TSTP Solution File: NUM856+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM856+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 : n013.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 11:50:27 EDT 2023
% Result : Theorem 10.79s 2.37s
% Output : Proof 14.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM856+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 09:11:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.79/1.28 Prover 4: Preprocessing ...
% 3.79/1.28 Prover 1: Preprocessing ...
% 4.14/1.32 Prover 6: Preprocessing ...
% 4.14/1.32 Prover 2: Preprocessing ...
% 4.14/1.32 Prover 0: Preprocessing ...
% 4.14/1.32 Prover 5: Preprocessing ...
% 4.14/1.32 Prover 3: Preprocessing ...
% 8.34/1.94 Prover 1: Warning: ignoring some quantifiers
% 8.34/1.96 Prover 3: Warning: ignoring some quantifiers
% 8.34/1.98 Prover 6: Proving ...
% 8.83/2.00 Prover 5: Proving ...
% 8.83/2.00 Prover 1: Constructing countermodel ...
% 8.83/2.00 Prover 3: Constructing countermodel ...
% 8.83/2.01 Prover 4: Warning: ignoring some quantifiers
% 8.83/2.02 Prover 2: Proving ...
% 9.38/2.09 Prover 4: Constructing countermodel ...
% 9.38/2.13 Prover 0: Proving ...
% 10.79/2.37 Prover 5: proved (1717ms)
% 10.79/2.37
% 10.79/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.79/2.37
% 11.54/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.54/2.37 Prover 6: stopped
% 11.54/2.37 Prover 0: stopped
% 11.54/2.37 Prover 2: stopped
% 11.54/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.54/2.37 Prover 3: stopped
% 11.54/2.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.54/2.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.54/2.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.91/2.46 Prover 8: Preprocessing ...
% 12.48/2.50 Prover 11: Preprocessing ...
% 12.48/2.51 Prover 10: Preprocessing ...
% 12.48/2.52 Prover 7: Preprocessing ...
% 12.48/2.52 Prover 13: Preprocessing ...
% 13.04/2.62 Prover 8: Warning: ignoring some quantifiers
% 13.04/2.63 Prover 7: Warning: ignoring some quantifiers
% 13.04/2.64 Prover 10: Warning: ignoring some quantifiers
% 13.04/2.64 Prover 8: Constructing countermodel ...
% 13.04/2.65 Prover 10: Constructing countermodel ...
% 13.04/2.66 Prover 7: Constructing countermodel ...
% 13.79/2.69 Prover 1: Found proof (size 168)
% 13.99/2.70 Prover 1: proved (2046ms)
% 13.99/2.70 Prover 10: stopped
% 13.99/2.70 Prover 7: stopped
% 13.99/2.70 Prover 8: stopped
% 13.99/2.70 Prover 13: Warning: ignoring some quantifiers
% 13.99/2.70 Prover 4: stopped
% 13.99/2.71 Prover 13: Constructing countermodel ...
% 13.99/2.71 Prover 11: Warning: ignoring some quantifiers
% 13.99/2.72 Prover 13: stopped
% 14.15/2.73 Prover 11: Constructing countermodel ...
