TSTP Solution File: NUM849+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM849+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 : n003.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 11:50:23 EDT 2023
% Result : Theorem 11.77s 2.29s
% Output : Proof 14.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM849+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 14:12:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.44/1.27 Prover 4: Preprocessing ...
% 4.44/1.28 Prover 1: Preprocessing ...
% 4.44/1.31 Prover 5: Preprocessing ...
% 4.44/1.31 Prover 3: Preprocessing ...
% 4.44/1.31 Prover 6: Preprocessing ...
% 4.44/1.31 Prover 0: Preprocessing ...
% 4.44/1.31 Prover 2: Preprocessing ...
% 8.93/1.89 Prover 1: Warning: ignoring some quantifiers
% 9.64/1.96 Prover 1: Constructing countermodel ...
% 9.64/1.99 Prover 3: Warning: ignoring some quantifiers
% 9.83/2.01 Prover 6: Proving ...
% 9.83/2.01 Prover 5: Proving ...
% 9.83/2.01 Prover 3: Constructing countermodel ...
% 9.83/2.02 Prover 4: Warning: ignoring some quantifiers
% 9.83/2.13 Prover 4: Constructing countermodel ...
% 10.85/2.17 Prover 2: Proving ...
% 10.85/2.18 Prover 0: Proving ...
% 11.77/2.28 Prover 3: proved (1666ms)
% 11.77/2.29
% 11.77/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.77/2.29
% 11.77/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.77/2.29 Prover 2: stopped
% 11.77/2.29 Prover 0: stopped
% 11.77/2.29 Prover 5: stopped
% 11.77/2.29 Prover 6: stopped
% 11.77/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.77/2.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.77/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.77/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.34/2.37 Prover 10: Preprocessing ...
% 12.55/2.38 Prover 8: Preprocessing ...
% 12.55/2.40 Prover 7: Preprocessing ...
% 12.55/2.41 Prover 11: Preprocessing ...
% 12.55/2.42 Prover 13: Preprocessing ...
% 13.02/2.46 Prover 1: Found proof (size 77)
% 13.02/2.46 Prover 1: proved (1846ms)
% 13.02/2.46 Prover 10: stopped
% 13.02/2.46 Prover 4: stopped
% 13.02/2.48 Prover 7: stopped
% 13.02/2.49 Prover 11: stopped
% 13.02/2.50 Prover 13: stopped
% 13.50/2.54 Prover 8: Warning: ignoring some quantifiers
% 13.50/2.56 Prover 8: Constructing countermodel ...
% 13.77/2.57 Prover 8: stopped
% 13.77/2.57
% 13.77/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.77/2.57
% 13.77/2.59 % SZS output start Proof for theBenchmark
% 13.77/2.60 Assumptions after simplification:
% 13.77/2.60 ---------------------------------
% 13.77/2.60
% 13.77/2.60 (ass(cond(253, 0), 0))
% 13.77/2.64 $i(v1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (vmul(v1, v0) = v1) | ~
% 13.77/2.64 $i(v0))
% 13.77/2.64
% 13.77/2.64 (ass(cond(270, 0), 0))
% 13.77/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1)
% 13.77/2.64 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2)))
% 13.77/2.64
% 13.77/2.64 (ass(cond(281, 0), 0))
% 13.77/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.77/2.64 $i] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) =
% 13.77/2.64 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vplus(v1, v2) =
% 13.77/2.64 v6 & vmul(v0, v6) = v5 & $i(v6) & $i(v5)))
% 13.77/2.64
% 13.77/2.64 (ass(cond(conseq(292), 1), 0))
% 13.77/2.64 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 13.77/2.64 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 13.77/2.64 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 13.77/2.64 [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449, v7) = v8
% 13.77/2.64 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 & vmul(vd448, v5) = v6 &
% 13.77/2.64 vmul(vd448, v3) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 13.77/2.64 $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 = v6))))
