TSTP Solution File: NUM849+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM849+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 : n017.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 11:50:24 EDT 2023
% Result : Theorem 6.32s 1.53s
% Output : Proof 8.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM849+2 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 16:56:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 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
% 2.44/1.00 Prover 4: Preprocessing ...
% 2.44/1.00 Prover 1: Preprocessing ...
% 2.44/1.05 Prover 6: Preprocessing ...
% 2.44/1.05 Prover 5: Preprocessing ...
% 2.44/1.05 Prover 3: Preprocessing ...
% 2.44/1.05 Prover 0: Preprocessing ...
% 2.44/1.05 Prover 2: Preprocessing ...
% 4.05/1.28 Prover 1: Warning: ignoring some quantifiers
% 4.66/1.30 Prover 3: Warning: ignoring some quantifiers
% 4.66/1.32 Prover 1: Constructing countermodel ...
% 4.66/1.32 Prover 3: Constructing countermodel ...
% 4.66/1.34 Prover 6: Proving ...
% 4.66/1.40 Prover 4: Constructing countermodel ...
% 5.82/1.46 Prover 5: Proving ...
% 5.82/1.46 Prover 0: Proving ...
% 6.32/1.52 Prover 3: proved (897ms)
% 6.32/1.53
% 6.32/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.32/1.53
% 6.32/1.53 Prover 2: Proving ...
% 6.32/1.53 Prover 5: stopped
% 6.32/1.53 Prover 0: stopped
% 6.32/1.53 Prover 6: stopped
% 6.32/1.53 Prover 2: stopped
% 6.32/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.32/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.32/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.32/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.32/1.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.46/1.57 Prover 7: Preprocessing ...
% 6.46/1.58 Prover 11: Preprocessing ...
% 6.46/1.58 Prover 8: Preprocessing ...
% 6.46/1.58 Prover 10: Preprocessing ...
% 6.46/1.59 Prover 13: Preprocessing ...
% 7.46/1.68 Prover 8: Warning: ignoring some quantifiers
% 7.46/1.69 Prover 8: Constructing countermodel ...
% 7.46/1.70 Prover 10: Constructing countermodel ...
% 7.46/1.71 Prover 13: Warning: ignoring some quantifiers
% 7.46/1.72 Prover 13: Constructing countermodel ...
% 7.46/1.75 Prover 7: Constructing countermodel ...
% 8.00/1.76 Prover 11: Constructing countermodel ...
% 8.15/1.77 Prover 1: Found proof (size 60)
% 8.15/1.77 Prover 1: proved (1163ms)
% 8.15/1.78 Prover 4: stopped
% 8.15/1.78 Prover 8: stopped
% 8.15/1.78 Prover 13: stopped
% 8.15/1.78 Prover 10: stopped
% 8.15/1.78 Prover 11: stopped
% 8.15/1.78 Prover 7: stopped
% 8.15/1.78
% 8.15/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.15/1.78
% 8.15/1.79 % SZS output start Proof for theBenchmark
% 8.15/1.80 Assumptions after simplification:
% 8.15/1.80 ---------------------------------
% 8.15/1.80
% 8.15/1.80 (ass(cond(270, 0), 0))
% 8.38/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1)
% 8.38/1.82 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2)))
% 8.38/1.83
% 8.38/1.83 (ass(cond(281, 0), 0))
% 8.38/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.38/1.83 $i] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) =
% 8.38/1.83 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vplus(v1, v2) =
% 8.38/1.83 v6 & vmul(v0, v6) = v5 & $i(v6) & $i(v5)))
% 8.38/1.83
% 8.38/1.83 (ass(cond(conseq(292), 1), 0))
% 8.38/1.83 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 8.38/1.83 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 8.38/1.83 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 8.38/1.83 [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449, v7) = v8
% 8.38/1.83 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 & vmul(vd448, v5) = v6 &
% 8.38/1.83 vmul(vd448, v3) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 8.38/1.83 $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 = v6))))
% 8.38/1.83
% 8.38/1.83 (ass(cond(conseq(292), 1), 1))
% 8.38/1.84 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 8.38/1.84 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 8.38/1.84 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) =
% 8.38/1.84 v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448, v6) = v7
% 8.38/1.84 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & (
% 8.38/1.84 ~ (v4 = v2) | v7 = v5))))
% 8.38/1.84
% 8.38/1.84 (ass(cond(conseq(292), 1), 2))
% 8.38/1.84 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 8.38/1.84 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 8.38/1.84 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2,
% 8.38/1.84 v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6) &
% 8.38/1.84 $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5))))
% 8.38/1.84
% 8.38/1.84 (ass(cond(conseq(292), 1), 3))
% 8.52/1.84 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & !
% 8.52/1.84 [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 8.52/1.84 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) =
% 8.52/1.84 v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 &
% 8.52/1.84 vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~
% 8.52/1.84 (v4 = v2) | v7 = v6))))
% 8.52/1.84
% 8.52/1.84 (holds(293, 450, 1))
% 8.52/1.84 $i(v1) & $i(vd449) & $i(vd448) & ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1)
% 8.52/1.84 = v1 & vmul(vd448, v1) = v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0))
% 8.52/1.84
% 8.52/1.84 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))))
% 8.52/1.85 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.52/1.85 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 8.52/1.85 $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3))) & ?
% 8.52/1.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~
% 8.52/1.85 $i(v1) | ~ $i(v0))
% 8.52/1.85
% 8.52/1.85 (qu(ind(296), imp(296)))
% 8.52/1.85 $i(vd449) & $i(vd448) & ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ?
% 8.52/1.85 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 8.52/1.85 $i] : ? [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 &
% 8.52/1.85 vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 &
% 8.52/1.85 vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) & $i(v5) &
% 8.52/1.85 $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 8.52/1.85
% 8.52/1.85 (function-axioms)
% 8.52/1.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.52/1.85 (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 8.52/1.85 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3,
% 8.52/1.85 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 8.52/1.85 (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 8.52/1.85
% 8.52/1.85 Further assumptions not needed in the proof:
% 8.52/1.85 --------------------------------------------
% 8.52/1.85 ass(cond(261, 0), 0), ass(cond(61, 0), 0), qu(cond(conseq(axiom(3)), 3),
% 8.52/1.85 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))
% 8.52/1.85
% 8.52/1.85 Those formulas are unsatisfiable:
% 8.52/1.85 ---------------------------------
% 8.52/1.85
% 8.52/1.85 Begin of proof
% 8.52/1.85 |
% 8.52/1.85 | ALPHA: (ass(cond(conseq(292), 1), 0)) implies:
% 8.52/1.86 | (1) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 8.52/1.86 | [v9: $i] : (vplus(v3, vd449) = v5 & vsucc(v1) = v7 & vmul(vd449,
% 8.52/1.86 | v7) = v8 & vmul(vd449, v1) = v3 & vmul(vd448, v8) = v9 &
% 8.52/1.86 | vmul(vd448, v5) = v6 & vmul(vd448, v3) = v4 & $i(v9) & $i(v8) &
% 8.52/1.86 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v9 =
% 8.52/1.86 | v6))))
% 8.52/1.86 |
% 8.52/1.86 | ALPHA: (ass(cond(conseq(292), 1), 1)) implies:
% 8.52/1.86 | (2) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v4, v0) =
% 8.52/1.86 | v5 & vplus(v3, vd449) = v6 & vmul(vd449, v1) = v3 & vmul(vd448,
% 8.52/1.86 | v6) = v7 & vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) &
% 8.52/1.86 | $i(v4) & $i(v3) & ( ~ (v4 = v2) | v7 = v5))))
% 8.52/1.86 |
% 8.52/1.86 | ALPHA: (ass(cond(conseq(292), 1), 2)) implies:
% 8.52/1.86 | (3) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v4, v0) = v6 & vplus(v2,
% 8.52/1.86 | v0) = v5 & vmul(vd449, v1) = v3 & vmul(vd448, v3) = v4 & $i(v6)
% 8.52/1.86 | & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5))))
% 8.52/1.86 |
% 8.52/1.86 | ALPHA: (ass(cond(conseq(292), 1), 3)) implies:
% 8.52/1.86 | (4) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 8.52/1.86 | $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 8.52/1.86 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vplus(v2, v0) =
% 8.52/1.86 | v7 & vsucc(v1) = v5 & vmul(v0, v5) = v6 & vmul(vd449, v1) = v3 &
% 8.52/1.86 | vmul(vd448, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 8.52/1.86 | & ( ~ (v4 = v2) | v7 = v6))))
% 8.52/1.86 |
% 8.52/1.86 | ALPHA: (holds(293, 450, 1)) implies:
% 8.52/1.86 | (5) ? [v0: $i] : ? [v1: $i] : (vmul(vd449, v1) = v1 & vmul(vd448, v1) =
% 8.52/1.86 | v0 & vmul(vd448, vd449) = v0 & $i(v1) & $i(v0))
% 8.52/1.86 |
% 8.52/1.86 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 8.52/1.86 | holds(definiens(249), 398, 0)))) implies:
% 8.52/1.86 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1)
% 8.52/1.86 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 8.52/1.86 | $i] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4 & $i(v4) & $i(v3)))
% 8.52/1.86 |
% 8.52/1.86 | ALPHA: (qu(ind(296), imp(296))) implies:
% 8.52/1.86 | (7) $i(vd448)
% 8.52/1.86 | (8) $i(vd449)
% 8.52/1.87 | (9) ? [v0: $i] : (vmul(vd448, vd449) = v0 & $i(v0) & ? [v1: $i] : ? [v2:
% 8.52/1.87 | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ?
% 8.52/1.87 | [v7: $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 &
% 8.52/1.87 | vmul(v0, v1) = v2 & vmul(vd449, v4) = v6 & vmul(vd449, v1) = v3 &
% 8.52/1.87 | vmul(vd448, v6) = v7 & vmul(vd448, v3) = v2 & $i(v7) & $i(v6) &
% 8.52/1.87 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 8.52/1.87 |
% 8.52/1.87 | ALPHA: (function-axioms) implies:
% 8.52/1.87 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.52/1.87 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 8.52/1.87 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.52/1.87 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 8.52/1.87 |
% 8.52/1.87 | DELTA: instantiating (5) with fresh symbols all_14_0, all_14_1 gives:
% 8.52/1.87 | (12) vmul(vd449, v1) = all_14_0 & vmul(vd448, all_14_0) = all_14_1 &