% 14.15/2.74 Prover 11: stopped
% 14.15/2.74
% 14.15/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.15/2.75
% 14.15/2.76 % SZS output start Proof for theBenchmark
% 14.15/2.76 Assumptions after simplification:
% 14.15/2.76 ---------------------------------
% 14.15/2.76
% 14.15/2.76 (ass(cond(270, 0), 0))
% 14.15/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1)
% 14.15/2.79 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2)))
% 14.15/2.79
% 14.15/2.79 (ass(cond(299, 0), 2))
% 14.15/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.15/2.79 int] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ~
% 14.15/2.79 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] :
% 14.15/2.79 ( ~ (v6 = 0) & greater(v1, v2) = v6))
% 14.15/2.79
% 14.15/2.79 (ass(cond(312, 0), 0))
% 14.15/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.15/2.79 $i] : ! [v6: int] : (v6 = 0 | ~ (vmul(v1, v3) = v5) | ~ (vmul(v0, v2) =
% 14.15/2.79 v4) | ~ (greater(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.15/2.79 $i(v0) | ? [v7: any] : ? [v8: any] : (greater(v2, v3) = v7 & greater(v0,
% 14.15/2.79 v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 14.15/2.79
% 14.15/2.79 (def(cond(conseq(axiom(3)), 16), 1))
% 14.15/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) = v2) |
% 14.15/2.79 ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) &
% 14.15/2.79 greater(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 14.15/2.79 (geq(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | greater(v1, v0) = 0)
% 14.15/2.79
% 14.15/2.79 (dis(antec(scope(318))))
% 14.15/2.80 $i(vd520) & $i(vd518) & $i(vd519) & $i(vd517) & ? [v0: any] : ? [v1: any] :
% 14.15/2.80 ? [v2: any] : ? [v3: any] : (geq(vd519, vd520) = v2 & geq(vd517, vd518) = v1
% 14.15/2.80 & greater(vd519, vd520) = v0 & greater(vd517, vd518) = v3 & ((v3 = 0 & v2 =
% 14.15/2.80 0) | (v1 = 0 & v0 = 0)))
% 14.15/2.80
% 14.15/2.80 (holds(conseq(scope(318)), 525, 0))
% 14.15/2.80 $i(vd520) & $i(vd518) & $i(vd519) & $i(vd517) & ? [v0: $i] : ? [v1: $i] : ?
% 14.15/2.80 [v2: int] : ( ~ (v2 = 0) & vmul(vd518, vd520) = v1 & vmul(vd517, vd519) = v0 &
% 14.15/2.80 greater(v0, v1) = v2 & $i(v1) & $i(v0))
% 14.15/2.80
% 14.15/2.80 (function-axioms)
% 14.15/2.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.15/2.80 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 14.15/2.80 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2)
% 14.15/2.80 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.15/2.80 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2)
% 14.15/2.80 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 14.15/2.80 : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) &
% 14.15/2.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.15/2.80 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 14.15/2.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.15/2.80 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 14.15/2.80 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 14.15/2.80 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 14.15/2.80 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 14.15/2.80
% 14.15/2.80 Further assumptions not needed in the proof:
% 14.15/2.80 --------------------------------------------
% 14.15/2.80 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 14.15/2.80 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 14.15/2.80 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 14.15/2.80 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 14.15/2.80 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290,
% 14.15/2.80 0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 1), ass(cond(33, 0), 0),