% 13.77/2.64
% 13.77/2.64 (ass(cond(conseq(292), 1), 1))
% 13.77/2.65 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 13.77/2.65 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 13.77/2.65 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) =
% 13.77/2.65 v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448, v6) = v7
% 13.77/2.65 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & (
% 13.77/2.65 ~ (v4 = v2) | v7 = v5))))
% 13.77/2.65
% 13.77/2.65 (ass(cond(conseq(292), 1), 2))
% 13.77/2.65 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 13.77/2.65 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 13.77/2.65 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2,
% 13.77/2.65 v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6) &
% 13.77/2.65 $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5))))
% 13.77/2.65
% 13.77/2.65 (ass(cond(conseq(292), 1), 3))
% 14.16/2.65 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 14.16/2.65 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 14.16/2.65 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) =
% 14.16/2.65 v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 &
% 14.16/2.65 vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~
% 14.16/2.65 (v4 = v2) | v7 = v6))))
% 14.16/2.65
% 14.16/2.65 (holds(293, 450, 0))
% 14.16/2.65 $i(v1) & $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(v0, v1) = v0 &
% 14.16/2.65 vmul(vd448, vd449) = v0 & $i(v0))
% 14.16/2.65
% 14.16/2.65 (holds(293, 450, 1))
% 14.16/2.65 $i(v1) & $i(vd449) & $i(vd448) & ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1)
% 14.16/2.65 = v1 & vmul(vd448, v1) = v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0))
% 14.16/2.65
% 14.16/2.65 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))))
% 14.16/2.66 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.16/2.66 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 14.16/2.66 $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3))) & ?
% 14.16/2.66 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~
% 14.16/2.66 $i(v1) | ~ $i(v0))
% 14.16/2.66
% 14.16/2.66 (qu(ind(296), imp(296)))
% 14.16/2.66 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ?
% 14.16/2.66 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 14.16/2.66 $i] : ? [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 &
% 14.16/2.66 vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 &
% 14.16/2.66 vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) & $i(v5) &
% 14.16/2.66 $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 14.16/2.66
% 14.16/2.66 (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)))
% 14.16/2.66 $i(v1) & ! [v0: $i] : ( ~ (vsucc(v0) = v1) | ~ $i(v0))
% 14.16/2.66
% 14.16/2.66 (function-axioms)
% 14.16/2.66 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.16/2.66 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 14.16/2.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.16/2.66 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 14.16/2.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.16/2.66 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 14.16/2.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.16/2.66 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 14.16/2.66 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~
% 14.16/2.66 (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.16/2.66 $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0:
% 14.16/2.66 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 14.16/2.66 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 14.16/2.66 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 14.16/2.66
% 14.16/2.66 Further assumptions not needed in the proof:
% 14.16/2.66 --------------------------------------------
% 14.16/2.66 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 14.16/2.66 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 14.16/2.66 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 14.16/2.66 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 14.16/2.66 ass(cond(261, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0),
% 14.16/2.66 0), ass(cond(6, 0), 0), ass(cond(61, 0), 0), ass(cond(73, 0), 0), ass(cond(81,
% 14.16/2.66 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1),
% 14.16/2.66 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0),
% 14.16/2.66 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 14.16/2.66 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0),
% 14.16/2.66 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88),
% 14.16/2.66 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 14.16/2.66 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 14.16/2.66 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 16), 1),
% 14.16/2.66 def(cond(conseq(axiom(3)), 17), 1), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 14.16/2.66 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 14.16/2.66 holds(definiens(29), 44, 0)))
% 14.16/2.66
% 14.16/2.66 Those formulas are unsatisfiable:
% 14.16/2.66 ---------------------------------
% 14.16/2.66
% 14.16/2.66 Begin of proof
% 14.16/2.66 |
% 14.16/2.66 | ALPHA: (ass(cond(conseq(292), 1), 0)) implies:
% 14.16/2.67 | (1) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 14.16/2.67 | [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449,
% 14.16/2.67 | v7) = v8 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 &
% 14.16/2.67 | vmul(vd448, v5) = v6 & vmul(vd448, v3) = v4 & $i(v9) & $i(v8) &
% 14.16/2.67 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 =
% 14.16/2.67 | v6))))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (ass(cond(conseq(292), 1), 1)) implies:
% 14.16/2.67 | (2) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) =
% 14.16/2.67 | v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448,
% 14.16/2.67 | v6) = v7 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) &
% 14.16/2.67 | $i(v4) & $i(v3) & ( ~ (v4 = v2) | v7 = v5))))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (ass(cond(conseq(292), 1), 2)) implies:
% 14.16/2.67 | (3) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2,
% 14.16/2.67 | v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6)
% 14.16/2.67 | & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5))))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (ass(cond(conseq(292), 1), 3)) implies:
% 14.16/2.67 | (4) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 14.16/2.67 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 14.16/2.67 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) =
% 14.16/2.67 | v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 &
% 14.16/2.67 | vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 14.16/2.67 | & ( ~ (v4 = v2) | v7 = v6))))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (holds(293, 450, 1)) implies:
% 14.16/2.67 | (5) ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1) = v1 & vmul(vd448, v1) =
% 14.16/2.67 | v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (holds(293, 450, 0)) implies:
% 14.16/2.67 | (6) ? [v0: $i] : (vmul(v0, v1) = v0 & vmul(vd448, vd449) = v0 & $i(v0))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (ass(cond(253, 0), 0)) implies:
% 14.16/2.67 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (vmul(v1, v0) = v1) | ~
% 14.16/2.67 | $i(v0))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 14.16/2.67 | holds(definiens(249), 398, 0)))) implies:
% 14.16/2.67 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1)
% 14.16/2.67 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 14.16/2.67 | $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3)))
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) implies:
% 14.16/2.67 | (9) $i(v1)
% 14.16/2.67 |
% 14.16/2.67 | ALPHA: (qu(ind(296), imp(296))) implies:
% 14.16/2.68 | (10) $i(vd448)
% 14.16/2.68 | (11) $i(vd449)
% 14.16/2.68 | (12) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ? [v1: $i] : ?
% 14.16/2.68 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 14.16/2.68 | ? [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 &
% 14.16/2.68 | vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 &
% 14.16/2.68 | vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) &
% 14.16/2.68 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 14.16/2.68 |
% 14.16/2.68 | ALPHA: (function-axioms) implies:
% 14.16/2.68 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.16/2.68 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 14.16/2.68 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.16/2.68 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 14.16/2.68 |
% 14.16/2.68 | DELTA: instantiating (6) with fresh symbol all_47_0 gives:
% 14.16/2.68 | (15) vmul(all_47_0, v1) = all_47_0 & vmul(vd448, vd449) = all_47_0 &
% 14.16/2.68 | $i(all_47_0)
% 14.16/2.68 |
% 14.16/2.68 | ALPHA: (15) implies:
% 14.16/2.68 | (16) vmul(vd448, vd449) = all_47_0
% 14.16/2.68 |
% 14.16/2.68 | DELTA: instantiating (5) with fresh symbols all_53_0, all_53_1 gives:
% 14.16/2.68 | (17) vmul(vd449, v1) = all_53_0 & vmul(vd448, all_53_0) = all_53_1 &
% 14.16/2.68 | vmul(vd448, vd449) = all_53_1 & $i(all_53_0) & $i(all_53_1)
% 14.16/2.68 |
% 14.16/2.68 | ALPHA: (17) implies:
% 14.16/2.68 | (18) $i(all_53_0)
% 14.16/2.68 | (19) vmul(vd448, vd449) = all_53_1
% 14.16/2.68 | (20) vmul(vd448, all_53_0) = all_53_1
% 14.16/2.68 | (21) vmul(vd449, v1) = all_53_0
% 14.16/2.68 |
% 14.16/2.68 | DELTA: instantiating (3) with fresh symbol all_60_0 gives:
% 14.16/2.68 | (22) vmul(vd448, vd449) = all_60_0 & $i(all_60_0) & ! [v0: $i] : ! [v1:
% 14.16/2.68 | $i] : ( ~ (vmul(all_60_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 14.16/2.68 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vplus(v3, all_60_0) = v5 &
% 14.16/2.68 | vplus(v1, all_60_0) = v4 & vmul(vd449, v0) = v2 & vmul(vd448, v2)
% 14.16/2.68 | = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v5 =
% 14.16/2.68 | v4)))
% 14.16/2.68 |
% 14.16/2.68 | ALPHA: (22) implies:
% 14.16/2.68 | (23) vmul(vd448, vd449) = all_60_0
% 14.16/2.68 |
% 14.16/2.68 | DELTA: instantiating (2) with fresh symbol all_63_0 gives:
% 14.16/2.68 | (24) vmul(vd448, vd449) = all_63_0 & $i(all_63_0) & ! [v0: $i] : ! [v1:
% 14.16/2.68 | $i] : ( ~ (vmul(all_63_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 14.16/2.68 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v3,
% 14.16/2.68 | all_63_0) = v4 & vplus(v2, vd449) = v5 & vmul(vd449, v0) = v2 &
% 14.16/2.68 | vmul(vd448, v5) = v6 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) &
% 14.16/2.68 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v4)))
% 14.16/2.68 |
% 14.16/2.68 | ALPHA: (24) implies:
% 14.16/2.68 | (25) vmul(vd448, vd449) = all_63_0
% 14.16/2.68 |
% 14.16/2.68 | DELTA: instantiating (4) with fresh symbol all_66_0 gives:
% 14.16/2.69 | (26) vmul(vd448, vd449) = all_66_0 & $i(all_66_0) & ! [v0: $i] : ! [v1:
% 14.16/2.69 | $i] : ( ~ (vmul(all_66_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 14.16/2.69 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v1,
% 14.16/2.69 | all_66_0) = v6 & vsucc(v0) = v4 & vmul(all_66_0, v4) = v5 &
% 14.16/2.69 | vmul(vd449, v0) = v2 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) &
