TSTP Solution File: NUM852+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 12.79s 2.40s
% Output : Proof 18.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n023.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 17:41:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.51/0.61 ________ _____
% 0.51/0.61 ___ __ \_________(_)________________________________
% 0.51/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.51/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.51/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.51/0.61
% 0.51/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.51/0.61 (2023-06-19)
% 0.51/0.61
% 0.51/0.61 (c) Philipp Rümmer, 2009-2023
% 0.51/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.51/0.61 Amanda Stjerna.
% 0.51/0.61 Free software under BSD-3-Clause.
% 0.51/0.61
% 0.51/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.51/0.61
% 0.51/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.51/0.62 Running up to 7 provers in parallel.
% 0.71/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.71/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.71/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.71/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.74/1.22 Prover 4: Preprocessing ...
% 3.74/1.23 Prover 1: Preprocessing ...
% 4.25/1.28 Prover 5: Preprocessing ...
% 4.25/1.28 Prover 6: Preprocessing ...
% 4.25/1.28 Prover 2: Preprocessing ...
% 4.25/1.28 Prover 0: Preprocessing ...
% 4.25/1.28 Prover 3: Preprocessing ...
% 9.71/2.04 Prover 1: Warning: ignoring some quantifiers
% 10.40/2.10 Prover 5: Proving ...
% 10.40/2.10 Prover 6: Proving ...
% 10.63/2.12 Prover 1: Constructing countermodel ...
% 10.63/2.13 Prover 3: Warning: ignoring some quantifiers
% 10.82/2.17 Prover 3: Constructing countermodel ...
% 10.82/2.18 Prover 4: Warning: ignoring some quantifiers
% 11.46/2.25 Prover 2: Proving ...
% 11.46/2.25 Prover 4: Constructing countermodel ...
% 11.91/2.35 Prover 0: Proving ...
% 12.50/2.40 Prover 5: proved (1767ms)
% 12.50/2.40
% 12.79/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.79/2.40
% 12.79/2.40 Prover 3: stopped
% 12.79/2.42 Prover 6: stopped
% 12.79/2.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.79/2.42 Prover 2: stopped
% 12.79/2.43 Prover 0: stopped
% 12.79/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.79/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.79/2.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.99/2.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.99/2.51 Prover 7: Preprocessing ...
% 13.67/2.53 Prover 8: Preprocessing ...
% 13.67/2.54 Prover 13: Preprocessing ...
% 13.67/2.56 Prover 11: Preprocessing ...
% 13.67/2.57 Prover 10: Preprocessing ...
% 15.38/2.75 Prover 1: gave up
% 15.38/2.76 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 16.06/2.84 Prover 4: Found proof (size 57)
% 16.06/2.84 Prover 4: proved (2212ms)
% 16.06/2.85 Prover 16: Preprocessing ...
% 16.06/2.85 Prover 10: Warning: ignoring some quantifiers
% 16.06/2.86 Prover 8: Warning: ignoring some quantifiers
% 16.06/2.87 Prover 7: Warning: ignoring some quantifiers
% 16.06/2.88 Prover 10: Constructing countermodel ...
% 16.06/2.88 Prover 13: Warning: ignoring some quantifiers
% 16.44/2.90 Prover 10: stopped
% 16.44/2.91 Prover 8: Constructing countermodel ...
% 16.44/2.91 Prover 7: Constructing countermodel ...
% 16.44/2.92 Prover 13: Constructing countermodel ...
% 16.44/2.94 Prover 8: stopped
% 16.44/2.94 Prover 13: stopped
% 16.44/2.94 Prover 7: stopped
% 16.91/2.96 Prover 16: stopped
% 16.91/2.97 Prover 11: Warning: ignoring some quantifiers
% 16.91/3.00 Prover 11: Constructing countermodel ...
% 17.17/3.03 Prover 11: stopped
% 17.17/3.03
% 17.17/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.17/3.03
% 17.39/3.05 % SZS output start Proof for theBenchmark
% 17.39/3.06 Assumptions after simplification:
% 17.39/3.06 ---------------------------------
% 17.39/3.06
% 17.39/3.06 (ass(cond(302, 0), 0))
% 17.39/3.11 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) =
% 17.39/3.11 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 17.39/3.11 ? [v6: $i] : ? [v7: any] : (vplus(v4, v5) = v6 & vmul(v2, vd469) = v5 &
% 17.39/3.11 vmul(v1, vd469) = v4 & greater(v6, v4) = v7 & greater(v0, v1) = v3 &
% 17.39/3.11 $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v7 = 0))) & ! [v0: $i] : !
