TSTP Solution File: NUM432+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM432+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 : n026.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 11:47:43 EDT 2023
% Result : Theorem 73.30s 10.38s
% Output : Proof 73.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM432+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 17:43:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.64 ________ _____
% 0.21/0.64 ___ __ \_________(_)________________________________
% 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64
% 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.66 Running up to 7 provers in parallel.
% 0.21/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.97/1.11 Prover 1: Preprocessing ...
% 2.97/1.11 Prover 4: Preprocessing ...
% 2.97/1.15 Prover 2: Preprocessing ...
% 2.97/1.15 Prover 0: Preprocessing ...
% 2.97/1.16 Prover 5: Preprocessing ...
% 2.97/1.16 Prover 6: Preprocessing ...
% 2.97/1.16 Prover 3: Preprocessing ...
% 6.38/1.61 Prover 3: Constructing countermodel ...
% 6.38/1.62 Prover 1: Constructing countermodel ...
% 6.38/1.64 Prover 6: Proving ...
% 6.38/1.67 Prover 5: Constructing countermodel ...
% 7.29/1.73 Prover 4: Constructing countermodel ...
% 7.29/1.80 Prover 0: Proving ...
% 7.99/1.82 Prover 2: Proving ...
% 9.23/2.07 Prover 3: gave up
% 9.82/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.31/2.15 Prover 7: Preprocessing ...
% 11.35/2.33 Prover 7: Constructing countermodel ...
% 12.59/2.51 Prover 1: gave up
% 12.59/2.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.20/2.55 Prover 8: Preprocessing ...
% 13.65/2.63 Prover 8: Warning: ignoring some quantifiers
% 13.65/2.65 Prover 8: Constructing countermodel ...
% 17.56/3.14 Prover 8: gave up
% 17.56/3.14 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 17.86/3.19 Prover 9: Preprocessing ...
% 18.76/3.44 Prover 9: Constructing countermodel ...
% 70.29/10.10 Prover 2: stopped
% 70.29/10.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 71.47/10.14 Prover 10: Preprocessing ...
% 71.47/10.21 Prover 10: Constructing countermodel ...
% 73.30/10.38 Prover 10: Found proof (size 45)
% 73.30/10.38 Prover 10: proved (270ms)
% 73.30/10.38 Prover 6: stopped
% 73.30/10.38 Prover 9: stopped
% 73.30/10.38 Prover 0: stopped
% 73.30/10.38 Prover 7: stopped
% 73.30/10.38 Prover 5: stopped
% 73.30/10.38 Prover 4: stopped
% 73.30/10.38
% 73.30/10.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.30/10.38
% 73.46/10.39 % SZS output start Proof for theBenchmark
% 73.46/10.39 Assumptions after simplification:
% 73.46/10.39 ---------------------------------
% 73.46/10.39
% 73.46/10.39 (mAddComm)
% 73.46/10.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 73.46/10.42 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtpldt0(v1, v0)
% 73.46/10.42 = v2 & $i(v2)))
% 73.46/10.42
% 73.46/10.42 (mDivisor)
% 73.60/10.42 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 73.60/10.42 (sdtasdt0(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 73.60/10.42 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0)) &
% 73.60/10.42 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v1, v0) |
% 73.60/10.42 ~ aInteger0(v0) | aInteger0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) |
% 73.60/10.42 ~ $i(v0) | ~ aDivisorOf0(v1, v0) | ~ aInteger0(v0) | ? [v2: $i] :
% 73.60/10.42 (sdtasdt0(v1, v2) = v0 & $i(v2) & aInteger0(v2))) & ! [v0: $i] : ( ~ $i(v0)
% 73.60/10.42 | ~ aDivisorOf0(sz00, v0) | ~ aInteger0(v0))
% 73.60/10.42
% 73.60/10.42 (mEquMod)
% 73.60/10.42 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 73.60/10.42 : (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) |
% 73.60/10.42 ~ $i(v1) | ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) | ~