% 14.15/2.80 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0),
% 14.15/2.80 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(conjunct1(307), 0), 0),
% 14.15/2.80 ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(conjunct2(conjunct2(307)),
% 14.15/2.80 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1),
% 14.15/2.80 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0),
% 14.15/2.80 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 14.15/2.80 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0),
% 14.15/2.80 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88),
% 14.15/2.80 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 14.15/2.80 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 14.15/2.80 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 17), 1),
% 14.15/2.80 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3),
% 14.15/2.80 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 14.15/2.80 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 14.15/2.80 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)),
% 14.15/2.80 holds(scope(axiom(1)), 2, 0))
% 14.15/2.80
% 14.15/2.80 Those formulas are unsatisfiable:
% 14.15/2.80 ---------------------------------
% 14.15/2.80
% 14.15/2.80 Begin of proof
% 14.15/2.80 |
% 14.15/2.81 | ALPHA: (dis(antec(scope(318)))) implies:
% 14.15/2.81 | (1) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : (geq(vd519,
% 14.15/2.81 | vd520) = v2 & geq(vd517, vd518) = v1 & greater(vd519, vd520) = v0 &
% 14.15/2.81 | greater(vd517, vd518) = v3 & ((v3 = 0 & v2 = 0) | (v1 = 0 & v0 = 0)))
% 14.15/2.81 |
% 14.15/2.81 | ALPHA: (def(cond(conseq(axiom(3)), 16), 1)) implies:
% 14.15/2.81 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1)
% 14.15/2.81 | | ~ $i(v0) | greater(v1, v0) = 0)
% 14.15/2.81 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) =
% 14.15/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~
% 14.15/2.81 | (v3 = 0) & greater(v1, v0) = v3)))
% 14.15/2.81 |
% 14.15/2.81 | ALPHA: (holds(conseq(scope(318)), 525, 0)) implies:
% 14.15/2.81 | (4) $i(vd517)
% 14.15/2.81 | (5) $i(vd519)
% 14.15/2.81 | (6) $i(vd518)
% 14.15/2.81 | (7) $i(vd520)
% 14.15/2.81 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vmul(vd518,
% 14.15/2.81 | vd520) = v1 & vmul(vd517, vd519) = v0 & greater(v0, v1) = v2 &
% 14.15/2.81 | $i(v1) & $i(v0))
% 14.15/2.81 |
% 14.15/2.81 | ALPHA: (function-axioms) implies:
% 14.15/2.81 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.15/2.81 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 14.15/2.81 | v2) = v0))
% 14.15/2.81 |
% 14.15/2.81 | DELTA: instantiating (8) with fresh symbols all_60_0, all_60_1, all_60_2
% 14.15/2.81 | gives:
% 14.15/2.81 | (10) ~ (all_60_0 = 0) & vmul(vd518, vd520) = all_60_1 & vmul(vd517, vd519)
% 14.15/2.81 | = all_60_2 & greater(all_60_2, all_60_1) = all_60_0 & $i(all_60_1) &
% 14.15/2.81 | $i(all_60_2)
% 14.15/2.81 |
% 14.15/2.81 | ALPHA: (10) implies:
% 14.15/2.81 | (11) ~ (all_60_0 = 0)
% 14.15/2.81 | (12) greater(all_60_2, all_60_1) = all_60_0
% 14.15/2.81 | (13) vmul(vd517, vd519) = all_60_2
% 14.15/2.81 | (14) vmul(vd518, vd520) = all_60_1
% 14.15/2.81 |
% 14.15/2.81 | DELTA: instantiating (1) with fresh symbols all_64_0, all_64_1, all_64_2,
% 14.15/2.81 | all_64_3 gives:
% 14.15/2.81 | (15) geq(vd519, vd520) = all_64_1 & geq(vd517, vd518) = all_64_2 &
% 14.15/2.81 | greater(vd519, vd520) = all_64_3 & greater(vd517, vd518) = all_64_0 &
% 14.15/2.81 | ((all_64_0 = 0 & all_64_1 = 0) | (all_64_2 = 0 & all_64_3 = 0))
% 14.15/2.81 |
% 14.15/2.81 | ALPHA: (15) implies:
% 14.15/2.82 | (16) greater(vd517, vd518) = all_64_0
% 14.15/2.82 | (17) greater(vd519, vd520) = all_64_3
