TSTP Solution File: NUM852+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 11:50:25 EDT 2023
% Result : Theorem 6.27s 1.60s
% Output : Proof 8.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 10:29:38 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.52/1.03 Prover 1: Preprocessing ...
% 2.52/1.03 Prover 4: Preprocessing ...
% 2.85/1.07 Prover 0: Preprocessing ...
% 2.85/1.07 Prover 5: Preprocessing ...
% 2.85/1.08 Prover 6: Preprocessing ...
% 2.85/1.08 Prover 3: Preprocessing ...
% 2.85/1.08 Prover 2: Preprocessing ...
% 5.20/1.41 Prover 6: Proving ...
% 5.20/1.41 Prover 5: Proving ...
% 5.20/1.41 Prover 3: Constructing countermodel ...
% 5.20/1.42 Prover 1: Constructing countermodel ...
% 5.20/1.42 Prover 4: Constructing countermodel ...
% 5.81/1.47 Prover 2: Proving ...
% 5.81/1.47 Prover 0: Proving ...
% 6.27/1.54 Prover 3: gave up
% 6.27/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.27/1.58 Prover 7: Preprocessing ...
% 6.27/1.60 Prover 0: proved (996ms)
% 6.27/1.60 Prover 5: proved (993ms)
% 6.27/1.60
% 6.27/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.27/1.61
% 6.27/1.61
% 6.27/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.27/1.61
% 6.27/1.61 Prover 2: stopped
% 6.27/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.27/1.61 Prover 6: stopped
% 6.27/1.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.27/1.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.27/1.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.86/1.63 Prover 1: gave up
% 6.86/1.63 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.86/1.65 Prover 8: Preprocessing ...
% 6.86/1.65 Prover 10: Preprocessing ...
% 6.86/1.66 Prover 11: Preprocessing ...
% 6.86/1.66 Prover 13: Preprocessing ...
% 6.86/1.66 Prover 16: Preprocessing ...
% 6.86/1.67 Prover 7: Warning: ignoring some quantifiers
% 7.38/1.69 Prover 7: Constructing countermodel ...
% 7.38/1.75 Prover 10: Warning: ignoring some quantifiers
% 7.38/1.75 Prover 13: Warning: ignoring some quantifiers
% 7.38/1.76 Prover 10: Constructing countermodel ...
% 7.38/1.76 Prover 16: Warning: ignoring some quantifiers
% 7.38/1.76 Prover 16: Constructing countermodel ...
% 7.38/1.76 Prover 13: Constructing countermodel ...
% 7.98/1.77 Prover 8: Warning: ignoring some quantifiers
% 8.07/1.78 Prover 4: Found proof (size 59)
% 8.07/1.78 Prover 4: proved (1172ms)
% 8.07/1.78 Prover 7: stopped
% 8.07/1.78 Prover 16: stopped
% 8.07/1.78 Prover 8: Constructing countermodel ...
% 8.07/1.78 Prover 13: stopped
% 8.07/1.79 Prover 10: stopped
% 8.07/1.79 Prover 8: stopped
% 8.07/1.80 Prover 11: Constructing countermodel ...
% 8.07/1.81 Prover 11: stopped
% 8.07/1.81
% 8.07/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.07/1.81
% 8.07/1.82 % SZS output start Proof for theBenchmark
% 8.07/1.82 Assumptions after simplification:
% 8.07/1.82 ---------------------------------
% 8.07/1.82
% 8.07/1.82 (ass(cond(302, 0), 0))
% 8.07/1.86 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) =
% 8.07/1.86 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 8.07/1.86 ? [v6: $i] : ? [v7: any] : (vplus(v4, v5) = v6 & vmul(v2, vd469) = v5 &
% 8.07/1.86 vmul(v1, vd469) = v4 & greater(v6, v4) = v7 & greater(v0, v1) = v3 &
% 8.07/1.86 $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v7 = 0))) & ! [v0: $i] : !