% 73.60/10.43 aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v2, v4)) &
% 73.60/10.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 =
% 73.60/10.43 sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~
% 73.60/10.43 $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v2, v4) | ~ aInteger0(v2) | ~
% 73.60/10.43 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v1, v2))
% 73.60/10.43
% 73.60/10.43 (mEquModRef)
% 73.60/10.43 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 73.60/10.43 aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 73.60/10.43
% 73.60/10.43 (mIntMult)
% 73.60/10.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 73.60/10.43 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2))
% 73.60/10.43
% 73.60/10.43 (mIntOne)
% 73.60/10.43 $i(sz10) & aInteger0(sz10)
% 73.60/10.43
% 73.60/10.43 (mIntPlus)
% 73.64/10.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 73.64/10.43 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | aInteger0(v2))
% 73.64/10.43
% 73.64/10.43 (mMulComm)
% 73.64/10.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 73.64/10.43 $i(v1) | ~ $i(v0) | ~ aInteger0(v1) | ~ aInteger0(v0) | (sdtasdt0(v1, v0)
% 73.64/10.43 = v2 & $i(v2)))
% 73.64/10.43
% 73.64/10.43 (mMulMinOne)
% 73.64/10.43 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 73.64/10.43 $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aInteger0(v1) |
% 73.64/10.43 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))))
% 73.64/10.43
% 73.64/10.43 (m__)
% 73.64/10.43 $i(xc) & $i(xq) & $i(xa) & ~ sdteqdtlpzmzozddtrp0(xa, xc, xq)
% 73.64/10.43
% 73.64/10.43 (m__818)
% 73.64/10.43 ~ (xq = sz00) & $i(xc) & $i(xq) & $i(xb) & $i(xa) & $i(sz00) & aInteger0(xc)
% 73.64/10.43 & aInteger0(xq) & aInteger0(xb) & aInteger0(xa)
% 73.64/10.43
% 73.64/10.43 (m__876)
% 73.64/10.43 $i(xn) & $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq,
% 73.64/10.43 xn) = v0 & sdtpldt0(xa, v1) = v0 & smndt0(xb) = v1 & $i(v1) & $i(v0) &
% 73.64/10.43 aInteger0(xn))
% 73.64/10.43
% 73.64/10.43 (m__899)
% 73.64/10.43 $i(xm) & $i(xc) & $i(xq) & $i(xb) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq,
% 73.64/10.43 xm) = v0 & sdtpldt0(xb, v1) = v0 & smndt0(xc) = v1 & $i(v1) & $i(v0) &
% 73.64/10.43 aInteger0(xm))
% 73.64/10.43
% 73.64/10.43 (m__924)
% 73.64/10.44 $i(xm) & $i(xn) & $i(xc) & $i(xq) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ?
% 73.64/10.44 [v2: $i] : (sdtasdt0(xq, v0) = v1 & sdtpldt0(xn, xm) = v0 & sdtpldt0(xa, v2) =
% 73.64/10.44 v1 & smndt0(xc) = v2 & $i(v2) & $i(v1) & $i(v0))
% 73.64/10.44
% 73.64/10.44 (function-axioms)
% 73.64/10.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 73.64/10.44 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 73.64/10.44 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 73.64/10.44 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 73.64/10.44 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 73.64/10.44
% 73.64/10.44 Further assumptions not needed in the proof:
% 73.64/10.44 --------------------------------------------
% 73.64/10.44 mAddAsso, mAddNeg, mAddZero, mDistrib, mEquModSym, mIntNeg, mIntZero, mIntegers,
% 73.64/10.44 mMulAsso, mMulOne, mMulZero, mZeroDiv, m__853
% 73.64/10.44
% 73.64/10.44 Those formulas are unsatisfiable:
% 73.64/10.44 ---------------------------------
% 73.64/10.44
% 73.64/10.44 Begin of proof
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (mIntOne) implies:
% 73.64/10.44 | (1) aInteger0(sz10)
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (mMulMinOne) implies:
% 73.64/10.44 | (2) $i(sz10)
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (mDivisor) implies:
% 73.64/10.44 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (sdtasdt0(v1,
% 73.64/10.44 | v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aInteger0(v2)
