TSTP Solution File: NUM845+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM845+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 11:50:21 EDT 2023
% Result : Theorem 13.01s 2.41s
% Output : Proof 15.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM845+1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n023.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 08:45:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.68/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.11/1.14 Prover 1: Preprocessing ...
% 3.11/1.15 Prover 4: Preprocessing ...
% 3.84/1.19 Prover 6: Preprocessing ...
% 3.84/1.19 Prover 0: Preprocessing ...
% 3.84/1.19 Prover 5: Preprocessing ...
% 3.84/1.19 Prover 2: Preprocessing ...
% 3.84/1.19 Prover 3: Preprocessing ...
% 8.38/1.81 Prover 1: Warning: ignoring some quantifiers
% 8.84/1.89 Prover 4: Warning: ignoring some quantifiers
% 8.84/1.89 Prover 3: Warning: ignoring some quantifiers
% 8.84/1.89 Prover 1: Constructing countermodel ...
% 8.84/1.90 Prover 6: Proving ...
% 8.84/1.91 Prover 3: Constructing countermodel ...
% 9.43/1.92 Prover 5: Proving ...
% 9.43/1.94 Prover 4: Constructing countermodel ...
% 9.88/1.98 Prover 2: Proving ...
% 9.88/2.00 Prover 0: Proving ...
% 13.01/2.41 Prover 0: proved (1803ms)
% 13.01/2.41
% 13.01/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.01/2.41
% 13.01/2.41 Prover 6: stopped
% 13.01/2.41 Prover 5: stopped
% 13.24/2.41 Prover 3: stopped
% 13.34/2.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.34/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.34/2.43 Prover 2: stopped
% 13.34/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.34/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.34/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.34/2.50 Prover 7: Preprocessing ...
% 13.34/2.50 Prover 10: Preprocessing ...
% 14.00/2.52 Prover 11: Preprocessing ...
% 14.00/2.56 Prover 8: Preprocessing ...
% 14.00/2.57 Prover 13: Preprocessing ...
% 14.48/2.62 Prover 1: Found proof (size 165)
% 14.48/2.62 Prover 1: proved (2008ms)
% 14.48/2.62 Prover 7: stopped
% 14.48/2.63 Prover 4: stopped
% 14.48/2.65 Prover 11: stopped
% 14.48/2.67 Prover 13: stopped
% 15.14/2.68 Prover 8: Warning: ignoring some quantifiers
% 15.24/2.69 Prover 10: Warning: ignoring some quantifiers
% 15.24/2.69 Prover 8: Constructing countermodel ...
% 15.24/2.70 Prover 10: Constructing countermodel ...
% 15.24/2.70 Prover 8: stopped
% 15.24/2.71 Prover 10: stopped
% 15.24/2.71
% 15.24/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.24/2.71
% 15.47/2.76 % SZS output start Proof for theBenchmark
% 15.47/2.76 Assumptions after simplification:
% 15.47/2.76 ---------------------------------
% 15.47/2.76
% 15.47/2.76 (ass(cond(33, 0), 0))
% 15.47/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.47/2.78 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 15.47/2.78 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) &
% 15.47/2.78 $i(v4)))
% 15.47/2.78
% 15.47/2.78 (ass(cond(52, 0), 0))
% 15.47/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v0) = v2) |
% 15.47/2.78 ~ (vplus(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (vsucc(v4) =
% 15.47/2.78 v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3)))
% 15.47/2.78
% 15.47/2.78 (ass(cond(6, 0), 0))
% 15.47/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~
% 15.47/2.78 (vsucc(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 15.47/2.78
% 15.47/2.78 (ass(cond(61, 0), 0))
% 15.47/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1)
% 15.47/2.79 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2)))
% 15.47/2.79
% 15.47/2.79 (ass(cond(conseq(263), 1), 0))
% 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v4) | ~
% 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v3, v4) = v5) | ~ (vplus(v2, vd411) =
% 15.47/2.79 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 15.47/2.79 : (vmul(v0, v1) = v6 & vmul(vd411, v4) = v8 & vplus(v8, v4) = v9 &
% 15.47/2.79 vplus(v2, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) |
% 15.47/2.79 v9 = v5))))
% 15.47/2.79
% 15.47/2.79 (ass(cond(conseq(263), 1), 1))
% 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v3) | ~
% 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v4, v3) = v5) | ~ (vplus(v2, vd411) =
% 15.47/2.79 v4) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 15.47/2.79 : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, v1) = v7 &
% 15.47/2.79 vplus(vd411, v3) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 =
% 15.47/2.79 v6) | v9 = v5))))
% 15.47/2.79
% 15.47/2.79 (ass(cond(conseq(263), 1), 2))
% 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~
% 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, v1) =
% 15.47/2.79 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 15.47/2.79 : ? [v10: $i] : (vsucc(v1) = v8 & vmul(v0, v1) = v6 & vplus(v2, v9) = v10
% 15.47/2.79 & vplus(v2, v1) = v7 & vplus(vd411, v8) = v9 & $i(v10) & $i(v9) & $i(v8)
% 15.47/2.79 & $i(v7) & $i(v6) & ( ~ (v7 = v6) | v10 = v5))))
% 15.47/2.79
% 15.47/2.79 (ass(cond(conseq(263), 1), 3))
% 15.47/2.79 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~
% 15.47/2.79 (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411, v1) =
% 15.47/2.79 v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 15.47/2.79 : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2, v1) = v7 & vplus(v0,
% 15.47/2.79 v1) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 =
% 15.47/2.80 v5))))
% 15.47/2.80
% 15.47/2.80 (ass(cond(conseq(263), 1), 4))
% 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.80 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~
% 15.47/2.80 (vplus(v2, v3) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v1) | ? [v5: $i] :
% 15.47/2.80 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(v0, v1) = v5 & vplus(v2,
% 15.47/2.80 v7) = v8 & vplus(v2, v1) = v6 & vplus(v1, v0) = v7 & $i(v8) & $i(v7) &
% 15.47/2.80 $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4))))
% 15.47/2.80
% 15.47/2.80 (ass(cond(conseq(263), 1), 5))
% 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.80 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~
% 15.47/2.80 (vplus(v2, v3) = v4) | ~ (vplus(v1, v0) = v3) | ~ $i(v1) | ? [v5: $i] :
% 15.47/2.80 ? [v6: $i] : ? [v7: $i] : (vmul(v0, v1) = v5 & vplus(v6, v0) = v7 &
% 15.47/2.80 vplus(v2, v1) = v6 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v7 =
% 15.47/2.80 v4))))
% 15.47/2.80
% 15.47/2.80 (ass(cond(conseq(263), 1), 6))
% 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.80 $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ?
% 15.47/2.80 [v5: $i] : ? [v6: $i] : (vmul(vd411, v1) = v3 & vplus(v4, v0) = v6 &
% 15.47/2.80 vplus(v3, v1) = v4 & vplus(v2, v0) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 15.47/2.80 $i(v3) & ( ~ (v4 = v2) | v6 = v5))))
% 15.47/2.80
% 15.47/2.80 (ass(cond(conseq(263), 1), 7))
% 15.47/2.80 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.47/2.80 $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ?