% 8.07/1.86 [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 8.07/1.86 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vskolem9(v0, v1) = v3 & vplus(v2,
% 8.07/1.86 v4) = v5 & vmul(v3, vd469) = v4 & vmul(v1, vd469) = v2 & greater(v5, v2)
% 8.07/1.86 = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 8.07/1.86
% 8.07/1.86 (ass(cond(302, 0), 1))
% 8.07/1.86 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) =
% 8.07/1.86 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 8.07/1.86 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vplus(v6, v7) = v8 & vplus(v1, v2)
% 8.07/1.86 = v4 & vmul(v4, vd469) = v5 & vmul(v2, vd469) = v7 & vmul(v1, vd469) = v6
% 8.07/1.86 & greater(v0, v1) = v3 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~
% 8.07/1.86 (v3 = 0) | v8 = v5))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1)
% 8.07/1.86 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.07/1.86 ? [v5: $i] : ? [v6: $i] : (vskolem9(v0, v1) = v2 & vplus(v5, v6) = v4 &
% 8.07/1.86 vplus(v1, v2) = v3 & vmul(v3, vd469) = v4 & vmul(v2, vd469) = v6 &
% 8.07/1.86 vmul(v1, vd469) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 8.07/1.86
% 8.07/1.86 (ass(cond(302, 0), 2))
% 8.07/1.87 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) =
% 8.07/1.87 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 8.07/1.87 ? [v6: $i] : (vplus(v1, v2) = v5 & vmul(v5, vd469) = v6 & vmul(v0, vd469) =
% 8.07/1.87 v4 & greater(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 =
% 8.07/1.87 v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~
% 8.07/1.87 $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (vskolem9(v0,
% 8.07/1.87 v1) = v3 & vplus(v1, v3) = v4 & vmul(v4, vd469) = v2 & vmul(v0, vd469) =
% 8.07/1.87 v2 & $i(v4) & $i(v3) & $i(v2)))
% 8.07/1.87
% 8.07/1.87 (ass(cond(302, 0), 3))
% 8.07/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) = v2) | ~
% 8.07/1.87 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (vplus(v1, v2) = v4 &
% 8.07/1.87 greater(v0, v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))) & ! [v0: $i] :
% 8.07/1.87 ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 8.07/1.87 (vskolem9(v0, v1) = v2 & vplus(v1, v2) = v0 & $i(v2)))
% 8.07/1.87
% 8.07/1.87 (holds(conseq_conjunct1(conseq(304)), 483, 0))
% 8.07/1.87 greater(vd481, vd480) = 0 & $i(vd480) & $i(vd481)
% 8.07/1.87
% 8.07/1.87 (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0))
% 8.45/1.87 $i(vd480) & $i(vd469) & $i(vd481) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 8.45/1.87 ( ~ (v2 = 0) & vmul(vd480, vd469) = v1 & vmul(vd481, vd469) = v0 & greater(v0,
% 8.45/1.87 v1) = v2 & $i(v1) & $i(v0))
% 8.45/1.87
% 8.45/1.87 (function-axioms)
% 8.45/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.45/1.88 (vskolem9(v3, v2) = v1) | ~ (vskolem9(v3, v2) = v0)) & ! [v0: $i] : !
