) sdtpldt0(all_21_1, xa) = all_21_0 & $i(all_21_0)
% 37.47/5.96 | |
% 37.47/5.96 | | ALPHA: (25) implies:
% 37.47/5.96 | | (26) $i(all_21_0)
% 37.47/5.96 | |
% 37.47/5.96 | | GROUND_INST: instantiating (mIntPlus) with xa, all_21_1, all_21_0,
% 37.47/5.96 | | simplifying with (6), (10), (16), (20), (22) gives:
% 37.47/5.96 | | (27) aInteger0(all_21_0)
% 37.47/5.96 | |
% 37.47/5.96 | | GROUND_INST: instantiating (3) with all_21_0, xq, simplifying with (12),
% 37.47/5.96 | | (24), (26) gives:
% 37.47/5.96 | | (28) ~ aInteger0(all_21_0) | ? [v0: $i] : (sdtasdt0(xq, v0) = all_21_0
% 37.47/5.96 | | & $i(v0) & aInteger0(v0))
% 37.47/5.96 | |
% 37.47/5.96 | | BETA: splitting (28) gives:
% 37.47/5.96 | |
% 37.47/5.96 | | Case 1:
% 37.47/5.96 | | |
% 37.47/5.96 | | | (29) ~ aInteger0(all_21_0)
% 37.47/5.96 | | |
% 37.47/5.96 | | | PRED_UNIFY: (27), (29) imply:
% 37.47/5.96 | | | (30) $false
% 37.47/5.96 | | |
% 37.47/5.96 | | | CLOSE: (30) is inconsistent.
% 37.47/5.96 | | |
% 37.47/5.96 | | Case 2:
% 37.47/5.96 | | |
% 37.47/5.96 | | | (31) ? [v0: $i] : (sdtasdt0(xq, v0) = all_21_0 & $i(v0) &
% 37.47/5.96 | | | aInteger0(v0))
% 37.47/5.96 | | |
% 37.47/5.96 | | | DELTA: instantiating (31) with fresh symbol all_102_0 gives:
% 37.47/5.96 | | | (32) sdtasdt0(xq, all_102_0) = all_21_0 & $i(all_102_0) &
% 37.47/5.96 | | | aInteger0(all_102_0)
% 37.47/5.96 | | |
% 37.47/5.96 | | | ALPHA: (32) implies:
% 37.47/5.97 | | | (33) aInteger0(all_102_0)
% 37.47/5.97 | | | (34) $i(all_102_0)
% 37.47/5.97 | | | (35) sdtasdt0(xq, all_102_0) = all_21_0
% 37.47/5.97 | | |
% 37.47/5.97 | | | GROUND_INST: instantiating (17) with all_102_0, simplifying with (33),
% 37.47/5.97 | | | (34), (35) gives:
% 37.47/5.97 | | | (36) $false
% 37.47/5.97 | | |
% 37.47/5.97 | | | CLOSE: (36) is inconsistent.
% 37.47/5.97 | | |
% 37.47/5.97 | | End of split
% 37.47/5.97 | |
% 37.47/5.97 | Case 2:
% 37.47/5.97 | |
% 37.47/5.97 | | (37) xq = sz00
% 37.47/5.97 | |
% 37.47/5.97 | | REDUCE: (5), (37) imply:
% 37.47/5.97 | | (38) $false
% 37.47/5.97 | |
% 37.47/5.97 | | CLOSE: (38) is inconsistent.
% 37.47/5.97 | |
% 37.47/5.97 | End of split
% 37.47/5.97 |
% 37.47/5.97 End of proof
% 37.47/5.97 % SZS output end Proof for theBenchmark
% 37.47/5.97
% 37.47/5.97 5354ms
%------------------------------------------------------------------------------