% 14.15/2.82 | (18) geq(vd517, vd518) = all_64_2
% 14.15/2.82 | (19) geq(vd519, vd520) = all_64_1
% 14.15/2.82 | (20) (all_64_0 = 0 & all_64_1 = 0) | (all_64_2 = 0 & all_64_3 = 0)
% 14.15/2.82 |
% 14.15/2.82 | GROUND_INST: instantiating (3) with vd518, vd517, all_64_2, simplifying with
% 14.15/2.82 | (4), (6), (18) gives:
% 14.15/2.82 | (21) all_64_2 = 0 | ( ~ (vd518 = vd517) & ? [v0: int] : ( ~ (v0 = 0) &
% 14.15/2.82 | greater(vd517, vd518) = v0))
% 14.15/2.82 |
% 14.15/2.82 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd517, vd519, all_60_2,
% 14.15/2.82 | simplifying with (4), (5), (13) gives:
% 14.15/2.82 | (22) vmul(vd519, vd517) = all_60_2 & $i(all_60_2)
% 14.15/2.82 |
% 14.15/2.82 | ALPHA: (22) implies:
% 14.15/2.82 | (23) vmul(vd519, vd517) = all_60_2
% 14.15/2.82 |
% 14.15/2.82 | GROUND_INST: instantiating (ass(cond(312, 0), 0)) with vd517, vd518, vd519,
% 14.15/2.82 | vd520, all_60_2, all_60_1, all_60_0, simplifying with (4), (5),
% 14.15/2.82 | (6), (7), (12), (13), (14) gives:
% 14.15/2.82 | (24) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) =
% 14.15/2.82 | v0 & greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.15/2.82 |
% 14.15/2.82 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd518, vd520, all_60_1,
% 14.15/2.82 | simplifying with (6), (7), (14) gives:
% 14.15/2.82 | (25) vmul(vd520, vd518) = all_60_1 & $i(all_60_1)
% 14.15/2.82 |
% 14.15/2.82 | ALPHA: (25) implies:
% 14.15/2.82 | (26) vmul(vd520, vd518) = all_60_1
% 14.15/2.82 |
% 14.15/2.82 | GROUND_INST: instantiating (ass(cond(312, 0), 0)) with vd519, vd520, vd517,
% 14.15/2.82 | vd518, all_60_2, all_60_1, all_60_0, simplifying with (4), (5),
% 14.15/2.82 | (6), (7), (12), (23), (26) gives:
% 14.15/2.82 | (27) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) =
% 14.15/2.82 | v1 & greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.15/2.82 |
% 14.15/2.82 | BETA: splitting (20) gives:
% 14.15/2.82 |
% 14.15/2.82 | Case 1:
% 14.15/2.82 | |
% 14.15/2.82 | | (28) all_64_0 = 0 & all_64_1 = 0
% 14.15/2.82 | |
% 14.15/2.82 | | ALPHA: (28) implies:
% 14.15/2.82 | | (29) all_64_1 = 0
% 14.15/2.82 | | (30) all_64_0 = 0
% 14.15/2.82 | |
% 14.15/2.82 | | REDUCE: (19), (29) imply:
% 14.15/2.82 | | (31) geq(vd519, vd520) = 0
% 14.15/2.82 | |
% 14.15/2.82 | | REDUCE: (16), (30) imply:
% 14.15/2.82 | | (32) greater(vd517, vd518) = 0
% 14.15/2.82 | |
% 14.15/2.82 | | BETA: splitting (27) gives:
% 14.15/2.82 | |
% 14.15/2.82 | | Case 1:
% 14.15/2.82 | | |
% 14.15/2.82 | | | (33) all_60_0 = 0
% 14.15/2.82 | | |
% 14.15/2.82 | | | REDUCE: (11), (33) imply:
% 14.15/2.82 | | | (34) $false
% 14.27/2.83 | | |
% 14.27/2.83 | | | CLOSE: (34) is inconsistent.
% 14.27/2.83 | | |
% 14.27/2.83 | | Case 2:
% 14.27/2.83 | | |
% 14.27/2.83 | | | (35) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v1 &
% 14.27/2.83 | | | greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.83 | | |
% 14.27/2.83 | | | DELTA: instantiating (35) with fresh symbols all_133_0, all_133_1 gives:
% 14.27/2.83 | | | (36) greater(vd519, vd520) = all_133_0 & greater(vd517, vd518) =
% 14.27/2.83 | | | all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0))
% 14.27/2.83 | | |
% 14.27/2.83 | | | ALPHA: (36) implies:
% 14.27/2.83 | | | (37) greater(vd517, vd518) = all_133_1
% 14.27/2.83 | | |
% 14.27/2.83 | | | BETA: splitting (24) gives:
% 14.27/2.83 | | |
% 14.27/2.83 | | | Case 1:
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | (38) all_60_0 = 0
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | REDUCE: (11), (38) imply:
% 14.27/2.83 | | | | (39) $false
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | CLOSE: (39) is inconsistent.