% 8.45/1.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~
% 8.45/1.88 (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.45/1.88 $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0:
% 8.45/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.45/1.88 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 8.45/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.45/1.88 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 8.45/1.88 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~
% 8.45/1.88 (vsucc(v2) = v0))
% 8.45/1.88
% 8.45/1.88 Further assumptions not needed in the proof:
% 8.45/1.88 --------------------------------------------
% 8.45/1.88 ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(261, 0), 0), ass(cond(270,
% 8.45/1.88 0), 0), ass(cond(281, 0), 0), ass(cond(290, 0), 0), ass(cond(303, 0), 0),
% 8.45/1.88 ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0),
% 8.45/1.88 2), ass(cond(goal(130), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 8.45/1.88 def(cond(conseq(axiom(3)), 12), 1), holds(antec(304), 482, 0)
% 8.45/1.88
% 8.45/1.88 Those formulas are unsatisfiable:
% 8.45/1.88 ---------------------------------
% 8.45/1.88
% 8.45/1.88 Begin of proof
% 8.45/1.88 |
% 8.45/1.88 | ALPHA: (holds(conseq_conjunct1(conseq(304)), 483, 0)) implies:
% 8.45/1.88 | (1) greater(vd481, vd480) = 0
% 8.45/1.88 |
% 8.45/1.88 | ALPHA: (ass(cond(302, 0), 0)) implies:
% 8.45/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 8.45/1.88 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 8.45/1.88 | (vskolem9(v0, v1) = v3 & vplus(v2, v4) = v5 & vmul(v3, vd469) = v4 &
% 8.45/1.88 | vmul(v1, vd469) = v2 & greater(v5, v2) = 0 & $i(v5) & $i(v4) &
% 8.45/1.88 | $i(v3) & $i(v2)))
% 8.45/1.88 |
% 8.45/1.88 | ALPHA: (ass(cond(302, 0), 1)) implies:
% 8.45/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 8.45/1.88 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 8.45/1.88 | [v6: $i] : (vskolem9(v0, v1) = v2 & vplus(v5, v6) = v4 & vplus(v1,
% 8.45/1.89 | v2) = v3 & vmul(v3, vd469) = v4 & vmul(v2, vd469) = v6 & vmul(v1,
% 8.45/1.89 | vd469) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 8.45/1.89 |
% 8.45/1.89 | ALPHA: (ass(cond(302, 0), 2)) implies:
% 8.45/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 8.45/1.89 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (vskolem9(v0, v1)
% 8.45/1.89 | = v3 & vplus(v1, v3) = v4 & vmul(v4, vd469) = v2 & vmul(v0, vd469)
% 8.45/1.89 | = v2 & $i(v4) & $i(v3) & $i(v2)))
% 8.45/1.89 |
% 8.45/1.89 | ALPHA: (ass(cond(302, 0), 3)) implies:
% 8.45/1.89 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 8.45/1.89 | $i(v0) | ? [v2: $i] : (vskolem9(v0, v1) = v2 & vplus(v1, v2) = v0 &
% 8.45/1.89 | $i(v2)))
% 8.45/1.89 |
% 8.45/1.89 | ALPHA: (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0))
% 8.45/1.89 | implies:
% 8.45/1.89 | (6) $i(vd481)
% 8.45/1.89 | (7) $i(vd480)
% 8.45/1.89 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vmul(vd480,
% 8.45/1.89 | vd469) = v1 & vmul(vd481, vd469) = v0 & greater(v0, v1) = v2 &
% 8.45/1.89 | $i(v1) & $i(v0))
% 8.45/1.89 |
% 8.45/1.89 | ALPHA: (function-axioms) implies:
% 8.45/1.89 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.45/1.89 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 8.45/1.89 | v2) = v0))