% 14.16/2.69 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v5)))
% 14.16/2.69 |
% 14.16/2.69 | ALPHA: (26) implies:
% 14.16/2.69 | (27) vmul(vd448, vd449) = all_66_0
% 14.16/2.69 |
% 14.16/2.69 | DELTA: instantiating (12) with fresh symbol all_69_0 gives:
% 14.16/2.69 | (28) vmul(vd448, vd449) = all_69_0 & $i(all_69_0) & ? [v0: $i] : ? [v1:
% 14.16/2.69 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 14.16/2.69 | [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & vmul(all_69_0, v3) = v4 &
% 14.16/2.69 | vmul(all_69_0, v0) = v1 & vmul(vd449, v3) = v5 & vmul(vd449, v0) =
% 14.16/2.69 | v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2) = v1 & $i(v6) & $i(v5) &
% 14.16/2.69 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.16/2.69 |
% 14.16/2.69 | ALPHA: (28) implies:
% 14.16/2.69 | (29) vmul(vd448, vd449) = all_69_0
% 14.16/2.69 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 14.16/2.69 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 &
% 14.16/2.69 | vmul(all_69_0, v3) = v4 & vmul(all_69_0, v0) = v1 & vmul(vd449, v3)
% 14.16/2.69 | = v5 & vmul(vd449, v0) = v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2)
% 14.16/2.69 | = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.16/2.69 |
% 14.16/2.69 | DELTA: instantiating (1) with fresh symbol all_71_0 gives:
% 14.16/2.69 | (31) vmul(vd448, vd449) = all_71_0 & $i(all_71_0) & ! [v0: $i] : ! [v1:
% 14.16/2.69 | $i] : ( ~ (vmul(all_71_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 14.16/2.69 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 14.16/2.69 | ? [v8: $i] : (vplus(v2, vd449) = v4 & vsucc(v0) = v6 & vmul(vd449,
% 14.16/2.69 | v6) = v7 & vmul(vd449, v0) = v2 & vmul(vd448, v7) = v8 &
% 14.16/2.69 | vmul(vd448, v4) = v5 & vmul(vd448, v2) = v3 & $i(v8) & $i(v7) &
% 14.16/2.69 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v8 =
% 14.16/2.69 | v5)))
% 14.16/2.69 |
% 14.16/2.69 | ALPHA: (31) implies:
% 14.16/2.69 | (32) vmul(vd448, vd449) = all_71_0
% 14.16/2.69 |
% 14.16/2.69 | DELTA: instantiating (30) with fresh symbols all_74_0, all_74_1, all_74_2,
% 14.16/2.69 | all_74_3, all_74_4, all_74_5, all_74_6 gives:
% 14.16/2.69 | (33) ~ (all_74_0 = all_74_2) & vsucc(all_74_6) = all_74_3 & vmul(all_69_0,
% 14.16/2.69 | all_74_3) = all_74_2 & vmul(all_69_0, all_74_6) = all_74_5 &
% 14.16/2.69 | vmul(vd449, all_74_3) = all_74_1 & vmul(vd449, all_74_6) = all_74_4 &
% 14.16/2.69 | vmul(vd448, all_74_1) = all_74_0 & vmul(vd448, all_74_4) = all_74_5 &
% 14.16/2.69 | $i(all_74_0) & $i(all_74_1) & $i(all_74_2) & $i(all_74_3) &
% 14.16/2.69 | $i(all_74_4) & $i(all_74_5) & $i(all_74_6)
% 14.16/2.69 |
% 14.16/2.69 | ALPHA: (33) implies:
% 14.16/2.69 | (34) ~ (all_74_0 = all_74_2)
% 14.16/2.69 | (35) $i(all_74_6)
% 14.16/2.69 | (36) vmul(vd448, all_74_4) = all_74_5
% 14.16/2.69 | (37) vmul(vd448, all_74_1) = all_74_0
% 14.16/2.69 | (38) vmul(vd449, all_74_6) = all_74_4
% 14.16/2.69 | (39) vmul(vd449, all_74_3) = all_74_1
% 14.16/2.69 | (40) vmul(all_69_0, all_74_6) = all_74_5
% 14.16/2.69 | (41) vmul(all_69_0, all_74_3) = all_74_2
% 14.16/2.69 | (42) vsucc(all_74_6) = all_74_3
% 14.16/2.69 |
% 14.16/2.70 | GROUND_INST: instantiating (13) with all_60_0, all_63_0, vd449, vd448,
% 14.16/2.70 | simplifying with (23), (25) gives:
% 14.16/2.70 | (43) all_63_0 = all_60_0
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (13) with all_53_1, all_63_0, vd449, vd448,
% 14.16/2.70 | simplifying with (19), (25) gives:
% 14.16/2.70 | (44) all_63_0 = all_53_1
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (13) with all_63_0, all_66_0, vd449, vd448,
% 14.16/2.70 | simplifying with (25), (27) gives:
% 14.16/2.70 | (45) all_66_0 = all_63_0