% 8.52/1.87 | vmul(vd448, vd449) = all_14_1 & $i(all_14_0) & $i(all_14_1)
% 8.52/1.87 |
% 8.52/1.87 | ALPHA: (12) implies:
% 8.52/1.87 | (13) $i(all_14_0)
% 8.52/1.87 | (14) vmul(vd448, vd449) = all_14_1
% 8.52/1.87 | (15) vmul(vd448, all_14_0) = all_14_1
% 8.52/1.87 |
% 8.52/1.87 | DELTA: instantiating (3) with fresh symbol all_16_0 gives:
% 8.52/1.87 | (16) vmul(vd448, vd449) = all_16_0 & $i(all_16_0) & ! [v0: $i] : ! [v1:
% 8.52/1.87 | $i] : ( ~ (vmul(all_16_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 8.52/1.87 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vplus(v3, all_16_0) = v5 &
% 8.52/1.87 | vplus(v1, all_16_0) = v4 & vmul(vd449, v0) = v2 & vmul(vd448, v2)
% 8.52/1.87 | = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v5 =
% 8.52/1.87 | v4)))
% 8.52/1.87 |
% 8.52/1.87 | ALPHA: (16) implies:
% 8.52/1.87 | (17) vmul(vd448, vd449) = all_16_0
% 8.52/1.87 |
% 8.52/1.87 | DELTA: instantiating (2) with fresh symbol all_19_0 gives:
% 8.52/1.87 | (18) vmul(vd448, vd449) = all_19_0 & $i(all_19_0) & ! [v0: $i] : ! [v1:
% 8.52/1.87 | $i] : ( ~ (vmul(all_19_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 8.52/1.87 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v3,
% 8.52/1.87 | all_19_0) = v4 & vplus(v2, vd449) = v5 & vmul(vd449, v0) = v2 &
% 8.52/1.87 | vmul(vd448, v5) = v6 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) &
% 8.52/1.87 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v4)))
% 8.52/1.87 |
% 8.52/1.87 | ALPHA: (18) implies:
% 8.52/1.87 | (19) vmul(vd448, vd449) = all_19_0
% 8.52/1.87 |
% 8.52/1.87 | DELTA: instantiating (4) with fresh symbol all_22_0 gives:
% 8.52/1.87 | (20) vmul(vd448, vd449) = all_22_0 & $i(all_22_0) & ! [v0: $i] : ! [v1:
% 8.52/1.87 | $i] : ( ~ (vmul(all_22_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 8.52/1.87 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vplus(v1,
% 8.52/1.87 | all_22_0) = v6 & vsucc(v0) = v4 & vmul(all_22_0, v4) = v5 &
% 8.52/1.87 | vmul(vd449, v0) = v2 & vmul(vd448, v2) = v3 & $i(v6) & $i(v5) &
% 8.52/1.87 | $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v6 = v5)))
% 8.52/1.87 |
% 8.52/1.87 | ALPHA: (20) implies:
% 8.52/1.87 | (21) vmul(vd448, vd449) = all_22_0
% 8.52/1.87 |
% 8.52/1.87 | DELTA: instantiating (9) with fresh symbol all_25_0 gives:
% 8.52/1.88 | (22) vmul(vd448, vd449) = all_25_0 & $i(all_25_0) & ? [v0: $i] : ? [v1:
% 8.52/1.88 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 8.52/1.88 | [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 & vmul(all_25_0, v3) = v4 &
% 8.52/1.88 | vmul(all_25_0, v0) = v1 & vmul(vd449, v3) = v5 & vmul(vd449, v0) =
% 8.52/1.88 | v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2) = v1 & $i(v6) & $i(v5) &