% 17.39/3.11 [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 17.39/3.11 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vskolem9(v0, v1) = v3 & vplus(v2,
% 17.39/3.11 v4) = v5 & vmul(v3, vd469) = v4 & vmul(v1, vd469) = v2 & greater(v5, v2)
% 17.39/3.11 = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 17.39/3.11
% 17.39/3.11 (ass(cond(302, 0), 1))
% 17.39/3.12 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) =
% 17.39/3.12 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 17.39/3.12 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vplus(v6, v7) = v8 & vplus(v1, v2)
% 17.39/3.12 = v4 & vmul(v4, vd469) = v5 & vmul(v2, vd469) = v7 & vmul(v1, vd469) = v6
% 17.39/3.12 & greater(v0, v1) = v3 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~
% 17.39/3.12 (v3 = 0) | v8 = v5))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1)
% 17.39/3.12 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 17.39/3.12 ? [v5: $i] : ? [v6: $i] : (vskolem9(v0, v1) = v2 & vplus(v5, v6) = v4 &
% 17.39/3.12 vplus(v1, v2) = v3 & vmul(v3, vd469) = v4 & vmul(v2, vd469) = v6 &
% 17.39/3.12 vmul(v1, vd469) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 17.39/3.12
% 17.39/3.12 (ass(cond(302, 0), 2))
% 17.39/3.13 $i(vd469) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) =
% 17.39/3.13 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 17.39/3.13 ? [v6: $i] : (vplus(v1, v2) = v5 & vmul(v5, vd469) = v6 & vmul(v0, vd469) =
% 17.39/3.13 v4 & greater(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 =
% 17.39/3.13 v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~
% 17.39/3.13 $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (vskolem9(v0,
% 17.39/3.13 v1) = v3 & vplus(v1, v3) = v4 & vmul(v4, vd469) = v2 & vmul(v0, vd469) =
% 17.39/3.13 v2 & $i(v4) & $i(v3) & $i(v2)))
% 17.39/3.13
% 17.39/3.13 (ass(cond(302, 0), 3))
% 17.39/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vskolem9(v0, v1) = v2) | ~
% 17.39/3.13 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (vplus(v1, v2) = v4 &
% 17.39/3.13 greater(v0, v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))) & ! [v0: $i] :
% 17.39/3.13 ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 17.39/3.13 (vskolem9(v0, v1) = v2 & vplus(v1, v2) = v0 & $i(v2)))
% 17.39/3.13
% 17.39/3.13 (holds(conseq_conjunct1(conseq(304)), 483, 0))
% 17.39/3.13 greater(vd481, vd480) = 0 & $i(vd480) & $i(vd481)
% 17.39/3.13
% 17.39/3.13 (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0))
% 17.39/3.13 $i(vd480) & $i(vd469) & $i(vd481) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 17.39/3.13 ( ~ (v2 = 0) & vmul(vd480, vd469) = v1 & vmul(vd481, vd469) = v0 & greater(v0,
% 17.39/3.13 v1) = v2 & $i(v1) & $i(v0))
% 17.39/3.13
% 17.39/3.13 (function-axioms)
% 17.39/3.14 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 17.39/3.14 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.39/3.14 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.39/3.14 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 17.39/3.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vskolem9(v3, v2) = v1) |
% 17.39/3.14 ~ (vskolem9(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.39/3.14 [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & !
% 17.39/3.14 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3,
% 17.39/3.14 v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.39/3.14 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3,
% 17.39/3.14 v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.39/3.14 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.39/3.14 (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.39/3.14 $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) =
% 17.39/3.14 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2)
% 17.39/3.14 = v1) | ~ (vsucc(v2) = v0))
% 17.39/3.14
% 17.39/3.14 Further assumptions not needed in the proof:
% 17.39/3.14 --------------------------------------------
% 17.39/3.14 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 17.39/3.14 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 17.39/3.14 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 17.39/3.14 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 17.39/3.14 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(270, 0), 0), ass(cond(281,
% 17.39/3.14 0), 0), ass(cond(290, 0), 0), ass(cond(303, 0), 0), ass(cond(33, 0), 0),
% 17.39/3.14 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0),
% 17.39/3.14 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 0),
% 17.39/3.14 ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0),
% 17.39/3.14 3), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 0),
% 17.39/3.14 ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0),
% 17.39/3.14 0), ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0), 2),
% 17.39/3.14 ass(cond(goal(216), 0), 0), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0),
% 17.39/3.14 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3),
% 17.39/3.14 def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), 1),
% 17.39/3.14 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 17.39/3.14 holds(antec(304), 482, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 17.39/3.14 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 17.39/3.14 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32),
% 17.39/3.14 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))),
% 17.39/3.14 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))
% 17.39/3.14
% 17.39/3.14 Those formulas are unsatisfiable:
% 17.39/3.14 ---------------------------------
% 17.39/3.14
% 17.39/3.14 Begin of proof
% 17.84/3.14 |
% 17.84/3.14 | ALPHA: (holds(conseq_conjunct1(conseq(304)), 483, 0)) implies:
% 17.84/3.14 | (1) greater(vd481, vd480) = 0
% 17.84/3.14 |
% 17.84/3.14 | ALPHA: (ass(cond(302, 0), 0)) implies:
% 17.84/3.15 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 17.84/3.15 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 17.84/3.15 | (vskolem9(v0, v1) = v3 & vplus(v2, v4) = v5 & vmul(v3, vd469) = v4 &
% 17.84/3.15 | vmul(v1, vd469) = v2 & greater(v5, v2) = 0 & $i(v5) & $i(v4) &
% 17.84/3.15 | $i(v3) & $i(v2)))
% 17.84/3.15 |
% 17.84/3.15 | ALPHA: (ass(cond(302, 0), 1)) implies:
% 17.84/3.15 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 17.84/3.15 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 17.84/3.15 | [v6: $i] : (vskolem9(v0, v1) = v2 & vplus(v5, v6) = v4 & vplus(v1,
% 17.84/3.15 | v2) = v3 & vmul(v3, vd469) = v4 & vmul(v2, vd469) = v6 & vmul(v1,
% 17.84/3.15 | vd469) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 17.84/3.15 |
% 17.84/3.15 | ALPHA: (ass(cond(302, 0), 2)) implies:
% 17.84/3.15 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 17.84/3.15 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (vskolem9(v0, v1)