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (13) with all_66_0, all_69_0, vd449, vd448,
% 14.16/2.70 | simplifying with (27), (29) gives:
% 14.16/2.70 | (46) all_69_0 = all_66_0
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (13) with all_69_0, all_71_0, vd449, vd448,
% 14.16/2.70 | simplifying with (29), (32) gives:
% 14.16/2.70 | (47) all_71_0 = all_69_0
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (13) with all_47_0, all_71_0, vd449, vd448,
% 14.16/2.70 | simplifying with (16), (32) gives:
% 14.16/2.70 | (48) all_71_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | COMBINE_EQS: (47), (48) imply:
% 14.16/2.70 | (49) all_69_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | SIMP: (49) implies:
% 14.16/2.70 | (50) all_69_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | COMBINE_EQS: (46), (50) imply:
% 14.16/2.70 | (51) all_66_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | SIMP: (51) implies:
% 14.16/2.70 | (52) all_66_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | COMBINE_EQS: (45), (52) imply:
% 14.16/2.70 | (53) all_63_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | SIMP: (53) implies:
% 14.16/2.70 | (54) all_63_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | COMBINE_EQS: (43), (44) imply:
% 14.16/2.70 | (55) all_60_0 = all_53_1
% 14.16/2.70 |
% 14.16/2.70 | COMBINE_EQS: (43), (54) imply:
% 14.16/2.70 | (56) all_60_0 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | COMBINE_EQS: (55), (56) imply:
% 14.16/2.70 | (57) all_53_1 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | SIMP: (57) implies:
% 14.16/2.70 | (58) all_53_1 = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | REDUCE: (41), (50) imply:
% 14.16/2.70 | (59) vmul(all_47_0, all_74_3) = all_74_2
% 14.16/2.70 |
% 14.16/2.70 | REDUCE: (40), (50) imply:
% 14.16/2.70 | (60) vmul(all_47_0, all_74_6) = all_74_5
% 14.16/2.70 |
% 14.16/2.70 | REDUCE: (20), (58) imply:
% 14.16/2.70 | (61) vmul(vd448, all_53_0) = all_47_0
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd448, all_53_0,
% 14.16/2.70 | all_47_0, simplifying with (10), (18), (61) gives:
% 14.16/2.70 | (62) vmul(all_53_0, vd448) = all_47_0 & $i(all_47_0)
% 14.16/2.70 |
% 14.16/2.70 | ALPHA: (62) implies:
% 14.16/2.70 | (63) $i(all_47_0)
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd449, v1, all_53_0,
% 14.16/2.70 | simplifying with (9), (11), (21) gives:
% 14.16/2.70 | (64) vmul(v1, vd449) = all_53_0 & $i(all_53_0)
% 14.16/2.70 |
% 14.16/2.70 | ALPHA: (64) implies:
% 14.16/2.70 | (65) vmul(v1, vd449) = all_53_0
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (8) with all_47_0, all_74_6, all_74_3, all_74_2,
% 14.16/2.70 | simplifying with (35), (42), (59), (63) gives:
% 14.16/2.70 | (66) ? [v0: $i] : (vplus(v0, all_47_0) = all_74_2 & vmul(all_47_0,
% 14.16/2.70 | all_74_6) = v0 & $i(v0) & $i(all_74_2))
% 14.16/2.70 |
% 14.16/2.70 | GROUND_INST: instantiating (8) with vd449, all_74_6, all_74_3, all_74_1,
% 14.16/2.70 | simplifying with (11), (35), (39), (42) gives:
% 14.16/2.70 | (67) ? [v0: $i] : (vplus(v0, vd449) = all_74_1 & vmul(vd449, all_74_6) =
% 14.16/2.70 | v0 & $i(v0) & $i(all_74_1))
% 14.16/2.70 |
% 14.16/2.70 | DELTA: instantiating (67) with fresh symbol all_86_0 gives:
% 14.16/2.71 | (68) vplus(all_86_0, vd449) = all_74_1 & vmul(vd449, all_74_6) = all_86_0 &
% 14.16/2.71 | $i(all_86_0) & $i(all_74_1)
% 14.16/2.71 |
% 14.16/2.71 | ALPHA: (68) implies:
% 14.16/2.71 | (69) $i(all_86_0)
% 14.16/2.71 | (70) vmul(vd449, all_74_6) = all_86_0
% 14.16/2.71 | (71) vplus(all_86_0, vd449) = all_74_1
% 14.16/2.71 |
% 14.16/2.71 | DELTA: instantiating (66) with fresh symbol all_88_0 gives:
% 14.16/2.71 | (72) vplus(all_88_0, all_47_0) = all_74_2 & vmul(all_47_0, all_74_6) =
% 14.16/2.71 | all_88_0 & $i(all_88_0) & $i(all_74_2)