% 14.27/2.83 | | | |
% 14.27/2.83 | | | Case 2:
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | (40) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v0 &
% 14.27/2.83 | | | | greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | DELTA: instantiating (40) with fresh symbols all_139_0, all_139_1 gives:
% 14.27/2.83 | | | | (41) greater(vd519, vd520) = all_139_1 & greater(vd517, vd518) =
% 14.27/2.83 | | | | all_139_0 & ( ~ (all_139_0 = 0) | ~ (all_139_1 = 0))
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | ALPHA: (41) implies:
% 14.27/2.83 | | | | (42) greater(vd517, vd518) = all_139_0
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | BETA: splitting (21) gives:
% 14.27/2.83 | | | |
% 14.27/2.83 | | | | Case 1:
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | (43) all_64_2 = 0
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | REDUCE: (18), (43) imply:
% 14.27/2.83 | | | | | (44) geq(vd517, vd518) = 0
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | GROUND_INST: instantiating (9) with all_133_1, all_139_0, vd518,
% 14.27/2.83 | | | | | vd517, simplifying with (37), (42) gives:
% 14.27/2.83 | | | | | (45) all_139_0 = all_133_1
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | GROUND_INST: instantiating (9) with 0, all_139_0, vd518, vd517,
% 14.27/2.83 | | | | | simplifying with (32), (42) gives:
% 14.27/2.83 | | | | | (46) all_139_0 = 0
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | COMBINE_EQS: (45), (46) imply:
% 14.27/2.83 | | | | | (47) all_133_1 = 0
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | SIMP: (47) implies:
% 14.27/2.83 | | | | | (48) all_133_1 = 0
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | GROUND_INST: instantiating (2) with vd520, vd519, simplifying with
% 14.27/2.83 | | | | | (5), (7), (31) gives:
% 14.27/2.83 | | | | | (49) vd520 = vd519 | greater(vd519, vd520) = 0
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | BETA: splitting (49) gives:
% 14.27/2.83 | | | | |
% 14.27/2.83 | | | | | Case 1:
% 14.27/2.83 | | | | | |
% 14.27/2.83 | | | | | | (50) greater(vd519, vd520) = 0
% 14.27/2.83 | | | | | |
% 14.27/2.83 | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23),
% 14.27/2.83 | | | | | | (24), (26), (27), (44), (50), (ass(cond(299, 0), 2)) are
% 14.27/2.83 | | | | | | inconsistent by sub-proof #2.
% 14.27/2.83 | | | | | |
% 14.27/2.83 | | | | | Case 2:
% 14.27/2.83 | | | | | |
% 14.27/2.83 | | | | | | (51) vd520 = vd519
% 14.27/2.83 | | | | | |
% 14.27/2.83 | | | | | | REDUCE: (14), (51) imply:
% 14.27/2.83 | | | | | | (52) vmul(vd518, vd519) = all_60_1
% 14.27/2.83 | | | | | |
% 14.27/2.83 | | | | | | GROUND_INST: instantiating (ass(cond(299, 0), 2)) with vd519, vd517,
% 14.27/2.83 | | | | | | vd518, all_60_2, all_60_1, all_60_0, simplifying with
% 14.27/2.83 | | | | | | (4), (5), (6), (12), (13), (52) gives:
% 14.27/2.84 | | | | | | (53) all_60_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd517,
% 14.27/2.84 | | | | | | vd518) = v0)
% 14.27/2.84 | | | | | |
% 14.27/2.84 | | | | | | BETA: splitting (53) gives:
% 14.27/2.84 | | | | | |
% 14.27/2.84 | | | | | | Case 1:
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | | (54) all_60_0 = 0
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | | REDUCE: (11), (54) imply:
% 14.27/2.84 | | | | | | | (55) $false
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | | CLOSE: (55) is inconsistent.
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | Case 2:
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & greater(vd517, vd518) = v0)
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | | DELTA: instantiating (56) with fresh symbol all_179_0 gives:
% 14.27/2.84 | | | | | | | (57) ~ (all_179_0 = 0) & greater(vd517, vd518) = all_179_0
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | | REF_CLOSE: (9), (32), (57) are inconsistent by sub-proof #1.