% 15.47/2.80 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vsucc(v1) = v5 & vmul(v0, v5) = v6
% 15.47/2.80 & vmul(vd411, v1) = v3 & vplus(v3, v1) = v4 & vplus(v2, v0) = v7 &
% 15.47/2.80 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v4 = v2) | v7 = v6))))
% 15.47/2.80
% 15.47/2.80 (holds(264, 412, 0))
% 15.47/2.80 $i(v1) & $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & vmul(v0, v1) = v0 &
% 15.47/2.80 $i(v0))
% 15.47/2.80
% 15.47/2.80 (holds(264, 412, 1))
% 15.47/2.80 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vsucc(v1) = v0 &
% 15.47/2.80 vsucc(vd411) = v0 & vmul(vd411, v1) = v1 & $i(v1) & $i(v0))
% 15.47/2.80
% 15.47/2.80 (holds(264, 412, 2))
% 15.47/2.80 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vsucc(v0) = v1 & vmul(vd411,
% 15.47/2.80 v1) = v0 & vplus(v0, v1) = v1 & $i(v1) & $i(v0))
% 15.47/2.80
% 15.47/2.80 (qu(antec(axiom(3)), imp(antec(axiom(3)))))
% 15.47/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~
% 15.47/2.80 (vsucc(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 15.47/2.80
% 15.47/2.80 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))))
% 15.47/2.80 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.47/2.80 (vsucc(v1) = v2) | ~ (vplus(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 15.47/2.80 $i] : (vsucc(v4) = v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3))) & ? [v0:
% 15.47/2.80 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v1, v1) = v2) | ~ $i(v1) | ~
% 15.47/2.80 $i(v0) | (vsucc(v1) = v2 & $i(v2)))
% 15.47/2.80
% 15.47/2.80 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))))
% 15.47/2.81 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.47/2.81 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 15.47/2.81 $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3))) & ?
% 15.47/2.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~
% 15.47/2.81 $i(v1) | ~ $i(v0))
% 15.47/2.81
% 15.47/2.81 (qu(ind(267), imp(267)))
% 15.47/2.81 $i(vd411) & ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ? [v1: $i] : ? [v2:
% 15.47/2.81 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 15.47/2.81 : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 & vmul(v0, v1) = v2 &
% 15.47/2.81 vmul(vd411, v4) = v6 & vmul(vd411, v1) = v3 & vplus(v6, v4) = v7 &
% 15.47/2.81 vplus(v3, v1) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 15.47/2.81 $i(v1)))
% 15.47/2.81
% 15.47/2.81 (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)))
% 15.47/2.81 $i(v1) & ! [v0: $i] : ( ~ (vsucc(v0) = v1) | ~ $i(v0))
% 15.47/2.81
% 15.47/2.81 (function-axioms)
% 15.47/2.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.47/2.81 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 15.47/2.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.47/2.81 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 15.47/2.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.47/2.81 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 15.47/2.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.47/2.81 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 15.47/2.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~
% 15.47/2.81 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 15.47/2.81 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i]
% 15.47/2.81 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 15.47/2.81 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 15.47/2.81 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 15.47/2.81
% 15.47/2.81 Further assumptions not needed in the proof:
% 15.47/2.81 --------------------------------------------
% 15.47/2.81 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 15.47/2.81 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 15.47/2.81 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 15.47/2.81 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 15.47/2.81 ass(cond(253, 0), 0), ass(cond(43, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0),
% 15.47/2.81 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1),
% 15.47/2.81 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0),
% 15.47/2.81 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 15.47/2.81 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0),
% 15.47/2.81 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88),
% 15.47/2.81 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 15.47/2.81 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 15.47/2.81 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 16), 1),
% 15.47/2.81 def(cond(conseq(axiom(3)), 17), 1)
% 15.47/2.81
% 15.47/2.81 Those formulas are unsatisfiable:
% 15.47/2.81 ---------------------------------
% 15.47/2.81
% 15.47/2.81 Begin of proof
% 15.47/2.81 |
% 15.47/2.81 | ALPHA: (ass(cond(conseq(263), 1), 0)) implies:
% 15.47/2.82 | (1) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.47/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v4) | ~
% 15.47/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v3, v4) = v5) | ~ (vplus(v2,
% 15.47/2.82 | vd411) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8:
% 15.47/2.82 | $i] : ? [v9: $i] : (vmul(v0, v1) = v6 & vmul(vd411, v4) = v8 &
% 15.47/2.82 | vplus(v8, v4) = v9 & vplus(v2, v1) = v7 & $i(v9) & $i(v8) &
% 15.47/2.82 | $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = v5))))
% 15.47/2.82 |
% 15.47/2.82 | ALPHA: (ass(cond(conseq(263), 1), 1)) implies:
% 15.47/2.82 | (2) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.47/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v1) = v3) | ~
% 15.47/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v4, v3) = v5) | ~ (vplus(v2,
% 15.47/2.82 | vd411) = v4) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8:
% 15.47/2.82 | $i] : ? [v9: $i] : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 &
% 15.47/2.82 | vplus(v2, v1) = v7 & vplus(vd411, v3) = v8 & $i(v9) & $i(v8) &
% 15.47/2.82 | $i(v7) & $i(v6) & ( ~ (v7 = v6) | v9 = v5))))
% 15.47/2.82 |
% 15.47/2.82 | ALPHA: (ass(cond(conseq(263), 1), 2)) implies:
% 15.89/2.82 | (3) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~
% 15.89/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411,
% 15.89/2.82 | v1) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 15.89/2.82 | : ? [v9: $i] : ? [v10: $i] : (vsucc(v1) = v8 & vmul(v0, v1) = v6
% 15.89/2.82 | & vplus(v2, v9) = v10 & vplus(v2, v1) = v7 & vplus(vd411, v8) =
% 15.89/2.82 | v9 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v7 = v6)
% 15.89/2.82 | | v10 = v5))))
% 15.89/2.82 |
% 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 3)) implies:
% 15.89/2.82 | (4) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (vsucc(v3) = v4) | ~
% 15.89/2.82 | (vmul(vd411, v1) = v2) | ~ (vplus(v2, v4) = v5) | ~ (vplus(vd411,
% 15.89/2.82 | v1) = v3) | ~ $i(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 15.89/2.82 | : ? [v9: $i] : (vmul(v0, v1) = v6 & vplus(v2, v8) = v9 & vplus(v2,
% 15.89/2.82 | v1) = v7 & vplus(v0, v1) = v8 & $i(v9) & $i(v8) & $i(v7) &
% 15.89/2.82 | $i(v6) & ( ~ (v7 = v6) | v9 = v5))))
% 15.89/2.82 |
% 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 4)) implies:
% 15.89/2.82 | (5) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~
% 15.89/2.82 | (vplus(v2, v3) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v1) | ?