% 8.52/1.88 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.52/1.88 |
% 8.52/1.88 | ALPHA: (22) implies:
% 8.52/1.88 | (23) vmul(vd448, vd449) = all_25_0
% 8.52/1.88 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.52/1.88 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 &
% 8.52/1.88 | vmul(all_25_0, v3) = v4 & vmul(all_25_0, v0) = v1 & vmul(vd449, v3)
% 8.52/1.88 | = v5 & vmul(vd449, v0) = v2 & vmul(vd448, v5) = v6 & vmul(vd448, v2)
% 8.52/1.88 | = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.52/1.88 |
% 8.52/1.88 | DELTA: instantiating (1) with fresh symbol all_27_0 gives:
% 8.52/1.88 | (25) vmul(vd448, vd449) = all_27_0 & $i(all_27_0) & ! [v0: $i] : ! [v1:
% 8.52/1.88 | $i] : ( ~ (vmul(all_27_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 8.52/1.88 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 8.52/1.88 | ? [v8: $i] : (vplus(v2, vd449) = v4 & vsucc(v0) = v6 & vmul(vd449,
% 8.52/1.88 | v6) = v7 & vmul(vd449, v0) = v2 & vmul(vd448, v7) = v8 &
% 8.52/1.88 | vmul(vd448, v4) = v5 & vmul(vd448, v2) = v3 & $i(v8) & $i(v7) &
% 8.52/1.88 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v8 =
% 8.52/1.88 | v5)))
% 8.52/1.88 |
% 8.52/1.88 | ALPHA: (25) implies:
% 8.52/1.88 | (26) vmul(vd448, vd449) = all_27_0
% 8.52/1.88 |
% 8.52/1.88 | DELTA: instantiating (24) with fresh symbols all_30_0, all_30_1, all_30_2,
% 8.52/1.88 | all_30_3, all_30_4, all_30_5, all_30_6 gives:
% 8.52/1.88 | (27) ~ (all_30_0 = all_30_2) & vsucc(all_30_6) = all_30_3 & vmul(all_25_0,
% 8.52/1.88 | all_30_3) = all_30_2 & vmul(all_25_0, all_30_6) = all_30_5 &
% 8.52/1.88 | vmul(vd449, all_30_3) = all_30_1 & vmul(vd449, all_30_6) = all_30_4 &
% 8.52/1.88 | vmul(vd448, all_30_1) = all_30_0 & vmul(vd448, all_30_4) = all_30_5 &
% 8.52/1.88 | $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & $i(all_30_3) &
% 8.52/1.88 | $i(all_30_4) & $i(all_30_5) & $i(all_30_6)
% 8.52/1.88 |
% 8.52/1.88 | ALPHA: (27) implies:
% 8.52/1.88 | (28) ~ (all_30_0 = all_30_2)
% 8.52/1.88 | (29) $i(all_30_6)
% 8.52/1.88 | (30) vmul(vd448, all_30_4) = all_30_5
% 8.52/1.88 | (31) vmul(vd448, all_30_1) = all_30_0
% 8.52/1.88 | (32) vmul(vd449, all_30_6) = all_30_4
% 8.52/1.88 | (33) vmul(vd449, all_30_3) = all_30_1
% 8.52/1.88 | (34) vmul(all_25_0, all_30_6) = all_30_5
% 8.52/1.88 | (35) vmul(all_25_0, all_30_3) = all_30_2
% 8.52/1.88 | (36) vsucc(all_30_6) = all_30_3
% 8.52/1.88 |
% 8.52/1.88 | GROUND_INST: instantiating (10) with all_16_0, all_22_0, vd449, vd448,
% 8.52/1.88 | simplifying with (17), (21) gives:
% 8.52/1.88 | (37) all_22_0 = all_16_0
% 8.52/1.88 |
% 8.52/1.88 | GROUND_INST: instantiating (10) with all_22_0, all_25_0, vd449, vd448,
% 8.52/1.88 | simplifying with (21), (23) gives:
% 8.52/1.88 | (38) all_25_0 = all_22_0
% 8.52/1.88 |
% 8.52/1.88 | GROUND_INST: instantiating (10) with all_19_0, all_25_0, vd449, vd448,
% 8.52/1.88 | simplifying with (19), (23) gives:
% 8.52/1.88 | (39) all_25_0 = all_19_0
% 8.52/1.89 |
% 8.52/1.89 | GROUND_INST: instantiating (10) with all_22_0, all_27_0, vd449, vd448,
% 8.52/1.89 | simplifying with (21), (26) gives:
% 8.52/1.89 | (40) all_27_0 = all_22_0
% 8.52/1.89 |
% 8.52/1.89 | GROUND_INST: instantiating (10) with all_14_1, all_27_0, vd449, vd448,
% 8.52/1.89 | simplifying with (14), (26) gives:
% 8.52/1.89 | (41) all_27_0 = all_14_1
% 8.52/1.89 |
% 8.52/1.89 | COMBINE_EQS: (40), (41) imply:
% 8.52/1.89 | (42) all_22_0 = all_14_1
% 8.52/1.89 |
% 8.52/1.89 | SIMP: (42) implies:
% 8.52/1.89 | (43) all_22_0 = all_14_1
% 8.52/1.89 |
% 8.52/1.89 | COMBINE_EQS: (38), (39) imply:
% 8.52/1.89 | (44) all_22_0 = all_19_0
% 8.52/1.89 |
% 8.52/1.89 | SIMP: (44) implies:
% 8.52/1.89 | (45) all_22_0 = all_19_0
% 8.52/1.89 |
% 8.52/1.89 | COMBINE_EQS: (37), (45) imply:
% 8.52/1.89 | (46) all_19_0 = all_16_0
% 8.52/1.89 |
% 8.52/1.89 | COMBINE_EQS: (43), (45) imply:
% 8.52/1.89 | (47) all_19_0 = all_14_1
% 8.52/1.89 |
% 8.52/1.89 | COMBINE_EQS: (46), (47) imply:
% 8.52/1.89 | (48) all_16_0 = all_14_1
% 8.52/1.89 |
% 8.52/1.89 | COMBINE_EQS: (39), (47) imply:
% 8.52/1.89 | (49) all_25_0 = all_14_1
% 8.52/1.89 |
% 8.52/1.89 | REDUCE: (35), (49) imply:
% 8.52/1.89 | (50) vmul(all_14_1, all_30_3) = all_30_2
% 8.52/1.89 |
% 8.52/1.89 | REDUCE: (34), (49) imply:
% 8.52/1.89 | (51) vmul(all_14_1, all_30_6) = all_30_5
% 8.52/1.89 |
% 8.52/1.89 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd448, all_14_0,
% 8.52/1.89 | all_14_1, simplifying with (7), (13), (15) gives:
% 8.52/1.89 | (52) vmul(all_14_0, vd448) = all_14_1 & $i(all_14_1)
% 8.52/1.89 |
% 8.52/1.89 | ALPHA: (52) implies:
% 8.52/1.89 | (53) $i(all_14_1)
% 8.52/1.89 |
% 8.52/1.89 | GROUND_INST: instantiating (6) with all_14_1, all_30_6, all_30_3, all_30_2,
% 8.52/1.89 | simplifying with (29), (36), (50), (53) gives:
% 8.52/1.89 | (54) ? [v0: $i] : (vplus(v0, all_14_1) = all_30_2 & vmul(all_14_1,
% 8.52/1.89 | all_30_6) = v0 & $i(v0) & $i(all_30_2))
% 8.52/1.89 |
% 8.52/1.89 | GROUND_INST: instantiating (6) with vd449, all_30_6, all_30_3, all_30_1,
% 8.52/1.89 | simplifying with (8), (29), (33), (36) gives:
% 8.52/1.89 | (55) ? [v0: $i] : (vplus(v0, vd449) = all_30_1 & vmul(vd449, all_30_6) =
% 8.52/1.89 | v0 & $i(v0) & $i(all_30_1))
% 8.52/1.89 |
% 8.52/1.89 | DELTA: instantiating (55) with fresh symbol all_42_0 gives:
% 8.52/1.89 | (56) vplus(all_42_0, vd449) = all_30_1 & vmul(vd449, all_30_6) = all_42_0 &
% 8.52/1.89 | $i(all_42_0) & $i(all_30_1)
% 8.52/1.89 |
% 8.52/1.89 | ALPHA: (56) implies:
% 8.52/1.89 | (57) $i(all_42_0)
% 8.52/1.89 | (58) vmul(vd449, all_30_6) = all_42_0
% 8.52/1.89 | (59) vplus(all_42_0, vd449) = all_30_1
% 8.52/1.89 |
% 8.52/1.89 | DELTA: instantiating (54) with fresh symbol all_44_0 gives:
% 8.52/1.89 | (60) vplus(all_44_0, all_14_1) = all_30_2 & vmul(all_14_1, all_30_6) =
% 8.52/1.89 | all_44_0 & $i(all_44_0) & $i(all_30_2)
% 8.52/1.89 |
% 8.52/1.89 | ALPHA: (60) implies:
% 8.52/1.89 | (61) vmul(all_14_1, all_30_6) = all_44_0
% 8.52/1.89 | (62) vplus(all_44_0, all_14_1) = all_30_2
% 8.52/1.89 |
% 8.52/1.89 | GROUND_INST: instantiating (10) with all_30_4, all_42_0, all_30_6, vd449,
% 8.52/1.89 | simplifying with (32), (58) gives:
% 8.52/1.89 | (63) all_42_0 = all_30_4
% 8.52/1.89 |
% 8.52/1.89 | GROUND_INST: instantiating (10) with all_30_5, all_44_0, all_30_6, all_14_1,
% 8.52/1.89 | simplifying with (51), (61) gives:
% 8.52/1.89 | (64) all_44_0 = all_30_5
% 8.52/1.89 |
% 8.52/1.90 | REDUCE: (62), (64) imply:
% 8.52/1.90 | (65) vplus(all_30_5, all_14_1) = all_30_2
% 8.52/1.90 |
% 8.52/1.90 | REDUCE: (59), (63) imply:
% 8.52/1.90 | (66) vplus(all_30_4, vd449) = all_30_1
% 8.52/1.90 |
% 8.52/1.90 | REDUCE: (57), (63) imply:
% 8.52/1.90 | (67) $i(all_30_4)
% 8.52/1.90 |
% 8.52/1.90 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd448, all_30_4, vd449,
% 8.52/1.90 | all_30_5, all_14_1, all_30_2, simplifying with (7), (8), (14),
% 8.52/1.90 | (30), (65), (67) gives:
% 8.52/1.90 | (68) ? [v0: $i] : (vplus(all_30_4, vd449) = v0 & vmul(vd448, v0) =
% 8.52/1.90 | all_30_2 & $i(v0) & $i(all_30_2))
% 8.52/1.90 |
% 8.52/1.90 | DELTA: instantiating (68) with fresh symbol all_58_0 gives:
% 8.52/1.90 | (69) vplus(all_30_4, vd449) = all_58_0 & vmul(vd448, all_58_0) = all_30_2 &
% 8.52/1.90 | $i(all_58_0) & $i(all_30_2)
% 8.52/1.90 |
% 8.52/1.90 | ALPHA: (69) implies:
% 8.52/1.90 | (70) vmul(vd448, all_58_0) = all_30_2
% 8.52/1.90 | (71) vplus(all_30_4, vd449) = all_58_0
% 8.52/1.90 |
% 8.52/1.90 | GROUND_INST: instantiating (11) with all_30_1, all_58_0, vd449, all_30_4,
% 8.52/1.90 | simplifying with (66), (71) gives:
% 8.52/1.90 | (72) all_58_0 = all_30_1
% 8.52/1.90 |
% 8.52/1.90 | REDUCE: (70), (72) imply:
% 8.52/1.90 | (73) vmul(vd448, all_30_1) = all_30_2
% 8.52/1.90 |
% 8.52/1.90 | GROUND_INST: instantiating (10) with all_30_0, all_30_2, all_30_1, vd448,
% 8.52/1.90 | simplifying with (31), (73) gives:
% 8.52/1.90 | (74) all_30_0 = all_30_2
% 8.52/1.90 |
% 8.52/1.90 | REDUCE: (28), (74) imply:
% 8.52/1.90 | (75) $false
% 8.52/1.90 |
% 8.52/1.90 | CLOSE: (75) is inconsistent.
% 8.52/1.90 |
% 8.52/1.90 End of proof
% 8.52/1.90 % SZS output end Proof for theBenchmark
% 8.52/1.90
% 8.52/1.90 1307ms
%------------------------------------------------------------------------------