% 17.84/3.15 | = v3 & vplus(v1, v3) = v4 & vmul(v4, vd469) = v2 & vmul(v0, vd469)
% 17.84/3.15 | = v2 & $i(v4) & $i(v3) & $i(v2)))
% 17.84/3.15 |
% 17.84/3.15 | ALPHA: (ass(cond(302, 0), 3)) implies:
% 17.84/3.15 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 17.84/3.15 | $i(v0) | ? [v2: $i] : (vskolem9(v0, v1) = v2 & vplus(v1, v2) = v0 &
% 17.84/3.15 | $i(v2)))
% 17.84/3.15 |
% 17.84/3.15 | ALPHA: (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0))
% 17.84/3.15 | implies:
% 17.84/3.15 | (6) $i(vd481)
% 17.84/3.16 | (7) $i(vd480)
% 17.84/3.16 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vmul(vd480,
% 17.84/3.16 | vd469) = v1 & vmul(vd481, vd469) = v0 & greater(v0, v1) = v2 &
% 17.84/3.16 | $i(v1) & $i(v0))
% 17.84/3.16 |
% 17.84/3.16 | ALPHA: (function-axioms) implies:
% 17.84/3.16 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.84/3.16 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 17.84/3.16 | v2) = v0))
% 17.84/3.16 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.84/3.16 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 17.84/3.16 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.84/3.16 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 17.84/3.16 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.84/3.16 | (vskolem9(v3, v2) = v1) | ~ (vskolem9(v3, v2) = v0))
% 17.84/3.16 |
% 17.84/3.16 | DELTA: instantiating (8) with fresh symbols all_55_0, all_55_1, all_55_2
% 17.84/3.16 | gives:
% 17.84/3.16 | (13) ~ (all_55_0 = 0) & vmul(vd480, vd469) = all_55_1 & vmul(vd481, vd469)
% 17.84/3.16 | = all_55_2 & greater(all_55_2, all_55_1) = all_55_0 & $i(all_55_1) &
% 17.84/3.16 | $i(all_55_2)
% 17.84/3.16 |
% 17.84/3.16 | ALPHA: (13) implies:
% 17.84/3.16 | (14) ~ (all_55_0 = 0)
% 17.84/3.16 | (15) greater(all_55_2, all_55_1) = all_55_0
% 17.84/3.16 | (16) vmul(vd481, vd469) = all_55_2
% 17.84/3.16 | (17) vmul(vd480, vd469) = all_55_1
% 17.84/3.16 |
% 17.84/3.17 | GROUND_INST: instantiating (3) with vd481, vd480, simplifying with (1), (6),
% 17.84/3.17 | (7) gives:
% 17.84/3.17 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 17.84/3.17 | (vskolem9(vd481, vd480) = v0 & vplus(v3, v4) = v2 & vplus(vd480, v0) =
% 17.84/3.17 | v1 & vmul(v1, vd469) = v2 & vmul(v0, vd469) = v4 & vmul(vd480,
% 17.84/3.17 | vd469) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.84/3.17 |
% 17.84/3.17 | GROUND_INST: instantiating (2) with vd481, vd480, simplifying with (1), (6),
% 17.84/3.17 | (7) gives:
% 17.84/3.17 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.84/3.17 | (vskolem9(vd481, vd480) = v1 & vplus(v0, v2) = v3 & vmul(v1, vd469) =
% 17.84/3.17 | v2 & vmul(vd480, vd469) = v0 & greater(v3, v0) = 0 & $i(v3) & $i(v2)
% 17.84/3.17 | & $i(v1) & $i(v0))
% 17.84/3.17 |
% 17.84/3.17 | GROUND_INST: instantiating (4) with vd481, vd480, simplifying with (1), (6),
% 17.84/3.17 | (7) gives:
% 17.84/3.17 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vskolem9(vd481, vd480) = v1
% 17.84/3.17 | & vplus(vd480, v1) = v2 & vmul(v2, vd469) = v0 & vmul(vd481, vd469)
% 17.84/3.17 | = v0 & $i(v2) & $i(v1) & $i(v0))
% 17.84/3.17 |
% 17.84/3.17 | GROUND_INST: instantiating (5) with vd481, vd480, simplifying with (1), (6),
% 17.84/3.17 | (7) gives:
% 17.84/3.18 | (21) ? [v0: $i] : (vskolem9(vd481, vd480) = v0 & vplus(vd480, v0) = vd481
% 17.84/3.18 | & $i(v0))
% 17.84/3.18 |
% 17.84/3.18 | DELTA: instantiating (21) with fresh symbol all_72_0 gives:
% 17.84/3.18 | (22) vskolem9(vd481, vd480) = all_72_0 & vplus(vd480, all_72_0) = vd481 &