% 15.89/2.82 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(v0, v1)
% 15.89/2.82 | = v5 & vplus(v2, v7) = v8 & vplus(v2, v1) = v6 & vplus(v1, v0) =
% 15.89/2.82 | v7 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 =
% 15.89/2.82 | v4))))
% 15.89/2.82 |
% 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 5)) implies:
% 15.89/2.82 | (6) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.89/2.82 | ! [v3: $i] : ! [v4: $i] : ( ~ (vmul(vd411, v1) = v2) | ~
% 15.89/2.82 | (vplus(v2, v3) = v4) | ~ (vplus(v1, v0) = v3) | ~ $i(v1) | ?
% 15.89/2.82 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vmul(v0, v1) = v5 &
% 15.89/2.82 | vplus(v6, v0) = v7 & vplus(v2, v1) = v6 & $i(v7) & $i(v6) &
% 15.89/2.82 | $i(v5) & ( ~ (v6 = v5) | v7 = v4))))
% 15.89/2.82 |
% 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 6)) implies:
% 15.89/2.82 | (7) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.89/2.82 | ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ?
% 15.89/2.82 | [v5: $i] : ? [v6: $i] : (vmul(vd411, v1) = v3 & vplus(v4, v0) = v6
% 15.89/2.82 | & vplus(v3, v1) = v4 & vplus(v2, v0) = v5 & $i(v6) & $i(v5) &
% 15.89/2.82 | $i(v4) & $i(v3) & ( ~ (v4 = v2) | v6 = v5))))
% 15.89/2.82 |
% 15.89/2.82 | ALPHA: (ass(cond(conseq(263), 1), 7)) implies:
% 15.89/2.83 | (8) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.89/2.83 | ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] : ?
% 15.89/2.83 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vsucc(v1) = v5 & vmul(v0,
% 15.89/2.83 | v5) = v6 & vmul(vd411, v1) = v3 & vplus(v3, v1) = v4 &
% 15.89/2.83 | vplus(v2, v0) = v7 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 15.89/2.83 | ( ~ (v4 = v2) | v7 = v6))))
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (holds(264, 412, 2)) implies:
% 15.89/2.83 | (9) ? [v0: $i] : ? [v1: $i] : (vsucc(v0) = v1 & vmul(vd411, v1) = v0 &
% 15.89/2.83 | vplus(v0, v1) = v1 & $i(v1) & $i(v0))
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (holds(264, 412, 1)) implies:
% 15.89/2.83 | (10) ? [v0: $i] : ? [v1: $i] : (vsucc(v1) = v0 & vsucc(vd411) = v0 &
% 15.89/2.83 | vmul(vd411, v1) = v1 & $i(v1) & $i(v0))
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (holds(264, 412, 0)) implies:
% 15.89/2.83 | (11) ? [v0: $i] : (vsucc(vd411) = v0 & vmul(v0, v1) = v0 & $i(v0))
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 15.89/2.83 | holds(definiens(249), 398, 0)))) implies:
% 15.89/2.83 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1)
% 15.89/2.83 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 15.89/2.83 | $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3)))
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 15.89/2.83 | holds(definiens(29), 44, 0)))) implies:
% 15.89/2.83 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1)
% 15.89/2.83 | = v2) | ~ (vplus(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 15.89/2.83 | $i] : (vsucc(v4) = v3 & vplus(v0, v1) = v4 & $i(v4) & $i(v3)))
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) implies:
% 15.89/2.83 | (14) $i(v1)
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (qu(ind(267), imp(267))) implies:
% 15.89/2.83 | (15) $i(vd411)
% 15.89/2.83 | (16) ? [v0: $i] : (vsucc(vd411) = v0 & $i(v0) & ? [v1: $i] : ? [v2: $i]
% 15.89/2.83 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 15.89/2.83 | $i] : ( ~ (v7 = v5) & vsucc(v1) = v4 & vmul(v0, v4) = v5 &
% 15.89/2.83 | vmul(v0, v1) = v2 & vmul(vd411, v4) = v6 & vmul(vd411, v1) = v3 &
% 15.89/2.83 | vplus(v6, v4) = v7 & vplus(v3, v1) = v2 & $i(v7) & $i(v6) & $i(v5)
% 15.89/2.83 | & $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (function-axioms) implies:
% 15.89/2.83 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) =
% 15.89/2.83 | v1) | ~ (vsucc(v2) = v0))
% 15.89/2.83 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.89/2.83 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 15.89/2.83 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.89/2.83 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 15.89/2.83 |
% 15.89/2.83 | DELTA: instantiating (11) with fresh symbol all_45_0 gives:
% 15.89/2.83 | (20) vsucc(vd411) = all_45_0 & vmul(all_45_0, v1) = all_45_0 & $i(all_45_0)
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (20) implies:
% 15.89/2.83 | (21) vsucc(vd411) = all_45_0
% 15.89/2.83 |
% 15.89/2.83 | DELTA: instantiating (9) with fresh symbols all_52_0, all_52_1 gives:
% 15.89/2.83 | (22) vsucc(all_52_1) = all_52_0 & vmul(vd411, v1) = all_52_1 &
% 15.89/2.83 | vplus(all_52_1, v1) = all_52_0 & $i(all_52_0) & $i(all_52_1)
% 15.89/2.83 |
% 15.89/2.83 | ALPHA: (22) implies:
% 15.89/2.84 | (23) vplus(all_52_1, v1) = all_52_0
% 15.89/2.84 | (24) vmul(vd411, v1) = all_52_1
% 15.89/2.84 | (25) vsucc(all_52_1) = all_52_0
% 15.89/2.84 |
% 15.89/2.84 | DELTA: instantiating (10) with fresh symbols all_54_0, all_54_1 gives:
% 15.89/2.84 | (26) vsucc(all_54_0) = all_54_1 & vsucc(vd411) = all_54_1 & vmul(vd411, v1)
% 15.89/2.84 | = all_54_0 & $i(all_54_0) & $i(all_54_1)
% 15.89/2.84 |
% 15.89/2.84 | ALPHA: (26) implies:
% 15.89/2.84 | (27) $i(all_54_0)
% 15.89/2.84 | (28) vmul(vd411, v1) = all_54_0
% 15.89/2.84 | (29) vsucc(vd411) = all_54_1
% 15.89/2.84 | (30) vsucc(all_54_0) = all_54_1
% 15.89/2.84 |
% 15.89/2.84 | DELTA: instantiating (6) with fresh symbol all_59_0 gives:
% 15.89/2.84 | (31) vsucc(vd411) = all_59_0 & $i(all_59_0) & ! [v0: $i] : ! [v1: $i] :
% 15.89/2.84 | ! [v2: $i] : ! [v3: $i] : ( ~ (vmul(vd411, v0) = v1) | ~ (vplus(v1,
% 15.89/2.84 | v2) = v3) | ~ (vplus(v0, all_59_0) = v2) | ~ $i(v0) | ? [v4:
% 15.89/2.84 | $i] : ? [v5: $i] : ? [v6: $i] : (vmul(all_59_0, v0) = v4 &
% 15.89/2.84 | vplus(v5, all_59_0) = v6 & vplus(v1, v0) = v5 & $i(v6) & $i(v5) &
% 15.89/2.84 | $i(v4) & ( ~ (v5 = v4) | v6 = v3)))
% 15.89/2.84 |
% 15.89/2.84 | ALPHA: (31) implies:
% 15.89/2.84 | (32) vsucc(vd411) = all_59_0
% 15.89/2.84 |
% 15.89/2.84 | DELTA: instantiating (7) with fresh symbol all_62_0 gives:
% 15.89/2.84 | (33) vsucc(vd411) = all_62_0 & $i(all_62_0) & ! [v0: $i] : ! [v1: $i] : (
% 15.89/2.84 | ~ (vmul(all_62_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i]
% 15.89/2.84 | : ? [v4: $i] : ? [v5: $i] : (vmul(vd411, v0) = v2 & vplus(v3,
% 15.89/2.84 | all_62_0) = v5 & vplus(v2, v0) = v3 & vplus(v1, all_62_0) = v4 &
% 15.89/2.84 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v3 = v1) | v5 = v4)))
% 15.89/2.84 |
% 15.89/2.84 | ALPHA: (33) implies:
% 15.89/2.84 | (34) vsucc(vd411) = all_62_0
% 15.89/2.84 |
% 15.89/2.84 | DELTA: instantiating (8) with fresh symbol all_65_0 gives:
% 15.89/2.84 | (35) vsucc(vd411) = all_65_0 & $i(all_65_0) & ! [v0: $i] : ! [v1: $i] : (
% 15.89/2.84 | ~ (vmul(all_65_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i]
% 15.89/2.84 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (vsucc(v0) = v4 &
% 15.89/2.84 | vmul(all_65_0, v4) = v5 & vmul(vd411, v0) = v2 & vplus(v2, v0) =
% 15.89/2.84 | v3 & vplus(v1, all_65_0) = v6 & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 15.89/2.84 | & $i(v2) & ( ~ (v3 = v1) | v6 = v5)))
% 15.89/2.84 |
% 15.89/2.84 | ALPHA: (35) implies:
% 15.89/2.84 | (36) vsucc(vd411) = all_65_0
% 15.89/2.84 |
% 15.89/2.84 | DELTA: instantiating (5) with fresh symbol all_68_0 gives:
% 15.89/2.84 | (37) vsucc(vd411) = all_68_0 & $i(all_68_0) & ! [v0: $i] : ! [v1: $i] :
% 15.89/2.84 | ! [v2: $i] : ! [v3: $i] : ( ~ (vmul(vd411, v0) = v1) | ~ (vplus(v1,
% 15.89/2.84 | v2) = v3) | ~ (vplus(all_68_0, v0) = v2) | ~ $i(v0) | ? [v4:
% 15.89/2.84 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (vmul(all_68_0,
% 15.89/2.84 | v0) = v4 & vplus(v1, v6) = v7 & vplus(v1, v0) = v5 & vplus(v0,
% 15.89/2.84 | all_68_0) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v5 =
% 15.89/2.84 | v4) | v7 = v3)))
% 15.89/2.84 |
% 15.89/2.84 | ALPHA: (37) implies:
% 15.89/2.84 | (38) vsucc(vd411) = all_68_0
% 15.89/2.84 |
% 15.89/2.84 | DELTA: instantiating (2) with fresh symbol all_71_0 gives:
% 15.89/2.84 | (39) vsucc(vd411) = all_71_0 & $i(all_71_0) & ! [v0: $i] : ! [v1: $i] :
% 15.89/2.84 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v0) = v2) | ~
% 15.89/2.84 | (vmul(vd411, v0) = v1) | ~ (vplus(v3, v2) = v4) | ~ (vplus(v1,
% 15.89/2.84 | vd411) = v3) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7:
% 15.89/2.84 | $i] : ? [v8: $i] : (vmul(all_71_0, v0) = v5 & vplus(v1, v7) = v8
% 15.89/2.84 | & vplus(v1, v0) = v6 & vplus(vd411, v2) = v7 & $i(v8) & $i(v7) &
% 15.89/2.84 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4)))
% 15.89/2.84 |
% 15.89/2.84 | ALPHA: (39) implies:
% 15.89/2.84 | (40) vsucc(vd411) = all_71_0
% 15.89/2.85 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.89/2.85 | ( ~ (vsucc(v0) = v2) | ~ (vmul(vd411, v0) = v1) | ~ (vplus(v3, v2) =
% 15.89/2.85 | v4) | ~ (vplus(v1, vd411) = v3) | ~ $i(v0) | ? [v5: $i] : ?
% 15.89/2.85 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : (vmul(all_71_0, v0) = v5 &
% 15.89/2.85 | vplus(v1, v7) = v8 & vplus(v1, v0) = v6 & vplus(vd411, v2) = v7 &
% 15.89/2.85 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4)))
% 15.89/2.85 |
% 15.89/2.85 | DELTA: instantiating (4) with fresh symbol all_74_0 gives:
% 15.89/2.85 | (42) vsucc(vd411) = all_74_0 & $i(all_74_0) & ! [v0: $i] : ! [v1: $i] :
% 15.89/2.85 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v2) = v3) | ~
% 15.89/2.85 | (vmul(vd411, v0) = v1) | ~ (vplus(v1, v3) = v4) | ~ (vplus(vd411,
% 15.89/2.85 | v0) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 15.89/2.85 | : ? [v8: $i] : (vmul(all_74_0, v0) = v5 & vplus(v1, v7) = v8 &
% 15.89/2.85 | vplus(v1, v0) = v6 & vplus(all_74_0, v0) = v7 & $i(v8) & $i(v7) &
% 15.89/2.85 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4)))
% 15.89/2.85 |
% 15.89/2.85 | ALPHA: (42) implies:
% 15.89/2.85 | (43) vsucc(vd411) = all_74_0
% 15.89/2.85 |
% 15.89/2.85 | DELTA: instantiating (16) with fresh symbol all_77_0 gives:
% 15.89/2.85 | (44) vsucc(vd411) = all_77_0 & $i(all_77_0) & ? [v0: $i] : ? [v1: $i] :
% 15.89/2.85 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (
% 15.89/2.85 | ~ (v6 = v4) & vsucc(v0) = v3 & vmul(all_77_0, v3) = v4 &
% 15.89/2.85 | vmul(all_77_0, v0) = v1 & vmul(vd411, v3) = v5 & vmul(vd411, v0) =
% 15.89/2.85 | v2 & vplus(v5, v3) = v6 & vplus(v2, v0) = v1 & $i(v6) & $i(v5) &
% 15.89/2.85 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 15.89/2.85 |
% 15.89/2.85 | ALPHA: (44) implies:
% 15.89/2.85 | (45) vsucc(vd411) = all_77_0
% 15.89/2.85 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 15.89/2.85 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & vsucc(v0) = v3 &
% 15.89/2.85 | vmul(all_77_0, v3) = v4 & vmul(all_77_0, v0) = v1 & vmul(vd411, v3)
% 15.89/2.85 | = v5 & vmul(vd411, v0) = v2 & vplus(v5, v3) = v6 & vplus(v2, v0) =
% 15.89/2.85 | v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 15.89/2.85 |
% 15.89/2.85 | DELTA: instantiating (1) with fresh symbol all_79_0 gives:
% 15.89/2.85 | (47) vsucc(vd411) = all_79_0 & $i(all_79_0) & ! [v0: $i] : ! [v1: $i] :
% 15.89/2.85 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v0) = v3) | ~
