TSTP Solution File: NUM425+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM425+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 : n028.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 11:47:40 EDT 2023
% Result : Theorem 35.96s 5.54s
% Output : Proof 35.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM425+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n028.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri Aug 25 13:57:21 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.57 ________ _____
% 0.19/0.57 ___ __ \_________(_)________________________________
% 0.19/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.57 (2023-06-19)
% 0.19/0.57
% 0.19/0.57 (c) Philipp Rümmer, 2009-2023
% 0.19/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.57 Amanda Stjerna.
% 0.19/0.57 Free software under BSD-3-Clause.
% 0.19/0.57
% 0.19/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.57
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.63/1.05 Prover 4: Preprocessing ...
% 2.63/1.05 Prover 1: Preprocessing ...
% 3.00/1.09 Prover 6: Preprocessing ...
% 3.00/1.09 Prover 2: Preprocessing ...
% 3.00/1.09 Prover 3: Preprocessing ...
% 3.00/1.09 Prover 5: Preprocessing ...
% 3.00/1.09 Prover 0: Preprocessing ...
% 5.09/1.53 Prover 1: Constructing countermodel ...
% 5.09/1.53 Prover 3: Constructing countermodel ...
% 6.36/1.59 Prover 6: Proving ...
% 6.92/1.64 Prover 5: Constructing countermodel ...
% 6.92/1.69 Prover 4: Constructing countermodel ...
% 6.92/1.70 Prover 2: Proving ...
% 8.09/1.80 Prover 0: Proving ...
% 8.54/1.87 Prover 3: gave up
% 8.54/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.88/1.93 Prover 1: gave up
% 8.88/1.93 Prover 7: Preprocessing ...
% 8.88/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.22/1.96 Prover 8: Preprocessing ...
% 10.36/2.13 Prover 8: Warning: ignoring some quantifiers
% 10.36/2.14 Prover 7: Constructing countermodel ...
% 10.36/2.15 Prover 8: Constructing countermodel ...
% 12.55/2.41 Prover 8: gave up
% 12.55/2.41 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 12.55/2.43 Prover 9: Preprocessing ...
% 14.28/2.64 Prover 9: Constructing countermodel ...
% 35.96/5.53 Prover 7: Found proof (size 38)
% 35.96/5.53 Prover 7: proved (3648ms)
% 35.96/5.54 Prover 5: stopped
% 35.96/5.54 Prover 9: stopped
% 35.96/5.54 Prover 2: stopped
% 35.96/5.54 Prover 0: stopped
% 35.96/5.54 Prover 6: stopped
% 35.96/5.54 Prover 4: stopped
% 35.96/5.54
% 35.96/5.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.96/5.54
% 35.96/5.54 % SZS output start Proof for theBenchmark
% 35.96/5.55 Assumptions after simplification:
% 35.96/5.55 ---------------------------------
% 35.96/5.55
% 35.96/5.55 (mAddComm)
% 35.96/5.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~
% 35.96/5.57 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v0, v1)
% 35.96/5.58 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 35.96/5.58 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~
% 35.96/5.58 aInteger0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 35.96/5.58
% 35.96/5.58 (mDivisor)
% 35.96/5.58 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 35.96/5.58 (sdtasdt0(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 35.96/5.58 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) &
% 35.96/5.58 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1, v0) |
% 35.96/5.58 ~ aInteger0(v0) | aInteger0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 35.96/5.58 ~ $i(v0) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0) | ? [v2: $i] :
% 35.96/5.58 (sdtasdt0(v1, v2) = v0 & $i(v2) & aInteger0(v2))) & ! [v0: $i] : ( ~ $i(v0)
% 35.96/5.58 | ~ aDivisorOf0(sz00, v0) | ~ aInteger0(v0))
% 35.96/5.58
% 35.96/5.58 (mEquMod)
% 35.96/5.58 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 35.96/5.58 : (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) |
% 35.96/5.58 ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) | ~
% 35.96/5.58 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v2, v4)) &
% 35.96/5.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 =
% 35.96/5.58 sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~
% 35.96/5.58 $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v2, v4) | ~ aInteger0(v2) | ~
% 35.96/5.58 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v1, v2))
% 35.96/5.58
% 35.96/5.58 (mEquModRef)
% 35.96/5.58 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 35.96/5.58 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 35.96/5.58
% 35.96/5.58 (mIntNeg)
% 35.96/5.58 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 35.96/5.58 aInteger0(v0) | aInteger0(v1))
% 35.96/5.58
% 35.96/5.58 (mIntPlus)
% 35.96/5.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 35.96/5.59 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2))
% 35.96/5.59
% 35.96/5.59 (mMulMinOne)
% 35.96/5.59 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 35.96/5.59 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 35.96/5.59 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 35.96/5.59 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 35.96/5.59 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : !
% 35.96/5.59 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 35.96/5.59 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2))))
% 35.96/5.59
% 35.96/5.59 (m__)
% 35.96/5.59 $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1
% 35.96/5.59 & smndt0(xb) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) =
% 35.96/5.59 v1) | ~ $i(v2) | ~ aInteger0(v2)))
% 35.96/5.59
% 35.96/5.59 (m__704)
% 35.96/5.59 ~ (xq = sz00) & $i(xq) & $i(xb) & $i(xa) & $i(sz00) & aInteger0(xq) &
% 35.96/5.59 aInteger0(xb) & aInteger0(xa)
% 35.96/5.59
% 35.96/5.59 (m__724)
% 35.96/5.59 $i(xq) & $i(xb) & $i(xa) & sdteqdtlpzmzozddtrp0(xa, xb, xq)
% 35.96/5.59
% 35.96/5.59 Further assumptions not needed in the proof:
% 35.96/5.59 --------------------------------------------
% 35.96/5.59 mAddAsso, mAddNeg, mAddZero, mDistrib, mIntMult, mIntOne, mIntZero, mIntegers,
% 35.96/5.59 mMulAsso, mMulComm, mMulOne, mMulZero, mZeroDiv
% 35.96/5.59
% 35.96/5.59 Those formulas are unsatisfiable:
% 35.96/5.59 ---------------------------------
% 35.96/5.59
% 35.96/5.59 Begin of proof
% 35.96/5.59 |
% 35.96/5.59 | ALPHA: (mAddComm) implies:
% 35.96/5.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) |
% 35.96/5.59 | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 35.96/5.59 | (sdtpldt0(v0, v1) = v2 & $i(v2)))
% 35.96/5.59 |
% 35.96/5.59 | ALPHA: (mMulMinOne) implies:
% 35.96/5.59 | (2) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 35.96/5.59 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 35.96/5.59 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] :
% 35.96/5.59 | ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~
% 35.96/5.59 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2)))
% 35.96/5.59 | & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~
% 35.96/5.59 | aInteger0(v1) | (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 &
% 35.96/5.59 | $i(v2))))
% 35.96/5.59 |
% 35.96/5.59 | ALPHA: (mDivisor) implies:
% 35.96/5.60 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1,
% 35.96/5.60 | v0) | ~ aInteger0(v0) | ? [v2: $i] : (sdtasdt0(v1, v2) = v0 &
% 35.96/5.60 | $i(v2) & aInteger0(v2)))
% 35.96/5.60 |
% 35.96/5.60 | ALPHA: (mEquMod) implies:
% 35.96/5.60 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 35.96/5.60 | (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~
% 35.96/5.60 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2)
% 35.96/5.60 | | ~ aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 35.96/5.60 | aDivisorOf0(v2, v4))
% 35.96/5.60 |
% 35.96/5.60 | ALPHA: (mEquModRef) implies:
% 35.96/5.60 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 35.96/5.60 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 35.96/5.60 |
% 35.96/5.60 | ALPHA: (m__704) implies:
% 35.96/5.60 | (6) ~ (xq = sz00)
% 35.96/5.60 | (7) aInteger0(xa)
% 35.96/5.60 | (8) aInteger0(xb)
% 35.96/5.60 | (9) aInteger0(xq)
% 35.96/5.60 |
% 35.96/5.60 | ALPHA: (m__724) implies:
% 35.96/5.60 | (10) sdteqdtlpzmzozddtrp0(xa, xb, xq)
% 35.96/5.60 |
% 35.96/5.60 | ALPHA: (m__) implies:
% 35.96/5.60 | (11) $i(xa)
% 35.96/5.60 | (12) $i(xb)
% 35.96/5.60 | (13) $i(xq)
% 35.96/5.60 | (14) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1 & smndt0(xb) = v0 &
% 35.96/5.60 | $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) = v1) | ~
% 35.96/5.60 | $i(v2) | ~ aInteger0(v2)))
% 35.96/5.60 |
% 35.96/5.60 | DELTA: instantiating (14) with fresh symbols all_20_0, all_20_1 gives:
% 35.96/5.60 | (15) sdtpldt0(xa, all_20_1) = all_20_0 & smndt0(xb) = all_20_1 &
% 35.96/5.60 | $i(all_20_0) & $i(all_20_1) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) =
% 35.96/5.60 | all_20_0) | ~ $i(v0) | ~ aInteger0(v0))
% 35.96/5.60 |
% 35.96/5.60 | ALPHA: (15) implies:
% 35.96/5.60 | (16) smndt0(xb) = all_20_1
% 35.96/5.60 | (17) sdtpldt0(xa, all_20_1) = all_20_0
% 35.96/5.60 | (18) ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_20_0) | ~ $i(v0) | ~
% 35.96/5.60 | aInteger0(v0))
% 35.96/5.60 |
% 35.96/5.60 | DELTA: instantiating (2) with fresh symbol all_23_0 gives:
% 35.96/5.60 | (19) smndt0(sz10) = all_23_0 & $i(all_23_0) & ! [v0: $i] : ! [v1: $i] : (
% 35.96/5.60 | ~ (sdtasdt0(v0, all_23_0) = v1) | ~ $i(v0) | ~ aInteger0(v0) |
% 35.96/5.60 | (sdtasdt0(all_23_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0:
% 35.96/5.60 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_23_0, v0) = v1) | ~ $i(v0) |
% 35.96/5.60 | ~ aInteger0(v0) | (sdtasdt0(v0, all_23_0) = v1 & smndt0(v0) = v1 &
% 35.96/5.60 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~
% 35.96/5.60 | $i(v0) | ~ aInteger0(v0) | (sdtasdt0(v0, all_23_0) = v1 &
% 35.96/5.60 | sdtasdt0(all_23_0, v0) = v1 & $i(v1)))
% 35.96/5.60 |
% 35.96/5.60 | ALPHA: (19) implies:
% 35.96/5.60 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 35.96/5.60 | aInteger0(v0) | (sdtasdt0(v0, all_23_0) = v1 & sdtasdt0(all_23_0,
% 35.96/5.60 | v0) = v1 & $i(v1)))
% 35.96/5.60 |
% 35.96/5.60 | GROUND_INST: instantiating (5) with xb, xq, simplifying with (8), (9), (12),
% 35.96/5.60 | (13) gives:
% 35.96/5.60 | (21) xq = sz00 | sdteqdtlpzmzozddtrp0(xb, xb, xq)
% 35.96/5.60 |
% 35.96/5.60 | GROUND_INST: instantiating (mIntNeg) with xb, all_20_1, simplifying with (8),
% 35.96/5.60 | (12), (16) gives:
% 35.96/5.60 | (22) aInteger0(all_20_1)
% 35.96/5.60 |
% 35.96/5.60 | GROUND_INST: instantiating (20) with xb, all_20_1, simplifying with (8), (12),
% 35.96/5.60 | (16) gives:
% 35.96/5.61 | (23) sdtasdt0(all_23_0, xb) = all_20_1 & sdtasdt0(xb, all_23_0) = all_20_1
% 35.96/5.61 | & $i(all_20_1)
% 35.96/5.61 |
% 35.96/5.61 | ALPHA: (23) implies:
% 35.96/5.61 | (24) $i(all_20_1)
% 35.96/5.61 |
% 35.96/5.61 | GROUND_INST: instantiating (4) with xa, xb, xq, all_20_1, all_20_0,
% 35.96/5.61 | simplifying with (7), (8), (9), (10), (11), (12), (13), (16),
% 35.96/5.61 | (17) gives:
% 35.96/5.61 | (25) xq = sz00 | aDivisorOf0(xq, all_20_0)
% 35.96/5.61 |
% 35.96/5.61 | BETA: splitting (25) gives:
% 35.96/5.61 |
% 35.96/5.61 | Case 1:
% 35.96/5.61 | |
% 35.96/5.61 | | (26) aDivisorOf0(xq, all_20_0)
% 35.96/5.61 | |
% 35.96/5.61 | | BETA: splitting (21) gives:
% 35.96/5.61 | |