% 17.84/3.18 | $i(all_72_0)
% 17.84/3.18 |
% 17.84/3.18 | ALPHA: (22) implies:
% 17.84/3.18 | (23) vplus(vd480, all_72_0) = vd481
% 17.84/3.18 | (24) vskolem9(vd481, vd480) = all_72_0
% 17.84/3.18 |
% 17.84/3.18 | DELTA: instantiating (20) with fresh symbols all_84_0, all_84_1, all_84_2
% 17.84/3.18 | gives:
% 17.84/3.18 | (25) vskolem9(vd481, vd480) = all_84_1 & vplus(vd480, all_84_1) = all_84_0
% 17.84/3.18 | & vmul(all_84_0, vd469) = all_84_2 & vmul(vd481, vd469) = all_84_2 &
% 17.84/3.18 | $i(all_84_0) & $i(all_84_1) & $i(all_84_2)
% 17.84/3.18 |
% 17.84/3.18 | ALPHA: (25) implies:
% 17.84/3.18 | (26) vmul(vd481, vd469) = all_84_2
% 17.84/3.18 | (27) vmul(all_84_0, vd469) = all_84_2
% 17.84/3.18 | (28) vplus(vd480, all_84_1) = all_84_0
% 17.84/3.18 | (29) vskolem9(vd481, vd480) = all_84_1
% 17.84/3.18 |
% 17.84/3.18 | DELTA: instantiating (19) with fresh symbols all_86_0, all_86_1, all_86_2,
% 17.84/3.18 | all_86_3 gives:
% 17.84/3.18 | (30) vskolem9(vd481, vd480) = all_86_2 & vplus(all_86_3, all_86_1) =
% 17.84/3.18 | all_86_0 & vmul(all_86_2, vd469) = all_86_1 & vmul(vd480, vd469) =
% 17.84/3.18 | all_86_3 & greater(all_86_0, all_86_3) = 0 & $i(all_86_0) &
% 17.84/3.18 | $i(all_86_1) & $i(all_86_2) & $i(all_86_3)
% 17.84/3.18 |
% 17.84/3.18 | ALPHA: (30) implies:
% 17.84/3.18 | (31) greater(all_86_0, all_86_3) = 0
% 17.84/3.18 | (32) vmul(vd480, vd469) = all_86_3
% 17.84/3.18 | (33) vmul(all_86_2, vd469) = all_86_1
% 17.84/3.18 | (34) vplus(all_86_3, all_86_1) = all_86_0
% 17.84/3.18 | (35) vskolem9(vd481, vd480) = all_86_2
% 17.84/3.18 |
% 17.84/3.18 | DELTA: instantiating (18) with fresh symbols all_88_0, all_88_1, all_88_2,
% 17.84/3.18 | all_88_3, all_88_4 gives:
% 17.84/3.19 | (36) vskolem9(vd481, vd480) = all_88_4 & vplus(all_88_1, all_88_0) =
% 17.84/3.19 | all_88_2 & vplus(vd480, all_88_4) = all_88_3 & vmul(all_88_3, vd469) =
% 17.84/3.19 | all_88_2 & vmul(all_88_4, vd469) = all_88_0 & vmul(vd480, vd469) =
% 17.84/3.19 | all_88_1 & $i(all_88_0) & $i(all_88_1) & $i(all_88_2) & $i(all_88_3) &
% 17.84/3.19 | $i(all_88_4)
% 17.84/3.19 |
% 17.84/3.19 | ALPHA: (36) implies:
% 17.84/3.19 | (37) vmul(vd480, vd469) = all_88_1
% 17.84/3.19 | (38) vmul(all_88_4, vd469) = all_88_0
% 17.84/3.19 | (39) vmul(all_88_3, vd469) = all_88_2
% 17.84/3.19 | (40) vplus(vd480, all_88_4) = all_88_3
% 17.84/3.19 | (41) vplus(all_88_1, all_88_0) = all_88_2
% 17.84/3.19 | (42) vskolem9(vd481, vd480) = all_88_4
% 17.84/3.19 |
% 17.84/3.19 | GROUND_INST: instantiating (10) with all_55_2, all_84_2, vd469, vd481,
% 17.84/3.19 | simplifying with (16), (26) gives:
% 18.08/3.19 | (43) all_84_2 = all_55_2
% 18.08/3.19 |
% 18.08/3.19 | GROUND_INST: instantiating (10) with all_55_1, all_88_1, vd469, vd480,
% 18.08/3.19 | simplifying with (17), (37) gives:
% 18.08/3.19 | (44) all_88_1 = all_55_1
% 18.08/3.19 |
% 18.08/3.19 | GROUND_INST: instantiating (10) with all_86_3, all_88_1, vd469, vd480,
% 18.08/3.19 | simplifying with (32), (37) gives:
% 18.08/3.19 | (45) all_88_1 = all_86_3
% 18.08/3.19 |
% 18.08/3.19 | GROUND_INST: instantiating (12) with all_84_1, all_86_2, vd480, vd481,
% 18.08/3.19 | simplifying with (29), (35) gives:
% 18.08/3.19 | (46) all_86_2 = all_84_1
% 18.08/3.19 |
% 18.08/3.19 | GROUND_INST: instantiating (12) with all_86_2, all_88_4, vd480, vd481,
% 18.08/3.19 | simplifying with (35), (42) gives:
% 18.08/3.19 | (47) all_88_4 = all_86_2
% 18.08/3.19 |
% 18.08/3.19 | GROUND_INST: instantiating (12) with all_72_0, all_88_4, vd480, vd481,
% 18.08/3.19 | simplifying with (24), (42) gives:
% 18.08/3.19 | (48) all_88_4 = all_72_0
% 18.08/3.19 |
% 18.08/3.19 | COMBINE_EQS: (44), (45) imply:
% 18.08/3.20 | (49) all_86_3 = all_55_1
% 18.08/3.20 |
% 18.08/3.20 | COMBINE_EQS: (47), (48) imply:
% 18.08/3.20 | (50) all_86_2 = all_72_0
% 18.08/3.20 |
% 18.08/3.20 | SIMP: (50) implies:
% 18.08/3.20 | (51) all_86_2 = all_72_0
% 18.08/3.20 |
% 18.08/3.20 | COMBINE_EQS: (46), (51) imply:
% 18.08/3.20 | (52) all_84_1 = all_72_0
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (41), (44) imply:
% 18.08/3.20 | (53) vplus(all_55_1, all_88_0) = all_88_2
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (34), (49) imply:
% 18.08/3.20 | (54) vplus(all_55_1, all_86_1) = all_86_0
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (40), (48) imply:
% 18.08/3.20 | (55) vplus(vd480, all_72_0) = all_88_3
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (28), (52) imply:
% 18.08/3.20 | (56) vplus(vd480, all_72_0) = all_84_0
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (38), (48) imply:
% 18.08/3.20 | (57) vmul(all_72_0, vd469) = all_88_0
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (33), (51) imply:
% 18.08/3.20 | (58) vmul(all_72_0, vd469) = all_86_1
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (27), (43) imply:
% 18.08/3.20 | (59) vmul(all_84_0, vd469) = all_55_2
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (31), (49) imply:
% 18.08/3.20 | (60) greater(all_86_0, all_55_1) = 0
% 18.08/3.20 |
% 18.08/3.20 | GROUND_INST: instantiating (10) with all_86_1, all_88_0, vd469, all_72_0,
% 18.08/3.20 | simplifying with (57), (58) gives:
% 18.08/3.20 | (61) all_88_0 = all_86_1
% 18.08/3.20 |
% 18.08/3.20 | GROUND_INST: instantiating (11) with vd481, all_88_3, all_72_0, vd480,
% 18.08/3.20 | simplifying with (23), (55) gives:
% 18.08/3.20 | (62) all_88_3 = vd481
% 18.08/3.20 |
% 18.08/3.20 | GROUND_INST: instantiating (11) with all_84_0, all_88_3, all_72_0, vd480,
% 18.08/3.20 | simplifying with (55), (56) gives:
% 18.08/3.20 | (63) all_88_3 = all_84_0
% 18.08/3.20 |
% 18.08/3.20 | COMBINE_EQS: (62), (63) imply:
% 18.08/3.20 | (64) all_84_0 = vd481
% 18.08/3.20 |
% 18.08/3.20 | SIMP: (64) implies:
% 18.08/3.20 | (65) all_84_0 = vd481
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (53), (61) imply:
% 18.08/3.20 | (66) vplus(all_55_1, all_86_1) = all_88_2
% 18.08/3.20 |
% 18.08/3.20 | REDUCE: (39), (62) imply:
% 18.08/3.21 | (67) vmul(vd481, vd469) = all_88_2
% 18.08/3.21 |
% 18.08/3.21 | GROUND_INST: instantiating (10) with all_55_2, all_88_2, vd469, vd481,
% 18.08/3.21 | simplifying with (16), (67) gives:
% 18.08/3.21 | (68) all_88_2 = all_55_2
% 18.08/3.21 |
% 18.08/3.21 | GROUND_INST: instantiating (11) with all_86_0, all_88_2, all_86_1, all_55_1,
% 18.08/3.21 | simplifying with (54), (66) gives:
% 18.08/3.21 | (69) all_88_2 = all_86_0
% 18.08/3.21 |
% 18.08/3.21 | COMBINE_EQS: (68), (69) imply:
% 18.08/3.21 | (70) all_86_0 = all_55_2
% 18.08/3.21 |
% 18.08/3.21 | REDUCE: (60), (70) imply:
% 18.08/3.21 | (71) greater(all_55_2, all_55_1) = 0
% 18.08/3.21 |
% 18.08/3.21 | GROUND_INST: instantiating (9) with all_55_0, 0, all_55_1, all_55_2,
% 18.08/3.21 | simplifying with (15), (71) gives:
% 18.08/3.21 | (72) all_55_0 = 0
% 18.08/3.21 |
% 18.08/3.21 | REDUCE: (14), (72) imply:
% 18.08/3.21 | (73) $false
% 18.08/3.22 |
% 18.08/3.22 | CLOSE: (73) is inconsistent.
% 18.08/3.22 |
% 18.08/3.22 End of proof
% 18.08/3.22 % SZS output end Proof for theBenchmark
% 18.08/3.22
% 18.08/3.22 2610ms
%------------------------------------------------------------------------------