TSTP Solution File: NUM429+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM429+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 11:47:42 EDT 2023
% Result : Theorem 7.74s 1.89s
% Output : Proof 10.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM429+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Aug 25 08:14:57 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.50 ________ _____
% 0.14/0.50 ___ __ \_________(_)________________________________
% 0.14/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.50
% 0.14/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.50 (2023-06-19)
% 0.14/0.50
% 0.14/0.50 (c) Philipp Rümmer, 2009-2023
% 0.14/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.50 Amanda Stjerna.
% 0.14/0.50 Free software under BSD-3-Clause.
% 0.14/0.50
% 0.14/0.50 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.50
% 0.14/0.50 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.51 Running up to 7 provers in parallel.
% 0.14/0.52 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.52 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.52 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.14/0.52 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.16/0.96 Prover 4: Preprocessing ...
% 2.16/0.96 Prover 1: Preprocessing ...
% 2.16/0.99 Prover 0: Preprocessing ...
% 2.16/0.99 Prover 2: Preprocessing ...
% 2.16/0.99 Prover 5: Preprocessing ...
% 2.16/0.99 Prover 3: Preprocessing ...
% 2.16/0.99 Prover 6: Preprocessing ...
% 5.73/1.54 Prover 1: Constructing countermodel ...
% 5.73/1.58 Prover 3: Constructing countermodel ...
% 6.38/1.65 Prover 6: Proving ...
% 6.38/1.65 Prover 4: Constructing countermodel ...
% 6.38/1.65 Prover 5: Constructing countermodel ...
% 6.94/1.77 Prover 0: Proving ...
% 7.57/1.79 Prover 2: Proving ...
% 7.74/1.88 Prover 3: proved (1361ms)
% 7.74/1.88
% 7.74/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.74/1.89
% 7.74/1.89 Prover 5: stopped
% 7.74/1.89 Prover 6: stopped
% 8.38/1.91 Prover 0: stopped
% 8.38/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.38/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.38/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.38/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.38/1.94 Prover 2: stopped
% 8.38/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.85/1.99 Prover 11: Preprocessing ...
% 8.85/1.99 Prover 10: Preprocessing ...
% 8.85/2.00 Prover 7: Preprocessing ...
% 8.85/2.02 Prover 8: Preprocessing ...
% 8.85/2.05 Prover 13: Preprocessing ...
% 9.47/2.19 Prover 10: Constructing countermodel ...
% 9.47/2.20 Prover 8: Warning: ignoring some quantifiers
% 9.47/2.21 Prover 7: Constructing countermodel ...
% 9.47/2.24 Prover 8: Constructing countermodel ...
% 10.14/2.25 Prover 1: Found proof (size 31)
% 10.14/2.25 Prover 1: proved (1731ms)
% 10.14/2.25 Prover 4: stopped
% 10.14/2.25 Prover 10: stopped
% 10.14/2.25 Prover 7: stopped
% 10.14/2.25 Prover 8: stopped
% 10.14/2.26 Prover 13: Constructing countermodel ...
% 10.56/2.27 Prover 13: stopped
% 10.63/2.28 Prover 11: Constructing countermodel ...