% 14.27/2.84 | | | | | | |
% 14.27/2.84 | | | | | | End of split
% 14.27/2.84 | | | | | |
% 14.27/2.84 | | | | | End of split
% 14.27/2.84 | | | | |
% 14.27/2.84 | | | | Case 2:
% 14.27/2.84 | | | | |
% 14.27/2.84 | | | | | (58) ~ (vd518 = vd517) & ? [v0: int] : ( ~ (v0 = 0) &
% 14.27/2.84 | | | | | greater(vd517, vd518) = v0)
% 14.27/2.84 | | | | |
% 14.27/2.84 | | | | | ALPHA: (58) implies:
% 14.27/2.84 | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & greater(vd517, vd518) = v0)
% 14.27/2.84 | | | | |
% 14.27/2.84 | | | | | DELTA: instantiating (59) with fresh symbol all_179_0 gives:
% 14.27/2.84 | | | | | (60) ~ (all_179_0 = 0) & greater(vd517, vd518) = all_179_0
% 14.27/2.84 | | | | |
% 14.27/2.84 | | | | | REF_CLOSE: (9), (32), (60) are inconsistent by sub-proof #1.
% 14.27/2.84 | | | | |
% 14.27/2.84 | | | | End of split
% 14.27/2.84 | | | |
% 14.27/2.84 | | | End of split
% 14.27/2.84 | | |
% 14.27/2.84 | | End of split
% 14.27/2.84 | |
% 14.27/2.84 | Case 2:
% 14.27/2.84 | |
% 14.27/2.84 | | (61) all_64_2 = 0 & all_64_3 = 0
% 14.27/2.84 | |
% 14.27/2.84 | | ALPHA: (61) implies:
% 14.27/2.84 | | (62) all_64_3 = 0
% 14.27/2.84 | | (63) all_64_2 = 0
% 14.27/2.84 | |
% 14.27/2.84 | | REDUCE: (18), (63) imply:
% 14.27/2.84 | | (64) geq(vd517, vd518) = 0
% 14.27/2.84 | |
% 14.27/2.84 | | REDUCE: (17), (62) imply:
% 14.27/2.84 | | (65) greater(vd519, vd520) = 0
% 14.27/2.84 | |
% 14.27/2.84 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23), (24), (26),
% 14.27/2.84 | | (27), (64), (65), (ass(cond(299, 0), 2)) are inconsistent by
% 14.27/2.84 | | sub-proof #2.
% 14.27/2.84 | |
% 14.27/2.84 | End of split
% 14.27/2.84 |
% 14.27/2.84 End of proof
% 14.27/2.84
% 14.27/2.84 Sub-proof #1 shows that the following formulas are inconsistent:
% 14.27/2.84 ----------------------------------------------------------------
% 14.27/2.84 (1) ~ (all_179_0 = 0) & greater(vd517, vd518) = all_179_0
% 14.27/2.84 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.27/2.84 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) =
% 14.27/2.84 v0))
% 14.27/2.84 (3) greater(vd517, vd518) = 0
% 14.27/2.84
% 14.27/2.84 Begin of proof
% 14.27/2.84 |
% 14.27/2.84 | ALPHA: (1) implies:
% 14.27/2.84 | (4) ~ (all_179_0 = 0)
% 14.27/2.84 | (5) greater(vd517, vd518) = all_179_0
% 14.27/2.84 |
% 14.27/2.84 | GROUND_INST: instantiating (2) with 0, all_179_0, vd518, vd517, simplifying
% 14.27/2.84 | with (3), (5) gives:
% 14.27/2.84 | (6) all_179_0 = 0
% 14.27/2.84 |
% 14.27/2.84 | REDUCE: (4), (6) imply:
% 14.27/2.84 | (7) $false
% 14.27/2.84 |
% 14.27/2.84 | CLOSE: (7) is inconsistent.