% 8.45/1.89 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.45/1.89 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 8.65/1.89 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.65/1.89 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 8.65/1.89 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.65/1.89 | (vskolem9(v3, v2) = v1) | ~ (vskolem9(v3, v2) = v0))
% 8.65/1.89 |
% 8.65/1.89 | DELTA: instantiating (8) with fresh symbols all_20_0, all_20_1, all_20_2
% 8.65/1.89 | gives:
% 8.65/1.89 | (13) ~ (all_20_0 = 0) & vmul(vd480, vd469) = all_20_1 & vmul(vd481, vd469)
% 8.65/1.89 | = all_20_2 & greater(all_20_2, all_20_1) = all_20_0 & $i(all_20_1) &
% 8.65/1.89 | $i(all_20_2)
% 8.65/1.89 |
% 8.65/1.89 | ALPHA: (13) implies:
% 8.65/1.89 | (14) ~ (all_20_0 = 0)
% 8.65/1.89 | (15) greater(all_20_2, all_20_1) = all_20_0
% 8.65/1.89 | (16) vmul(vd481, vd469) = all_20_2
% 8.65/1.89 | (17) vmul(vd480, vd469) = all_20_1
% 8.65/1.89 |
% 8.65/1.90 | GROUND_INST: instantiating (3) with vd481, vd480, simplifying with (1), (6),
% 8.65/1.90 | (7) gives:
% 8.65/1.90 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.65/1.90 | (vskolem9(vd481, vd480) = v0 & vplus(v3, v4) = v2 & vplus(vd480, v0) =
% 8.65/1.90 | v1 & vmul(v1, vd469) = v2 & vmul(v0, vd469) = v4 & vmul(vd480,
% 8.65/1.90 | vd469) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.65/1.90 |
% 8.65/1.90 | GROUND_INST: instantiating (2) with vd481, vd480, simplifying with (1), (6),
% 8.65/1.90 | (7) gives:
% 8.65/1.90 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 8.65/1.90 | (vskolem9(vd481, vd480) = v1 & vplus(v0, v2) = v3 & vmul(v1, vd469) =
% 8.65/1.90 | v2 & vmul(vd480, vd469) = v0 & greater(v3, v0) = 0 & $i(v3) & $i(v2)
% 8.65/1.90 | & $i(v1) & $i(v0))
% 8.65/1.90 |
% 8.65/1.90 | GROUND_INST: instantiating (4) with vd481, vd480, simplifying with (1), (6),
% 8.65/1.90 | (7) gives:
% 8.65/1.90 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vskolem9(vd481, vd480) = v1
% 8.65/1.90 | & vplus(vd480, v1) = v2 & vmul(v2, vd469) = v0 & vmul(vd481, vd469)
% 8.65/1.90 | = v0 & $i(v2) & $i(v1) & $i(v0))
% 8.65/1.90 |
% 8.65/1.90 | GROUND_INST: instantiating (5) with vd481, vd480, simplifying with (1), (6),
% 8.65/1.90 | (7) gives:
% 8.65/1.90 | (21) ? [v0: $i] : (vskolem9(vd481, vd480) = v0 & vplus(vd480, v0) = vd481
% 8.65/1.90 | & $i(v0))
% 8.65/1.90 |
% 8.65/1.90 | DELTA: instantiating (21) with fresh symbol all_34_0 gives:
% 8.65/1.90 | (22) vskolem9(vd481, vd480) = all_34_0 & vplus(vd480, all_34_0) = vd481 &
% 8.65/1.90 | $i(all_34_0)
% 8.65/1.90 |
% 8.65/1.90 | ALPHA: (22) implies:
% 8.65/1.90 | (23) vplus(vd480, all_34_0) = vd481
% 8.65/1.90 | (24) vskolem9(vd481, vd480) = all_34_0
% 8.65/1.90 |
% 8.65/1.90 | DELTA: instantiating (20) with fresh symbols all_40_0, all_40_1, all_40_2
% 8.65/1.90 | gives:
% 8.65/1.90 | (25) vskolem9(vd481, vd480) = all_40_1 & vplus(vd480, all_40_1) = all_40_0
% 8.65/1.90 | & vmul(all_40_0, vd469) = all_40_2 & vmul(vd481, vd469) = all_40_2 &
% 8.65/1.90 | $i(all_40_0) & $i(all_40_1) & $i(all_40_2)
% 8.65/1.90 |
% 8.65/1.90 | ALPHA: (25) implies:
% 8.65/1.90 | (26) vmul(vd481, vd469) = all_40_2
% 8.65/1.90 | (27) vmul(all_40_0, vd469) = all_40_2