% 10.63/2.29 Prover 11: stopped
% 10.63/2.29
% 10.63/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.63/2.29
% 10.63/2.30 % SZS output start Proof for theBenchmark
% 10.63/2.30 Assumptions after simplification:
% 10.63/2.30 ---------------------------------
% 10.63/2.30
% 10.63/2.30 (mIntMult)
% 10.81/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 10.81/2.33 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 10.81/2.33 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0)
% 10.81/2.33 | ~ (v3 = 0) | v5 = 0)))
% 10.81/2.33
% 10.81/2.33 (mMulComm)
% 10.81/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 10.81/2.33 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 10.81/2.33 (sdtasdt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) &
% 10.81/2.33 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 10.81/2.33
% 10.81/2.33 (m__)
% 10.81/2.33 $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1
% 10.81/2.33 & smndt0(xb) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) =
% 10.81/2.33 v1) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v2) = v3)))
% 10.81/2.33
% 10.81/2.33 (m__853)
% 10.95/2.34 $i(xc) & $i(xq) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 10.95/2.34 ? [v3: $i] : (sdteqdtlpzmzozddtrp0(xb, xc, xq) = 0 & sdteqdtlpzmzozddtrp0(xa,
% 10.95/2.34 xb, xq) = 0 & aDivisorOf0(xq, v3) = 0 & aDivisorOf0(xq, v1) = 0 &
% 10.95/2.34 sdtpldt0(xb, v2) = v3 & sdtpldt0(xa, v0) = v1 & smndt0(xc) = v2 & smndt0(xb)
% 10.95/2.34 = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v4: $i] : (sdtasdt0(xq, v4) =
% 10.95/2.34 v3 & aInteger0(v4) = 0 & $i(v4)) & ? [v4: $i] : (sdtasdt0(xq, v4) = v1 &
% 10.95/2.34 aInteger0(v4) = 0 & $i(v4)))
% 10.95/2.34
% 10.95/2.34 (function-axioms)
% 10.95/2.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.95/2.34 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1)
% 10.95/2.34 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 10.95/2.34 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.95/2.34 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: $i] :
% 10.95/2.34 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 10.95/2.34 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 10.95/2.34 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 10.95/2.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) |
% 10.95/2.34 ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.95/2.34 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~
% 10.95/2.34 (aInteger0(v2) = v0))
% 10.95/2.34
% 10.95/2.34 Further assumptions not needed in the proof:
% 10.95/2.34 --------------------------------------------
% 10.95/2.34 mAddAsso, mAddComm, mAddNeg, mAddZero, mDistrib, mDivisor, mEquMod, mEquModRef,
% 10.95/2.34 mEquModSym, mIntNeg, mIntOne, mIntPlus, mIntZero, mIntegers, mMulAsso,
% 10.95/2.34 mMulMinOne, mMulOne, mMulZero, mZeroDiv, m__818
% 10.95/2.34
% 10.95/2.34 Those formulas are unsatisfiable:
% 10.95/2.34 ---------------------------------
% 10.95/2.34
% 10.95/2.34 Begin of proof
% 10.95/2.34 |
% 10.95/2.34 | ALPHA: (m__853) implies:
% 10.95/2.35 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.95/2.35 | (sdteqdtlpzmzozddtrp0(xb, xc, xq) = 0 & sdteqdtlpzmzozddtrp0(xa, xb,
% 10.95/2.35 | xq) = 0 & aDivisorOf0(xq, v3) = 0 & aDivisorOf0(xq, v1) = 0 &
% 10.95/2.35 | sdtpldt0(xb, v2) = v3 & sdtpldt0(xa, v0) = v1 & smndt0(xc) = v2 &
% 10.95/2.35 | smndt0(xb) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v4: $i] :