% 14.16/2.71 |
% 14.16/2.71 | ALPHA: (72) implies:
% 14.16/2.71 | (73) vmul(all_47_0, all_74_6) = all_88_0
% 14.16/2.71 | (74) vplus(all_88_0, all_47_0) = all_74_2
% 14.16/2.71 |
% 14.16/2.71 | GROUND_INST: instantiating (13) with all_74_4, all_86_0, all_74_6, vd449,
% 14.16/2.71 | simplifying with (38), (70) gives:
% 14.16/2.71 | (75) all_86_0 = all_74_4
% 14.16/2.71 |
% 14.16/2.71 | GROUND_INST: instantiating (13) with all_74_5, all_88_0, all_74_6, all_47_0,
% 14.16/2.71 | simplifying with (60), (73) gives:
% 14.16/2.71 | (76) all_88_0 = all_74_5
% 14.16/2.71 |
% 14.16/2.71 | REDUCE: (74), (76) imply:
% 14.16/2.71 | (77) vplus(all_74_5, all_47_0) = all_74_2
% 14.16/2.71 |
% 14.16/2.71 | REDUCE: (71), (75) imply:
% 14.16/2.71 | (78) vplus(all_74_4, vd449) = all_74_1
% 14.16/2.71 |
% 14.16/2.71 | REDUCE: (69), (75) imply:
% 14.16/2.71 | (79) $i(all_74_4)
% 14.16/2.71 |
% 14.16/2.71 | GROUND_INST: instantiating (7) with vd449, all_53_0, simplifying with (11),
% 14.16/2.71 | (65) gives:
% 14.16/2.71 | (80) all_53_0 = vd449
% 14.16/2.71 |
% 14.16/2.71 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd448, all_74_4,
% 14.16/2.71 | all_53_0, all_74_5, all_47_0, all_74_2, simplifying with (10),
% 14.16/2.71 | (18), (36), (61), (77), (79) gives:
% 14.16/2.71 | (81) ? [v0: $i] : (vplus(all_74_4, all_53_0) = v0 & vmul(vd448, v0) =
% 14.16/2.71 | all_74_2 & $i(v0) & $i(all_74_2))
% 14.16/2.71 |
% 14.16/2.71 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd448, all_74_4, vd449,
% 14.16/2.71 | all_74_5, all_47_0, all_74_2, simplifying with (10), (11), (16),
% 14.16/2.71 | (36), (77), (79) gives:
% 14.16/2.71 | (82) ? [v0: $i] : (vplus(all_74_4, vd449) = v0 & vmul(vd448, v0) =
% 14.16/2.71 | all_74_2 & $i(v0) & $i(all_74_2))
% 14.16/2.71 |
% 14.16/2.71 | DELTA: instantiating (82) with fresh symbol all_102_0 gives:
% 14.16/2.71 | (83) vplus(all_74_4, vd449) = all_102_0 & vmul(vd448, all_102_0) = all_74_2
% 14.16/2.71 | & $i(all_102_0) & $i(all_74_2)
% 14.16/2.71 |
% 14.16/2.71 | ALPHA: (83) implies:
% 14.16/2.71 | (84) vmul(vd448, all_102_0) = all_74_2
% 14.16/2.71 | (85) vplus(all_74_4, vd449) = all_102_0
% 14.16/2.71 |
% 14.16/2.71 | DELTA: instantiating (81) with fresh symbol all_104_0 gives:
% 14.16/2.71 | (86) vplus(all_74_4, all_53_0) = all_104_0 & vmul(vd448, all_104_0) =
% 14.16/2.71 | all_74_2 & $i(all_104_0) & $i(all_74_2)
% 14.16/2.71 |
% 14.16/2.71 | ALPHA: (86) implies:
% 14.16/2.71 | (87) vplus(all_74_4, all_53_0) = all_104_0
% 14.16/2.71 |
% 14.16/2.71 | REDUCE: (80), (87) imply:
% 14.16/2.71 | (88) vplus(all_74_4, vd449) = all_104_0
% 14.16/2.71 |
% 14.16/2.71 | GROUND_INST: instantiating (14) with all_74_1, all_104_0, vd449, all_74_4,
% 14.16/2.71 | simplifying with (78), (88) gives:
% 14.16/2.71 | (89) all_104_0 = all_74_1
% 14.16/2.71 |
% 14.16/2.71 | GROUND_INST: instantiating (14) with all_102_0, all_104_0, vd449, all_74_4,
% 14.16/2.71 | simplifying with (85), (88) gives:
% 14.16/2.71 | (90) all_104_0 = all_102_0
% 14.16/2.72 |
% 14.16/2.72 | COMBINE_EQS: (89), (90) imply:
% 14.16/2.72 | (91) all_102_0 = all_74_1
% 14.16/2.72 |
% 14.16/2.72 | REDUCE: (84), (91) imply:
% 14.16/2.72 | (92) vmul(vd448, all_74_1) = all_74_2
% 14.16/2.72 |
% 14.16/2.72 | GROUND_INST: instantiating (13) with all_74_0, all_74_2, all_74_1, vd448,
% 14.16/2.72 | simplifying with (37), (92) gives:
% 14.16/2.72 | (93) all_74_0 = all_74_2
% 14.16/2.72 |
% 14.16/2.72 | REDUCE: (34), (93) imply:
% 14.16/2.72 | (94) $false
% 14.16/2.72 |
% 14.16/2.72 | CLOSE: (94) is inconsistent.
% 14.16/2.72 |
% 14.16/2.72 End of proof
% 14.16/2.72 % SZS output end Proof for theBenchmark
% 14.16/2.72
% 14.16/2.72 2119ms
%------------------------------------------------------------------------------