% 15.89/2.85 | (vmul(vd411, v0) = v1) | ~ (vplus(v2, v3) = v4) | ~ (vplus(v1,
% 15.89/2.85 | vd411) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7:
% 15.89/2.85 | $i] : ? [v8: $i] : (vmul(all_79_0, v0) = v5 & vmul(vd411, v3) =
% 15.89/2.85 | v7 & vplus(v7, v3) = v8 & vplus(v1, v0) = v6 & $i(v8) & $i(v7) &
% 15.89/2.85 | $i(v6) & $i(v5) & ( ~ (v6 = v5) | v8 = v4)))
% 15.89/2.85 |
% 15.89/2.85 | ALPHA: (47) implies:
% 15.89/2.85 | (48) vsucc(vd411) = all_79_0
% 15.89/2.85 |
% 15.89/2.85 | DELTA: instantiating (3) with fresh symbol all_82_0 gives:
% 15.89/2.85 | (49) vsucc(vd411) = all_82_0 & $i(all_82_0) & ! [v0: $i] : ! [v1: $i] :
% 15.89/2.85 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (vsucc(v2) = v3) | ~
% 15.89/2.85 | (vmul(vd411, v0) = v1) | ~ (vplus(v1, v3) = v4) | ~ (vplus(vd411,
% 15.89/2.85 | v0) = v2) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 15.89/2.85 | : ? [v8: $i] : ? [v9: $i] : (vsucc(v0) = v7 & vmul(all_82_0, v0) =
% 15.89/2.85 | v5 & vplus(v1, v8) = v9 & vplus(v1, v0) = v6 & vplus(vd411, v7) =
% 15.89/2.85 | v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v6 = v5) |
% 15.89/2.85 | v9 = v4)))
% 15.89/2.85 |
% 15.89/2.85 | ALPHA: (49) implies:
% 15.89/2.85 | (50) vsucc(vd411) = all_82_0
% 15.89/2.85 |
% 15.89/2.85 | DELTA: instantiating (46) with fresh symbols all_85_0, all_85_1, all_85_2,
% 15.89/2.85 | all_85_3, all_85_4, all_85_5, all_85_6 gives:
% 15.89/2.85 | (51) ~ (all_85_0 = all_85_2) & vsucc(all_85_6) = all_85_3 & vmul(all_77_0,
% 15.89/2.85 | all_85_3) = all_85_2 & vmul(all_77_0, all_85_6) = all_85_5 &
% 15.89/2.85 | vmul(vd411, all_85_3) = all_85_1 & vmul(vd411, all_85_6) = all_85_4 &
% 15.89/2.85 | vplus(all_85_1, all_85_3) = all_85_0 & vplus(all_85_4, all_85_6) =
% 15.89/2.85 | all_85_5 & $i(all_85_0) & $i(all_85_1) & $i(all_85_2) & $i(all_85_3) &
% 15.89/2.85 | $i(all_85_4) & $i(all_85_5) & $i(all_85_6)
% 15.89/2.85 |
% 15.89/2.85 | ALPHA: (51) implies:
% 15.89/2.85 | (52) ~ (all_85_0 = all_85_2)
% 15.89/2.85 | (53) $i(all_85_6)
% 15.89/2.85 | (54) $i(all_85_3)
% 15.89/2.85 | (55) $i(all_85_1)
% 15.89/2.85 | (56) vplus(all_85_4, all_85_6) = all_85_5
% 15.89/2.85 | (57) vplus(all_85_1, all_85_3) = all_85_0
% 15.89/2.85 | (58) vmul(vd411, all_85_6) = all_85_4
% 15.89/2.85 | (59) vmul(vd411, all_85_3) = all_85_1
% 15.89/2.85 | (60) vmul(all_77_0, all_85_6) = all_85_5
% 15.89/2.85 | (61) vmul(all_77_0, all_85_3) = all_85_2
% 15.89/2.85 | (62) vsucc(all_85_6) = all_85_3
% 15.89/2.85 |
% 15.89/2.86 | GROUND_INST: instantiating (19) with all_52_1, all_54_0, v1, vd411,
% 15.89/2.86 | simplifying with (24), (28) gives:
% 15.89/2.86 | (63) all_54_0 = all_52_1
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_59_0, all_62_0, vd411, simplifying
% 15.89/2.86 | with (32), (34) gives:
% 15.89/2.86 | (64) all_62_0 = all_59_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_62_0, all_65_0, vd411, simplifying
% 15.89/2.86 | with (34), (36) gives:
% 15.89/2.86 | (65) all_65_0 = all_62_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_65_0, all_71_0, vd411, simplifying
% 15.89/2.86 | with (36), (40) gives:
% 15.89/2.86 | (66) all_71_0 = all_65_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_71_0, all_74_0, vd411, simplifying
% 15.89/2.86 | with (40), (43) gives:
% 15.89/2.86 | (67) all_74_0 = all_71_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_71_0, all_77_0, vd411, simplifying
% 15.89/2.86 | with (40), (45) gives:
% 15.89/2.86 | (68) all_77_0 = all_71_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_68_0, all_77_0, vd411, simplifying
% 15.89/2.86 | with (38), (45) gives:
% 15.89/2.86 | (69) all_77_0 = all_68_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_59_0, all_79_0, vd411, simplifying
% 15.89/2.86 | with (32), (48) gives:
% 15.89/2.86 | (70) all_79_0 = all_59_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_54_1, all_79_0, vd411, simplifying
% 15.89/2.86 | with (29), (48) gives:
% 15.89/2.86 | (71) all_79_0 = all_54_1
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_74_0, all_82_0, vd411, simplifying
% 15.89/2.86 | with (43), (50) gives:
% 15.89/2.86 | (72) all_82_0 = all_74_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_45_0, all_82_0, vd411, simplifying
% 15.89/2.86 | with (21), (50) gives:
% 15.89/2.86 | (73) all_82_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (72), (73) imply:
% 15.89/2.86 | (74) all_74_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (74) implies:
% 15.89/2.86 | (75) all_74_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (70), (71) imply:
% 15.89/2.86 | (76) all_59_0 = all_54_1
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (76) implies:
% 15.89/2.86 | (77) all_59_0 = all_54_1
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (68), (69) imply:
% 15.89/2.86 | (78) all_71_0 = all_68_0
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (78) implies:
% 15.89/2.86 | (79) all_71_0 = all_68_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (67), (75) imply:
% 15.89/2.86 | (80) all_71_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (80) implies:
% 15.89/2.86 | (81) all_71_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (79), (81) imply:
% 15.89/2.86 | (82) all_68_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (66), (79) imply:
% 15.89/2.86 | (83) all_68_0 = all_65_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (82), (83) imply:
% 15.89/2.86 | (84) all_65_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (84) implies:
% 15.89/2.86 | (85) all_65_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (65), (85) imply:
% 15.89/2.86 | (86) all_62_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (86) implies:
% 15.89/2.86 | (87) all_62_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (64), (87) imply:
% 15.89/2.86 | (88) all_59_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (88) implies:
% 15.89/2.86 | (89) all_59_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (77), (89) imply:
% 15.89/2.86 | (90) all_54_1 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | SIMP: (90) implies:
% 15.89/2.86 | (91) all_54_1 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | COMBINE_EQS: (69), (82) imply:
% 15.89/2.86 | (92) all_77_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | REDUCE: (30), (63), (91) imply:
% 15.89/2.86 | (93) vsucc(all_52_1) = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | REDUCE: (61), (92) imply:
% 15.89/2.86 | (94) vmul(all_45_0, all_85_3) = all_85_2
% 15.89/2.86 |
% 15.89/2.86 | REDUCE: (60), (92) imply:
% 15.89/2.86 | (95) vmul(all_45_0, all_85_6) = all_85_5
% 15.89/2.86 |
% 15.89/2.86 | REDUCE: (27), (63) imply:
% 15.89/2.86 | (96) $i(all_52_1)
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (17) with all_52_0, all_45_0, all_52_1, simplifying
% 15.89/2.86 | with (25), (93) gives:
% 15.89/2.86 | (97) all_52_0 = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | REDUCE: (23), (97) imply:
% 15.89/2.86 | (98) vplus(all_52_1, v1) = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_52_1, v1, all_45_0,
% 15.89/2.86 | simplifying with (14), (96), (98) gives:
% 15.89/2.86 | (99) vplus(v1, all_52_1) = all_45_0 & $i(all_45_0)
% 15.89/2.86 |
% 15.89/2.86 | ALPHA: (99) implies:
% 15.89/2.86 | (100) $i(all_45_0)
% 15.89/2.86 | (101) vplus(v1, all_52_1) = all_45_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_1, all_85_3,
% 15.89/2.86 | all_85_0, simplifying with (54), (55), (57) gives:
% 15.89/2.86 | (102) vplus(all_85_3, all_85_1) = all_85_0 & $i(all_85_0)
% 15.89/2.86 |
% 15.89/2.86 | ALPHA: (102) implies:
% 15.89/2.86 | (103) vplus(all_85_3, all_85_1) = all_85_0
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (qu(antec(axiom(3)), imp(antec(axiom(3))))) with
% 15.89/2.86 | vd411, all_52_1, all_45_0, simplifying with (15), (21), (93),
% 15.89/2.86 | (96) gives:
% 15.89/2.86 | (104) all_52_1 = vd411
% 15.89/2.86 |
% 15.89/2.86 | GROUND_INST: instantiating (12) with all_45_0, all_85_6, all_85_3, all_85_2,
% 15.89/2.86 | simplifying with (53), (62), (94), (100) gives:
% 15.89/2.87 | (105) ? [v0: $i] : (vmul(all_45_0, all_85_6) = v0 & vplus(v0, all_45_0) =
% 15.89/2.87 | all_85_2 & $i(v0) & $i(all_85_2))
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (12) with vd411, all_85_6, all_85_3, all_85_1,
% 15.89/2.87 | simplifying with (15), (53), (59), (62) gives:
% 15.89/2.87 | (106) ? [v0: $i] : (vmul(vd411, all_85_6) = v0 & vplus(v0, vd411) =
% 15.89/2.87 | all_85_1 & $i(v0) & $i(all_85_1))
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (13) with all_85_1, all_85_6, all_85_3, all_85_0,
% 15.89/2.87 | simplifying with (53), (55), (57), (62) gives:
% 15.89/2.87 | (107) ? [v0: $i] : (vsucc(v0) = all_85_0 & vplus(all_85_1, all_85_6) = v0
% 15.89/2.87 | & $i(v0) & $i(all_85_0))
% 15.89/2.87 |
% 15.89/2.87 | DELTA: instantiating (107) with fresh symbol all_101_0 gives:
% 15.89/2.87 | (108) vsucc(all_101_0) = all_85_0 & vplus(all_85_1, all_85_6) = all_101_0 &
% 15.89/2.87 | $i(all_101_0) & $i(all_85_0)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (108) implies:
% 15.89/2.87 | (109) vplus(all_85_1, all_85_6) = all_101_0
% 15.89/2.87 |
% 15.89/2.87 | DELTA: instantiating (106) with fresh symbol all_103_0 gives:
% 15.89/2.87 | (110) vmul(vd411, all_85_6) = all_103_0 & vplus(all_103_0, vd411) =
% 15.89/2.87 | all_85_1 & $i(all_103_0) & $i(all_85_1)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (110) implies:
% 15.89/2.87 | (111) $i(all_103_0)
% 15.89/2.87 | (112) vplus(all_103_0, vd411) = all_85_1
% 15.89/2.87 | (113) vmul(vd411, all_85_6) = all_103_0
% 15.89/2.87 |
% 15.89/2.87 | DELTA: instantiating (105) with fresh symbol all_105_0 gives:
% 15.89/2.87 | (114) vmul(all_45_0, all_85_6) = all_105_0 & vplus(all_105_0, all_45_0) =
% 15.89/2.87 | all_85_2 & $i(all_105_0) & $i(all_85_2)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (114) implies:
% 15.89/2.87 | (115) $i(all_105_0)
% 15.89/2.87 | (116) vplus(all_105_0, all_45_0) = all_85_2
% 15.89/2.87 | (117) vmul(all_45_0, all_85_6) = all_105_0
% 15.89/2.87 |
% 15.89/2.87 | REDUCE: (101), (104) imply:
% 15.89/2.87 | (118) vplus(v1, vd411) = all_45_0
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (19) with all_85_4, all_103_0, all_85_6, vd411,
% 15.89/2.87 | simplifying with (58), (113) gives:
% 15.89/2.87 | (119) all_103_0 = all_85_4
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (19) with all_85_5, all_105_0, all_85_6, all_45_0,
% 15.89/2.87 | simplifying with (95), (117) gives:
% 15.89/2.87 | (120) all_105_0 = all_85_5
% 15.89/2.87 |
% 15.89/2.87 | REDUCE: (116), (120) imply:
% 15.89/2.87 | (121) vplus(all_85_5, all_45_0) = all_85_2
% 15.89/2.87 |
% 15.89/2.87 | REDUCE: (112), (119) imply:
% 15.89/2.87 | (122) vplus(all_85_4, vd411) = all_85_1
% 15.89/2.87 |
% 15.89/2.87 | REDUCE: (115), (120) imply:
% 15.89/2.87 | (123) $i(all_85_5)
% 15.89/2.87 |
% 15.89/2.87 | REDUCE: (111), (119) imply:
% 15.89/2.87 | (124) $i(all_85_4)
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (13) with all_85_5, vd411, all_45_0, all_85_2,
% 15.89/2.87 | simplifying with (15), (21), (121), (123) gives:
% 15.89/2.87 | (125) ? [v0: $i] : (vsucc(v0) = all_85_2 & vplus(all_85_5, vd411) = v0 &
% 15.89/2.87 | $i(v0) & $i(all_85_2))
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_85_4, all_85_6,
% 15.89/2.87 | all_45_0, all_85_5, all_85_2, simplifying with (53), (56), (100),
% 15.89/2.87 | (121), (124) gives:
% 15.89/2.87 | (126) ? [v0: $i] : (vplus(all_85_4, v0) = all_85_2 & vplus(all_85_6,
% 15.89/2.87 | all_45_0) = v0 & $i(v0) & $i(all_85_2))
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_5, all_45_0,
% 15.89/2.87 | all_85_2, simplifying with (100), (121), (123) gives:
% 15.89/2.87 | (127) vplus(all_45_0, all_85_5) = all_85_2 & $i(all_85_2)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (127) implies:
% 15.89/2.87 | (128) vplus(all_45_0, all_85_5) = all_85_2
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (41) with all_85_6, all_85_4, all_85_3, all_85_1,
% 15.89/2.87 | all_85_0, simplifying with (53), (57), (58), (62), (122) gives:
% 15.89/2.87 | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 15.89/2.87 | (vmul(all_71_0, all_85_6) = v0 & vplus(all_85_4, v2) = v3 &
% 15.89/2.87 | vplus(all_85_4, all_85_6) = v1 & vplus(vd411, all_85_3) = v2 &
% 15.89/2.87 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v1 = v0) | v3 = all_85_0))
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_4, vd411,
% 15.89/2.87 | all_85_1, simplifying with (15), (122), (124) gives:
% 15.89/2.87 | (130) vplus(vd411, all_85_4) = all_85_1 & $i(all_85_1)
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (ass(cond(52, 0), 0)) with all_85_6, all_85_1,
% 15.89/2.87 | all_85_3, all_85_0, simplifying with (53), (55), (62), (103)
% 15.89/2.87 | gives:
% 15.89/2.87 | (131) ? [v0: $i] : (vsucc(v0) = all_85_0 & vplus(all_85_6, all_85_1) = v0
% 15.89/2.87 | & $i(v0) & $i(all_85_0))
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_85_4, vd411,
% 15.89/2.87 | all_85_6, all_85_1, all_101_0, simplifying with (15), (53),
% 15.89/2.87 | (109), (122), (124) gives:
% 15.89/2.87 | (132) ? [v0: $i] : (vplus(all_85_4, v0) = all_101_0 & vplus(vd411,
% 15.89/2.87 | all_85_6) = v0 & $i(v0) & $i(all_101_0))
% 15.89/2.87 |
% 15.89/2.87 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_1, all_85_6,
% 15.89/2.87 | all_101_0, simplifying with (53), (55), (109) gives:
% 15.89/2.87 | (133) vplus(all_85_6, all_85_1) = all_101_0 & $i(all_101_0)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (133) implies:
% 15.89/2.87 | (134) vplus(all_85_6, all_85_1) = all_101_0
% 15.89/2.87 |
% 15.89/2.87 | DELTA: instantiating (131) with fresh symbol all_117_0 gives:
% 15.89/2.87 | (135) vsucc(all_117_0) = all_85_0 & vplus(all_85_6, all_85_1) = all_117_0 &
% 15.89/2.87 | $i(all_117_0) & $i(all_85_0)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (135) implies:
% 15.89/2.87 | (136) vplus(all_85_6, all_85_1) = all_117_0
% 15.89/2.87 | (137) vsucc(all_117_0) = all_85_0
% 15.89/2.87 |
% 15.89/2.87 | DELTA: instantiating (126) with fresh symbol all_123_0 gives:
% 15.89/2.87 | (138) vplus(all_85_4, all_123_0) = all_85_2 & vplus(all_85_6, all_45_0) =
% 15.89/2.87 | all_123_0 & $i(all_123_0) & $i(all_85_2)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (138) implies:
% 15.89/2.87 | (139) vplus(all_85_6, all_45_0) = all_123_0
% 15.89/2.87 |
% 15.89/2.87 | DELTA: instantiating (132) with fresh symbol all_125_0 gives:
% 15.89/2.87 | (140) vplus(all_85_4, all_125_0) = all_101_0 & vplus(vd411, all_85_6) =
% 15.89/2.87 | all_125_0 & $i(all_125_0) & $i(all_101_0)
% 15.89/2.87 |
% 15.89/2.87 | ALPHA: (140) implies:
% 15.89/2.88 | (141) vplus(vd411, all_85_6) = all_125_0
% 15.89/2.88 | (142) vplus(all_85_4, all_125_0) = all_101_0
% 15.89/2.88 |
% 15.89/2.88 | DELTA: instantiating (125) with fresh symbol all_127_0 gives:
% 15.89/2.88 | (143) vsucc(all_127_0) = all_85_2 & vplus(all_85_5, vd411) = all_127_0 &
% 15.89/2.88 | $i(all_127_0) & $i(all_85_2)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (143) implies:
% 15.89/2.88 | (144) vplus(all_85_5, vd411) = all_127_0
% 15.89/2.88 |
% 15.89/2.88 | DELTA: instantiating (129) with fresh symbols all_129_0, all_129_1, all_129_2,
% 15.89/2.88 | all_129_3 gives:
% 15.89/2.88 | (145) vmul(all_71_0, all_85_6) = all_129_3 & vplus(all_85_4, all_129_1) =
% 15.89/2.88 | all_129_0 & vplus(all_85_4, all_85_6) = all_129_2 & vplus(vd411,
% 15.89/2.88 | all_85_3) = all_129_1 & $i(all_129_0) & $i(all_129_1) &
% 15.89/2.88 | $i(all_129_2) & $i(all_129_3) & ( ~ (all_129_2 = all_129_3) |
% 15.89/2.88 | all_129_0 = all_85_0)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (145) implies:
% 15.89/2.88 | (146) $i(all_129_3)
% 15.89/2.88 | (147) vplus(all_85_4, all_85_6) = all_129_2
% 15.89/2.88 | (148) vmul(all_71_0, all_85_6) = all_129_3
% 15.89/2.88 |
% 15.89/2.88 | REDUCE: (81), (148) imply:
% 15.89/2.88 | (149) vmul(all_45_0, all_85_6) = all_129_3
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (18) with all_101_0, all_117_0, all_85_1, all_85_6,
% 15.89/2.88 | simplifying with (134), (136) gives:
% 15.89/2.88 | (150) all_117_0 = all_101_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (18) with all_85_5, all_129_2, all_85_6, all_85_4,
% 15.89/2.88 | simplifying with (56), (147) gives:
% 15.89/2.88 | (151) all_129_2 = all_85_5
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (19) with all_85_5, all_129_3, all_85_6, all_45_0,
% 15.89/2.88 | simplifying with (95), (149) gives:
% 15.89/2.88 | (152) all_129_3 = all_85_5
% 15.89/2.88 |
% 15.89/2.88 | REDUCE: (137), (150) imply:
% 15.89/2.88 | (153) vsucc(all_101_0) = all_85_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd411, all_85_6,