% 73.64/10.44 | | ~ aInteger0(v1) | ~ aInteger0(v0) | aDivisorOf0(v1, v0))
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (mEquMod) implies:
% 73.64/10.44 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 73.64/10.44 | (v2 = sz00 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~
% 73.64/10.44 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v2, v4) | ~
% 73.64/10.44 | aInteger0(v2) | ~ aInteger0(v1) | ~ aInteger0(v0) |
% 73.64/10.44 | sdteqdtlpzmzozddtrp0(v0, v1, v2))
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (mEquModRef) implies:
% 73.64/10.44 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 73.64/10.44 | aInteger0(v1) | ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (m__818) implies:
% 73.64/10.44 | (6) ~ (xq = sz00)
% 73.64/10.44 | (7) aInteger0(xa)
% 73.64/10.44 | (8) aInteger0(xq)
% 73.64/10.44 | (9) aInteger0(xc)
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (m__876) implies:
% 73.64/10.44 | (10) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xn) = v0 & sdtpldt0(xa, v1)
% 73.64/10.44 | = v0 & smndt0(xb) = v1 & $i(v1) & $i(v0) & aInteger0(xn))
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (m__899) implies:
% 73.64/10.44 | (11) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xq, xm) = v0 & sdtpldt0(xb, v1)
% 73.64/10.44 | = v0 & smndt0(xc) = v1 & $i(v1) & $i(v0) & aInteger0(xm))
% 73.64/10.44 |
% 73.64/10.44 | ALPHA: (m__924) implies:
% 73.64/10.44 | (12) $i(xn)
% 73.64/10.44 | (13) $i(xm)
% 73.64/10.45 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xq, v0) = v1 &
% 73.64/10.45 | sdtpldt0(xn, xm) = v0 & sdtpldt0(xa, v2) = v1 & smndt0(xc) = v2 &
% 73.64/10.45 | $i(v2) & $i(v1) & $i(v0))
% 73.64/10.45 |
% 73.64/10.45 | ALPHA: (m__) implies:
% 73.64/10.45 | (15) ~ sdteqdtlpzmzozddtrp0(xa, xc, xq)
% 73.64/10.45 | (16) $i(xa)
% 73.64/10.45 | (17) $i(xq)
% 73.64/10.45 | (18) $i(xc)
% 73.64/10.45 |
% 73.64/10.45 | ALPHA: (function-axioms) implies:
% 73.64/10.45 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 73.64/10.45 | v1) | ~ (smndt0(v2) = v0))
% 73.64/10.45 |
% 73.64/10.45 | DELTA: instantiating (10) with fresh symbols all_21_0, all_21_1 gives:
% 73.64/10.45 | (20) sdtasdt0(xq, xn) = all_21_1 & sdtpldt0(xa, all_21_0) = all_21_1 &
% 73.64/10.45 | smndt0(xb) = all_21_0 & $i(all_21_0) & $i(all_21_1) & aInteger0(xn)
% 73.64/10.45 |
% 73.64/10.45 | ALPHA: (20) implies:
% 73.64/10.45 | (21) aInteger0(xn)
% 73.64/10.45 |
% 73.64/10.45 | DELTA: instantiating (11) with fresh symbols all_23_0, all_23_1 gives:
% 73.64/10.45 | (22) sdtasdt0(xq, xm) = all_23_1 & sdtpldt0(xb, all_23_0) = all_23_1 &
% 73.64/10.45 | smndt0(xc) = all_23_0 & $i(all_23_0) & $i(all_23_1) & aInteger0(xm)
% 73.64/10.45 |
% 73.64/10.45 | ALPHA: (22) implies:
% 73.64/10.45 | (23) aInteger0(xm)
% 73.64/10.45 | (24) smndt0(xc) = all_23_0
% 73.64/10.45 |
% 73.64/10.45 | DELTA: instantiating (14) with fresh symbols all_25_0, all_25_1, all_25_2
% 73.64/10.45 | gives:
% 73.64/10.45 | (25) sdtasdt0(xq, all_25_2) = all_25_1 & sdtpldt0(xn, xm) = all_25_2 &
% 73.64/10.45 | sdtpldt0(xa, all_25_0) = all_25_1 & smndt0(xc) = all_25_0 &
% 73.64/10.45 | $i(all_25_0) & $i(all_25_1) & $i(all_25_2)
% 73.64/10.45 |
% 73.64/10.45 | ALPHA: (25) implies:
% 73.64/10.45 | (26) smndt0(xc) = all_25_0
% 73.64/10.45 | (27) sdtpldt0(xa, all_25_0) = all_25_1
% 73.64/10.45 | (28) sdtpldt0(xn, xm) = all_25_2
% 73.64/10.45 | (29) sdtasdt0(xq, all_25_2) = all_25_1
% 73.64/10.45 |
% 73.64/10.45 | GROUND_INST: instantiating (19) with all_23_0, all_25_0, xc, simplifying with
% 73.64/10.45 | (24), (26) gives:
% 73.64/10.45 | (30) all_25_0 = all_23_0
% 73.64/10.45 |
% 73.64/10.45 | REDUCE: (27), (30) imply:
% 73.64/10.45 | (31) sdtpldt0(xa, all_23_0) = all_25_1
% 73.64/10.45 |