% 35.96/5.61 | | Case 1:
% 35.96/5.61 | | |
% 35.96/5.61 | | |
% 35.96/5.61 | | | GROUND_INST: instantiating (1) with all_20_1, xa, all_20_0, simplifying
% 35.96/5.61 | | | with (7), (11), (17), (22), (24) gives:
% 35.96/5.61 | | | (27) sdtpldt0(all_20_1, xa) = all_20_0 & $i(all_20_0)
% 35.96/5.61 | | |
% 35.96/5.61 | | | ALPHA: (27) implies:
% 35.96/5.61 | | | (28) $i(all_20_0)
% 35.96/5.61 | | |
% 35.96/5.61 | | | GROUND_INST: instantiating (mIntPlus) with xa, all_20_1, all_20_0,
% 35.96/5.61 | | | simplifying with (7), (11), (17), (22), (24) gives:
% 35.96/5.61 | | | (29) aInteger0(all_20_0)
% 35.96/5.61 | | |
% 35.96/5.61 | | | GROUND_INST: instantiating (3) with all_20_0, xq, simplifying with (13),
% 35.96/5.61 | | | (26), (28) gives:
% 35.96/5.61 | | | (30) ~ aInteger0(all_20_0) | ? [v0: $i] : (sdtasdt0(xq, v0) =
% 35.96/5.61 | | | all_20_0 & $i(v0) & aInteger0(v0))
% 35.96/5.61 | | |
% 35.96/5.61 | | | BETA: splitting (30) gives:
% 35.96/5.61 | | |
% 35.96/5.61 | | | Case 1:
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | (31) ~ aInteger0(all_20_0)
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | PRED_UNIFY: (29), (31) imply:
% 35.96/5.61 | | | | (32) $false
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | CLOSE: (32) is inconsistent.
% 35.96/5.61 | | | |
% 35.96/5.61 | | | Case 2:
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | (33) ? [v0: $i] : (sdtasdt0(xq, v0) = all_20_0 & $i(v0) &
% 35.96/5.61 | | | | aInteger0(v0))
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | DELTA: instantiating (33) with fresh symbol all_85_0 gives:
% 35.96/5.61 | | | | (34) sdtasdt0(xq, all_85_0) = all_20_0 & $i(all_85_0) &
% 35.96/5.61 | | | | aInteger0(all_85_0)
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | ALPHA: (34) implies:
% 35.96/5.61 | | | | (35) aInteger0(all_85_0)
% 35.96/5.61 | | | | (36) $i(all_85_0)
% 35.96/5.61 | | | | (37) sdtasdt0(xq, all_85_0) = all_20_0
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | GROUND_INST: instantiating (18) with all_85_0, simplifying with (35),
% 35.96/5.61 | | | | (36), (37) gives:
% 35.96/5.61 | | | | (38) $false
% 35.96/5.61 | | | |
% 35.96/5.61 | | | | CLOSE: (38) is inconsistent.
% 35.96/5.61 | | | |
% 35.96/5.61 | | | End of split
% 35.96/5.61 | | |
% 35.96/5.61 | | Case 2:
% 35.96/5.61 | | |
% 35.96/5.61 | | | (39) xq = sz00
% 35.96/5.61 | | |
% 35.96/5.61 | | | REDUCE: (6), (39) imply:
% 35.96/5.61 | | | (40) $false
% 35.96/5.61 | | |
% 35.96/5.61 | | | CLOSE: (40) is inconsistent.
% 35.96/5.61 | | |
% 35.96/5.61 | | End of split
% 35.96/5.61 | |
% 35.96/5.61 | Case 2:
% 35.96/5.61 | |
% 35.96/5.61 | | (41) xq = sz00
% 35.96/5.61 | |
% 35.96/5.61 | | REDUCE: (6), (41) imply:
% 35.96/5.61 | | (42) $false
% 35.96/5.61 | |
% 35.96/5.61 | | CLOSE: (42) is inconsistent.
% 35.96/5.61 | |
% 35.96/5.61 | End of split
% 35.96/5.61 |
% 35.96/5.61 End of proof
% 35.96/5.61 % SZS output end Proof for theBenchmark
% 35.96/5.61
% 35.96/5.61 5037ms
%------------------------------------------------------------------------------