% 10.95/2.35 | (sdtasdt0(xq, v4) = v3 & aInteger0(v4) = 0 & $i(v4)) & ? [v4: $i] :
% 10.95/2.35 | (sdtasdt0(xq, v4) = v1 & aInteger0(v4) = 0 & $i(v4)))
% 10.95/2.35 |
% 10.95/2.35 | ALPHA: (m__) implies:
% 10.95/2.35 | (2) $i(xq)
% 10.95/2.35 | (3) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xa, v0) = v1 & smndt0(xb) = v0 &
% 10.95/2.35 | $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xq, v2) = v1) | ~
% 10.95/2.35 | $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & aInteger0(v2) = v3)))
% 10.95/2.35 |
% 10.95/2.35 | ALPHA: (function-axioms) implies:
% 10.95/2.35 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.95/2.35 | (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0))
% 10.95/2.35 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 10.95/2.35 | v1) | ~ (smndt0(v2) = v0))
% 10.95/2.35 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.95/2.35 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 10.95/2.35 |
% 10.95/2.35 | DELTA: instantiating (3) with fresh symbols all_21_0, all_21_1 gives:
% 10.95/2.35 | (7) sdtpldt0(xa, all_21_1) = all_21_0 & smndt0(xb) = all_21_1 &
% 10.95/2.35 | $i(all_21_0) & $i(all_21_1) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) =
% 10.95/2.35 | all_21_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aInteger0(v0)
% 10.95/2.35 | = v1))
% 10.95/2.35 |
% 10.95/2.35 | ALPHA: (7) implies:
% 10.95/2.35 | (8) smndt0(xb) = all_21_1
% 10.95/2.35 | (9) sdtpldt0(xa, all_21_1) = all_21_0
% 10.95/2.35 | (10) ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_21_0) | ~ $i(v0) | ? [v1:
% 10.95/2.35 | int] : ( ~ (v1 = 0) & aInteger0(v0) = v1))
% 10.95/2.35 |
% 10.95/2.35 | DELTA: instantiating (1) with fresh symbols all_27_0, all_27_1, all_27_2,
% 10.95/2.35 | all_27_3 gives:
% 10.95/2.35 | (11) sdteqdtlpzmzozddtrp0(xb, xc, xq) = 0 & sdteqdtlpzmzozddtrp0(xa, xb,
% 10.95/2.35 | xq) = 0 & aDivisorOf0(xq, all_27_0) = 0 & aDivisorOf0(xq, all_27_2)
% 10.95/2.35 | = 0 & sdtpldt0(xb, all_27_1) = all_27_0 & sdtpldt0(xa, all_27_3) =
% 10.95/2.35 | all_27_2 & smndt0(xc) = all_27_1 & smndt0(xb) = all_27_3 &
% 10.95/2.35 | $i(all_27_0) & $i(all_27_1) & $i(all_27_2) & $i(all_27_3) & ? [v0:
% 10.95/2.35 | $i] : (sdtasdt0(xq, v0) = all_27_0 & aInteger0(v0) = 0 & $i(v0)) &
% 10.95/2.35 | ? [v0: $i] : (sdtasdt0(xq, v0) = all_27_2 & aInteger0(v0) = 0 &
% 10.95/2.35 | $i(v0))
% 10.95/2.36 |
% 10.95/2.36 | ALPHA: (11) implies:
% 10.95/2.36 | (12) smndt0(xb) = all_27_3
% 10.95/2.36 | (13) sdtpldt0(xa, all_27_3) = all_27_2
% 10.95/2.36 | (14) ? [v0: $i] : (sdtasdt0(xq, v0) = all_27_2 & aInteger0(v0) = 0 &
% 10.95/2.36 | $i(v0))
% 10.95/2.36 |
% 10.95/2.36 | DELTA: instantiating (14) with fresh symbol all_31_0 gives:
% 10.95/2.36 | (15) sdtasdt0(xq, all_31_0) = all_27_2 & aInteger0(all_31_0) = 0 &
% 10.95/2.36 | $i(all_31_0)
% 10.95/2.36 |
% 10.95/2.36 | ALPHA: (15) implies:
% 10.95/2.36 | (16) $i(all_31_0)
% 10.95/2.36 | (17) aInteger0(all_31_0) = 0
% 10.95/2.36 | (18) sdtasdt0(xq, all_31_0) = all_27_2
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (5) with all_21_1, all_27_3, xb, simplifying with
% 10.95/2.36 | (8), (12) gives:
% 10.95/2.36 | (19) all_27_3 = all_21_1
% 10.95/2.36 |
% 10.95/2.36 | REDUCE: (13), (19) imply:
% 10.95/2.36 | (20) sdtpldt0(xa, all_21_1) = all_27_2
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (6) with all_21_0, all_27_2, all_21_1, xa,