% 15.89/2.88 | all_125_0, simplifying with (15), (53), (141) gives:
% 15.89/2.88 | (154) vplus(all_85_6, vd411) = all_125_0 & $i(all_125_0)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (154) implies:
% 15.89/2.88 | (155) vplus(all_85_6, vd411) = all_125_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (ass(cond(52, 0), 0)) with vd411, all_85_5,
% 15.89/2.88 | all_45_0, all_85_2, simplifying with (15), (21), (123), (128)
% 15.89/2.88 | gives:
% 15.89/2.88 | (156) ? [v0: $i] : (vsucc(v0) = all_85_2 & vplus(vd411, all_85_5) = v0 &
% 15.89/2.88 | $i(v0) & $i(all_85_2))
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with v1, vd411, all_85_5,
% 15.89/2.88 | all_45_0, all_85_2, simplifying with (14), (15), (118), (123),
% 15.89/2.88 | (128) gives:
% 15.89/2.88 | (157) ? [v0: $i] : (vplus(v1, v0) = all_85_2 & vplus(vd411, all_85_5) = v0
% 15.89/2.88 | & $i(v0) & $i(all_85_2))
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (13) with all_85_6, vd411, all_45_0, all_123_0,
% 15.89/2.88 | simplifying with (15), (21), (53), (139) gives:
% 15.89/2.88 | (158) ? [v0: $i] : (vsucc(v0) = all_123_0 & vplus(all_85_6, vd411) = v0 &
% 15.89/2.88 | $i(v0) & $i(all_123_0))
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_85_4, all_85_6,
% 15.89/2.88 | vd411, all_85_5, all_127_0, simplifying with (15), (53), (56),
% 15.89/2.88 | (124), (144) gives:
% 15.89/2.88 | (159) ? [v0: $i] : (vplus(all_85_4, v0) = all_127_0 & vplus(all_85_6,
% 15.89/2.88 | vd411) = v0 & $i(v0) & $i(all_127_0))
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_85_5, vd411,
% 15.89/2.88 | all_127_0, simplifying with (15), (123), (144) gives:
% 15.89/2.88 | (160) vplus(vd411, all_85_5) = all_127_0 & $i(all_127_0)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (160) implies:
% 15.89/2.88 | (161) vplus(vd411, all_85_5) = all_127_0
% 15.89/2.88 |
% 15.89/2.88 | DELTA: instantiating (156) with fresh symbol all_147_0 gives:
% 15.89/2.88 | (162) vsucc(all_147_0) = all_85_2 & vplus(vd411, all_85_5) = all_147_0 &
% 15.89/2.88 | $i(all_147_0) & $i(all_85_2)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (162) implies:
% 15.89/2.88 | (163) vplus(vd411, all_85_5) = all_147_0
% 15.89/2.88 | (164) vsucc(all_147_0) = all_85_2
% 15.89/2.88 |
% 15.89/2.88 | DELTA: instantiating (157) with fresh symbol all_153_0 gives:
% 15.89/2.88 | (165) vplus(v1, all_153_0) = all_85_2 & vplus(vd411, all_85_5) = all_153_0
% 15.89/2.88 | & $i(all_153_0) & $i(all_85_2)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (165) implies:
% 15.89/2.88 | (166) vplus(vd411, all_85_5) = all_153_0
% 15.89/2.88 |
% 15.89/2.88 | DELTA: instantiating (159) with fresh symbol all_157_0 gives:
% 15.89/2.88 | (167) vplus(all_85_4, all_157_0) = all_127_0 & vplus(all_85_6, vd411) =
% 15.89/2.88 | all_157_0 & $i(all_157_0) & $i(all_127_0)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (167) implies:
% 15.89/2.88 | (168) vplus(all_85_6, vd411) = all_157_0
% 15.89/2.88 | (169) vplus(all_85_4, all_157_0) = all_127_0
% 15.89/2.88 |
% 15.89/2.88 | DELTA: instantiating (158) with fresh symbol all_161_0 gives:
% 15.89/2.88 | (170) vsucc(all_161_0) = all_123_0 & vplus(all_85_6, vd411) = all_161_0 &
% 15.89/2.88 | $i(all_161_0) & $i(all_123_0)
% 15.89/2.88 |
% 15.89/2.88 | ALPHA: (170) implies:
% 15.89/2.88 | (171) vplus(all_85_6, vd411) = all_161_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (18) with all_147_0, all_153_0, all_85_5, vd411,
% 15.89/2.88 | simplifying with (163), (166) gives:
% 15.89/2.88 | (172) all_153_0 = all_147_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (18) with all_127_0, all_153_0, all_85_5, vd411,
% 15.89/2.88 | simplifying with (161), (166) gives:
% 15.89/2.88 | (173) all_153_0 = all_127_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (18) with all_157_0, all_161_0, vd411, all_85_6,
% 15.89/2.88 | simplifying with (168), (171) gives:
% 15.89/2.88 | (174) all_161_0 = all_157_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (18) with all_125_0, all_161_0, vd411, all_85_6,
% 15.89/2.88 | simplifying with (155), (171) gives:
% 15.89/2.88 | (175) all_161_0 = all_125_0
% 15.89/2.88 |
% 15.89/2.88 | COMBINE_EQS: (174), (175) imply:
% 15.89/2.88 | (176) all_157_0 = all_125_0
% 15.89/2.88 |
% 15.89/2.88 | SIMP: (176) implies:
% 15.89/2.88 | (177) all_157_0 = all_125_0
% 15.89/2.88 |
% 15.89/2.88 | COMBINE_EQS: (172), (173) imply:
% 15.89/2.88 | (178) all_147_0 = all_127_0
% 15.89/2.88 |
% 15.89/2.88 | REDUCE: (164), (178) imply:
% 15.89/2.88 | (179) vsucc(all_127_0) = all_85_2
% 15.89/2.88 |
% 15.89/2.88 | REDUCE: (169), (177) imply:
% 15.89/2.88 | (180) vplus(all_85_4, all_125_0) = all_127_0
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (18) with all_101_0, all_127_0, all_125_0,
% 15.89/2.88 | all_85_4, simplifying with (142), (180) gives:
% 15.89/2.88 | (181) all_127_0 = all_101_0
% 15.89/2.88 |
% 15.89/2.88 | REDUCE: (179), (181) imply:
% 15.89/2.88 | (182) vsucc(all_101_0) = all_85_2
% 15.89/2.88 |
% 15.89/2.88 | GROUND_INST: instantiating (17) with all_85_0, all_85_2, all_101_0,
% 15.89/2.88 | simplifying with (153), (182) gives:
% 15.89/2.89 | (183) all_85_0 = all_85_2
% 15.89/2.89 |
% 15.89/2.89 | REDUCE: (52), (183) imply:
% 15.89/2.89 | (184) $false
% 15.89/2.89 |
% 15.89/2.89 | CLOSE: (184) is inconsistent.
% 15.89/2.89 |
% 15.89/2.89 End of proof
% 15.89/2.89 % SZS output end Proof for theBenchmark
% 15.89/2.89
% 15.89/2.89 2296ms
%------------------------------------------------------------------------------