% 73.64/10.45 | GROUND_INST: instantiating (5) with sz10, xq, simplifying with (1), (2), (8),
% 73.64/10.45 | (17) gives:
% 73.64/10.45 | (32) xq = sz00 | sdteqdtlpzmzozddtrp0(sz10, sz10, xq)
% 73.64/10.45 |
% 73.64/10.45 | GROUND_INST: instantiating (mIntPlus) with xn, xm, all_25_2, simplifying with
% 73.64/10.45 | (12), (13), (21), (23), (28) gives:
% 73.64/10.45 | (33) aInteger0(all_25_2)
% 73.64/10.45 |
% 73.64/10.45 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_25_2, simplifying with
% 73.64/10.45 | (12), (13), (21), (23), (28) gives:
% 73.64/10.45 | (34) sdtpldt0(xm, xn) = all_25_2 & $i(all_25_2)
% 73.64/10.45 |
% 73.64/10.45 | ALPHA: (34) implies:
% 73.64/10.45 | (35) $i(all_25_2)
% 73.64/10.45 |
% 73.64/10.45 | BETA: splitting (32) gives:
% 73.64/10.45 |
% 73.64/10.45 | Case 1:
% 73.64/10.45 | |
% 73.64/10.45 | |
% 73.64/10.46 | | GROUND_INST: instantiating (mIntMult) with xq, all_25_2, all_25_1,
% 73.64/10.46 | | simplifying with (8), (17), (29), (33), (35) gives:
% 73.64/10.46 | | (36) aInteger0(all_25_1)
% 73.64/10.46 | |
% 73.64/10.46 | | GROUND_INST: instantiating (mMulComm) with xq, all_25_2, all_25_1,
% 73.64/10.46 | | simplifying with (8), (17), (29), (33), (35) gives:
% 73.64/10.46 | | (37) sdtasdt0(all_25_2, xq) = all_25_1 & $i(all_25_1)
% 73.64/10.46 | |
% 73.64/10.46 | | ALPHA: (37) implies:
% 73.64/10.46 | | (38) $i(all_25_1)
% 73.64/10.46 | |
% 73.64/10.46 | | GROUND_INST: instantiating (5) with all_25_2, xq, simplifying with (8),
% 73.64/10.46 | | (17), (33), (35) gives:
% 73.64/10.46 | | (39) xq = sz00 | sdteqdtlpzmzozddtrp0(all_25_2, all_25_2, xq)
% 73.64/10.46 | |
% 73.64/10.46 | | BETA: splitting (39) gives:
% 73.64/10.46 | |
% 73.64/10.46 | | Case 1:
% 73.64/10.46 | | |
% 73.64/10.46 | | |
% 73.64/10.46 | | | GROUND_INST: instantiating (3) with all_25_1, xq, all_25_2, simplifying
% 73.64/10.46 | | | with (8), (17), (29), (33), (35), (36), (38) gives:
% 73.64/10.46 | | | (40) xq = sz00 | aDivisorOf0(xq, all_25_1)
% 73.64/10.46 | | |
% 73.64/10.46 | | | BETA: splitting (40) gives:
% 73.64/10.46 | | |
% 73.64/10.46 | | | Case 1:
% 73.64/10.46 | | | |
% 73.64/10.46 | | | | (41) aDivisorOf0(xq, all_25_1)
% 73.64/10.46 | | | |
% 73.64/10.46 | | | | GROUND_INST: instantiating (4) with xa, xc, xq, all_23_0, all_25_1,
% 73.64/10.46 | | | | simplifying with (7), (8), (9), (15), (16), (17), (18),
% 73.64/10.46 | | | | (24), (31), (41) gives:
% 73.64/10.46 | | | | (42) xq = sz00
% 73.64/10.46 | | | |
% 73.64/10.46 | | | | REDUCE: (6), (42) imply:
% 73.64/10.46 | | | | (43) $false
% 73.64/10.46 | | | |
% 73.64/10.46 | | | | CLOSE: (43) is inconsistent.
% 73.64/10.46 | | | |
% 73.64/10.46 | | | Case 2:
% 73.64/10.46 | | | |
% 73.64/10.46 | | | | (44) xq = sz00
% 73.64/10.46 | | | |
% 73.64/10.46 | | | | REDUCE: (6), (44) imply:
% 73.64/10.46 | | | | (45) $false
% 73.64/10.46 | | | |
% 73.64/10.46 | | | | CLOSE: (45) is inconsistent.
% 73.64/10.46 | | | |
% 73.64/10.46 | | | End of split
% 73.64/10.46 | | |
% 73.64/10.46 | | Case 2:
% 73.64/10.46 | | |
% 73.64/10.46 | | | (46) xq = sz00
% 73.64/10.46 | | |
% 73.64/10.46 | | | REDUCE: (6), (46) imply:
% 73.64/10.46 | | | (47) $false
% 73.64/10.46 | | |
% 73.64/10.46 | | | CLOSE: (47) is inconsistent.
% 73.64/10.46 | | |
% 73.64/10.46 | | End of split
% 73.64/10.46 | |
% 73.64/10.46 | Case 2:
% 73.64/10.46 | |
% 73.64/10.46 | | (48) xq = sz00
% 73.64/10.46 | |
% 73.64/10.46 | | REDUCE: (6), (48) imply:
% 73.64/10.46 | | (49) $false
% 73.64/10.46 | |
% 73.64/10.46 | | CLOSE: (49) is inconsistent.
% 73.64/10.46 | |
% 73.64/10.46 | End of split
% 73.64/10.46 |
% 73.64/10.46 End of proof
% 73.64/10.46 % SZS output end Proof for theBenchmark
% 73.64/10.46
% 73.64/10.46 9820ms
%------------------------------------------------------------------------------