% 10.95/2.36 | simplifying with (9), (20) gives:
% 10.95/2.36 | (21) all_27_2 = all_21_0
% 10.95/2.36 |
% 10.95/2.36 | REDUCE: (18), (21) imply:
% 10.95/2.36 | (22) sdtasdt0(xq, all_31_0) = all_21_0
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (10) with all_31_0, simplifying with (16), (22)
% 10.95/2.36 | gives:
% 10.95/2.36 | (23) ? [v0: int] : ( ~ (v0 = 0) & aInteger0(all_31_0) = v0)
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (mMulComm) with xq, all_31_0, all_21_0, simplifying
% 10.95/2.36 | with (2), (16), (22) gives:
% 10.95/2.36 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_31_0, xq) =
% 10.95/2.36 | v2 & aInteger0(all_31_0) = v1 & aInteger0(xq) = v0 & $i(v2) & ( ~
% 10.95/2.36 | (v1 = 0) | ~ (v0 = 0) | v2 = all_21_0))
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (mIntMult) with xq, all_31_0, all_21_0, simplifying
% 10.95/2.36 | with (2), (16), (22) gives:
% 10.95/2.36 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_31_0) = v1
% 10.95/2.36 | & aInteger0(all_21_0) = v2 & aInteger0(xq) = v0 & ( ~ (v1 = 0) | ~
% 10.95/2.36 | (v0 = 0) | v2 = 0))
% 10.95/2.36 |
% 10.95/2.36 | DELTA: instantiating (23) with fresh symbol all_54_0 gives:
% 10.95/2.36 | (26) ~ (all_54_0 = 0) & aInteger0(all_31_0) = all_54_0
% 10.95/2.36 |
% 10.95/2.36 | ALPHA: (26) implies:
% 10.95/2.36 | (27) ~ (all_54_0 = 0)
% 10.95/2.36 | (28) aInteger0(all_31_0) = all_54_0
% 10.95/2.36 |
% 10.95/2.36 | DELTA: instantiating (25) with fresh symbols all_62_0, all_62_1, all_62_2
% 10.95/2.36 | gives:
% 10.95/2.36 | (29) aInteger0(all_31_0) = all_62_1 & aInteger0(all_21_0) = all_62_0 &
% 10.95/2.36 | aInteger0(xq) = all_62_2 & ( ~ (all_62_1 = 0) | ~ (all_62_2 = 0) |
% 10.95/2.36 | all_62_0 = 0)
% 10.95/2.36 |
% 10.95/2.36 | ALPHA: (29) implies:
% 10.95/2.36 | (30) aInteger0(all_31_0) = all_62_1
% 10.95/2.36 |
% 10.95/2.36 | DELTA: instantiating (24) with fresh symbols all_72_0, all_72_1, all_72_2
% 10.95/2.36 | gives:
% 10.95/2.36 | (31) sdtasdt0(all_31_0, xq) = all_72_0 & aInteger0(all_31_0) = all_72_1 &
% 10.95/2.36 | aInteger0(xq) = all_72_2 & $i(all_72_0) & ( ~ (all_72_1 = 0) | ~
% 10.95/2.36 | (all_72_2 = 0) | all_72_0 = all_21_0)
% 10.95/2.36 |
% 10.95/2.36 | ALPHA: (31) implies:
% 10.95/2.36 | (32) aInteger0(all_31_0) = all_72_1
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (4) with all_54_0, all_62_1, all_31_0, simplifying
% 10.95/2.36 | with (28), (30) gives:
% 10.95/2.36 | (33) all_62_1 = all_54_0
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (4) with 0, all_72_1, all_31_0, simplifying with
% 10.95/2.36 | (17), (32) gives:
% 10.95/2.36 | (34) all_72_1 = 0
% 10.95/2.36 |
% 10.95/2.36 | GROUND_INST: instantiating (4) with all_62_1, all_72_1, all_31_0, simplifying
% 10.95/2.36 | with (30), (32) gives:
% 10.95/2.36 | (35) all_72_1 = all_62_1
% 10.95/2.36 |
% 10.95/2.36 | COMBINE_EQS: (34), (35) imply:
% 10.95/2.36 | (36) all_62_1 = 0
% 10.95/2.36 |
% 10.95/2.37 | SIMP: (36) implies:
% 10.95/2.37 | (37) all_62_1 = 0
% 10.95/2.37 |
% 10.95/2.37 | COMBINE_EQS: (33), (37) imply:
% 10.95/2.37 | (38) all_54_0 = 0
% 10.95/2.37 |
% 10.95/2.37 | REDUCE: (27), (38) imply:
% 10.95/2.37 | (39) $false
% 10.95/2.37 |
% 10.95/2.37 | CLOSE: (39) is inconsistent.
% 10.95/2.37 |
% 10.95/2.37 End of proof
% 10.95/2.37 % SZS output end Proof for theBenchmark
% 10.95/2.37
% 10.95/2.37 1867ms
%------------------------------------------------------------------------------