% 8.65/1.90 | (28) vplus(vd480, all_40_1) = all_40_0
% 8.65/1.90 | (29) vskolem9(vd481, vd480) = all_40_1
% 8.65/1.90 |
% 8.65/1.90 | DELTA: instantiating (19) with fresh symbols all_42_0, all_42_1, all_42_2,
% 8.65/1.90 | all_42_3 gives:
% 8.65/1.90 | (30) vskolem9(vd481, vd480) = all_42_2 & vplus(all_42_3, all_42_1) =
% 8.65/1.90 | all_42_0 & vmul(all_42_2, vd469) = all_42_1 & vmul(vd480, vd469) =
% 8.65/1.90 | all_42_3 & greater(all_42_0, all_42_3) = 0 & $i(all_42_0) &
% 8.65/1.90 | $i(all_42_1) & $i(all_42_2) & $i(all_42_3)
% 8.65/1.90 |
% 8.65/1.90 | ALPHA: (30) implies:
% 8.65/1.90 | (31) greater(all_42_0, all_42_3) = 0
% 8.65/1.90 | (32) vmul(vd480, vd469) = all_42_3
% 8.65/1.90 | (33) vmul(all_42_2, vd469) = all_42_1
% 8.65/1.90 | (34) vplus(all_42_3, all_42_1) = all_42_0
% 8.65/1.91 | (35) vskolem9(vd481, vd480) = all_42_2
% 8.65/1.91 |
% 8.65/1.91 | DELTA: instantiating (18) with fresh symbols all_44_0, all_44_1, all_44_2,
% 8.65/1.91 | all_44_3, all_44_4 gives:
% 8.65/1.91 | (36) vskolem9(vd481, vd480) = all_44_4 & vplus(all_44_1, all_44_0) =
% 8.65/1.91 | all_44_2 & vplus(vd480, all_44_4) = all_44_3 & vmul(all_44_3, vd469) =
% 8.65/1.91 | all_44_2 & vmul(all_44_4, vd469) = all_44_0 & vmul(vd480, vd469) =
% 8.65/1.91 | all_44_1 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & $i(all_44_3) &
% 8.65/1.91 | $i(all_44_4)
% 8.65/1.91 |
% 8.65/1.91 | ALPHA: (36) implies:
% 8.65/1.91 | (37) vmul(vd480, vd469) = all_44_1
% 8.65/1.91 | (38) vmul(all_44_4, vd469) = all_44_0
% 8.65/1.91 | (39) vmul(all_44_3, vd469) = all_44_2
% 8.65/1.91 | (40) vplus(vd480, all_44_4) = all_44_3
% 8.65/1.91 | (41) vplus(all_44_1, all_44_0) = all_44_2
% 8.65/1.91 | (42) vskolem9(vd481, vd480) = all_44_4
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (10) with all_20_2, all_40_2, vd469, vd481,
% 8.65/1.91 | simplifying with (16), (26) gives:
% 8.65/1.91 | (43) all_40_2 = all_20_2
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (10) with all_20_1, all_44_1, vd469, vd480,
% 8.65/1.91 | simplifying with (17), (37) gives:
% 8.65/1.91 | (44) all_44_1 = all_20_1
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (10) with all_42_3, all_44_1, vd469, vd480,
% 8.65/1.91 | simplifying with (32), (37) gives:
% 8.65/1.91 | (45) all_44_1 = all_42_3
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (12) with all_34_0, all_42_2, vd480, vd481,
% 8.65/1.91 | simplifying with (24), (35) gives:
% 8.65/1.91 | (46) all_42_2 = all_34_0
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (12) with all_42_2, all_44_4, vd480, vd481,
% 8.65/1.91 | simplifying with (35), (42) gives:
% 8.65/1.91 | (47) all_44_4 = all_42_2
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (12) with all_40_1, all_44_4, vd480, vd481,
% 8.65/1.91 | simplifying with (29), (42) gives:
% 8.65/1.91 | (48) all_44_4 = all_40_1
% 8.65/1.91 |
% 8.65/1.91 | COMBINE_EQS: (44), (45) imply:
% 8.65/1.91 | (49) all_42_3 = all_20_1
% 8.65/1.91 |
% 8.65/1.91 | COMBINE_EQS: (47), (48) imply:
% 8.65/1.91 | (50) all_42_2 = all_40_1
% 8.65/1.91 |
% 8.65/1.91 | SIMP: (50) implies:
% 8.65/1.91 | (51) all_42_2 = all_40_1
% 8.65/1.91 |
% 8.65/1.91 | COMBINE_EQS: (46), (51) imply:
% 8.65/1.91 | (52) all_40_1 = all_34_0
% 8.65/1.91 |
% 8.65/1.91 | SIMP: (52) implies:
% 8.65/1.91 | (53) all_40_1 = all_34_0
% 8.65/1.91 |
% 8.65/1.91 | COMBINE_EQS: (48), (53) imply:
% 8.65/1.91 | (54) all_44_4 = all_34_0
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (41), (44) imply:
% 8.65/1.91 | (55) vplus(all_20_1, all_44_0) = all_44_2
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (34), (49) imply:
% 8.65/1.91 | (56) vplus(all_20_1, all_42_1) = all_42_0
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (40), (54) imply:
% 8.65/1.91 | (57) vplus(vd480, all_34_0) = all_44_3
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (28), (53) imply:
% 8.65/1.91 | (58) vplus(vd480, all_34_0) = all_40_0
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (38), (54) imply:
% 8.65/1.91 | (59) vmul(all_34_0, vd469) = all_44_0
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (33), (46) imply:
% 8.65/1.91 | (60) vmul(all_34_0, vd469) = all_42_1
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (27), (43) imply:
% 8.65/1.91 | (61) vmul(all_40_0, vd469) = all_20_2
% 8.65/1.91 |
% 8.65/1.91 | REDUCE: (31), (49) imply:
% 8.65/1.91 | (62) greater(all_42_0, all_20_1) = 0
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (10) with all_42_1, all_44_0, vd469, all_34_0,
% 8.65/1.91 | simplifying with (59), (60) gives:
% 8.65/1.91 | (63) all_44_0 = all_42_1
% 8.65/1.91 |
% 8.65/1.91 | GROUND_INST: instantiating (11) with vd481, all_44_3, all_34_0, vd480,
% 8.65/1.91 | simplifying with (23), (57) gives:
% 8.65/1.92 | (64) all_44_3 = vd481
% 8.65/1.92 |
% 8.65/1.92 | GROUND_INST: instantiating (11) with all_40_0, all_44_3, all_34_0, vd480,
% 8.65/1.92 | simplifying with (57), (58) gives:
% 8.65/1.92 | (65) all_44_3 = all_40_0
% 8.65/1.92 |
% 8.65/1.92 | COMBINE_EQS: (64), (65) imply:
% 8.65/1.92 | (66) all_40_0 = vd481
% 8.65/1.92 |
% 8.65/1.92 | SIMP: (66) implies:
% 8.65/1.92 | (67) all_40_0 = vd481
% 8.65/1.92 |
% 8.65/1.92 | REDUCE: (55), (63) imply:
% 8.65/1.92 | (68) vplus(all_20_1, all_42_1) = all_44_2
% 8.65/1.92 |
% 8.65/1.92 | REDUCE: (39), (64) imply:
% 8.65/1.92 | (69) vmul(vd481, vd469) = all_44_2
% 8.65/1.92 |
% 8.65/1.92 | GROUND_INST: instantiating (10) with all_20_2, all_44_2, vd469, vd481,
% 8.65/1.92 | simplifying with (16), (69) gives:
% 8.65/1.92 | (70) all_44_2 = all_20_2
% 8.65/1.92 |
% 8.65/1.92 | GROUND_INST: instantiating (11) with all_42_0, all_44_2, all_42_1, all_20_1,
% 8.65/1.92 | simplifying with (56), (68) gives:
% 8.65/1.92 | (71) all_44_2 = all_42_0
% 8.65/1.92 |
% 8.65/1.92 | COMBINE_EQS: (70), (71) imply:
% 8.65/1.92 | (72) all_42_0 = all_20_2
% 8.65/1.92 |
% 8.65/1.92 | SIMP: (72) implies:
% 8.65/1.92 | (73) all_42_0 = all_20_2
% 8.65/1.92 |
% 8.65/1.92 | REDUCE: (62), (73) imply:
% 8.65/1.92 | (74) greater(all_20_2, all_20_1) = 0
% 8.65/1.92 |
% 8.65/1.92 | GROUND_INST: instantiating (9) with all_20_0, 0, all_20_1, all_20_2,
% 8.65/1.92 | simplifying with (15), (74) gives:
% 8.65/1.92 | (75) all_20_0 = 0
% 8.65/1.92 |
% 8.65/1.92 | REDUCE: (14), (75) imply:
% 8.65/1.92 | (76) $false
% 8.65/1.92 |
% 8.65/1.92 | CLOSE: (76) is inconsistent.
% 8.65/1.92 |
% 8.65/1.92 End of proof
% 8.65/1.92 % SZS output end Proof for theBenchmark
% 8.65/1.92
% 8.65/1.92 1332ms
%------------------------------------------------------------------------------