% 14.27/2.84 |
% 14.27/2.84 End of proof
% 14.27/2.84
% 14.27/2.84 Sub-proof #2 shows that the following formulas are inconsistent:
% 14.27/2.84 ----------------------------------------------------------------
% 14.27/2.85 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 14.27/2.85 [v5: int] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) |
% 14.27/2.85 ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 14.27/2.85 int] : ( ~ (v6 = 0) & greater(v1, v2) = v6))
% 14.27/2.85 (2) vmul(vd520, vd518) = all_60_1
% 14.27/2.85 (3) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v0
% 14.27/2.85 & greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.85 (4) vmul(vd519, vd517) = all_60_2
% 14.27/2.85 (5) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v1
% 14.27/2.85 & greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.85 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.27/2.85 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) =
% 14.27/2.85 v0))
% 14.27/2.85 (7) geq(vd517, vd518) = 0
% 14.27/2.85 (8) ~ (all_60_0 = 0)
% 14.27/2.85 (9) $i(vd519)
% 14.27/2.85 (10) $i(vd520)
% 14.27/2.85 (11) $i(vd518)
% 14.27/2.85 (12) $i(vd517)
% 14.27/2.85 (13) greater(vd519, vd520) = 0
% 14.27/2.85 (14) greater(all_60_2, all_60_1) = all_60_0
% 14.27/2.85 (15) greater(vd517, vd518) = all_64_0
% 14.27/2.85 (16) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1)
% 14.27/2.85 | ~ $i(v0) | greater(v1, v0) = 0)
% 14.27/2.85
% 14.27/2.85 Begin of proof
% 14.27/2.85 |
% 14.27/2.85 | BETA: splitting (5) gives:
% 14.27/2.85 |
% 14.27/2.85 | Case 1:
% 14.27/2.85 | |
% 14.27/2.85 | | (17) all_60_0 = 0
% 14.27/2.85 | |
% 14.27/2.85 | | REDUCE: (8), (17) imply:
% 14.27/2.85 | | (18) $false
% 14.27/2.85 | |
% 14.27/2.85 | | CLOSE: (18) is inconsistent.
% 14.27/2.85 | |
% 14.27/2.85 | Case 2:
% 14.27/2.85 | |
% 14.27/2.85 | | (19) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v1 &
% 14.27/2.85 | | greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.85 | |
% 14.27/2.85 | | DELTA: instantiating (19) with fresh symbols all_133_0, all_133_1 gives:
% 14.27/2.85 | | (20) greater(vd519, vd520) = all_133_0 & greater(vd517, vd518) =
% 14.27/2.85 | | all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0))
% 14.27/2.85 | |
% 14.27/2.85 | | ALPHA: (20) implies:
% 14.27/2.85 | | (21) greater(vd517, vd518) = all_133_1
% 14.27/2.85 | | (22) greater(vd519, vd520) = all_133_0
% 14.27/2.85 | | (23) ~ (all_133_0 = 0) | ~ (all_133_1 = 0)
% 14.27/2.85 | |
% 14.27/2.85 | | BETA: splitting (3) gives:
% 14.27/2.85 | |
% 14.27/2.85 | | Case 1:
% 14.27/2.85 | | |
% 14.27/2.85 | | | (24) all_60_0 = 0
% 14.27/2.85 | | |
% 14.27/2.85 | | | REDUCE: (8), (24) imply:
% 14.27/2.85 | | | (25) $false
% 14.27/2.85 | | |
% 14.27/2.85 | | | CLOSE: (25) is inconsistent.
% 14.27/2.85 | | |
% 14.27/2.85 | | Case 2:
% 14.27/2.85 | | |
% 14.27/2.85 | | | (26) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v0 &
% 14.27/2.85 | | | greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.86 | | |
% 14.27/2.86 | | | DELTA: instantiating (26) with fresh symbols all_143_0, all_143_1 gives:
% 14.27/2.86 | | | (27) greater(vd519, vd520) = all_143_1 & greater(vd517, vd518) =
% 14.27/2.86 | | | all_143_0 & ( ~ (all_143_0 = 0) | ~ (all_143_1 = 0))
% 14.27/2.86 | | |
% 14.27/2.86 | | | ALPHA: (27) implies:
% 14.27/2.86 | | | (28) greater(vd517, vd518) = all_143_0
% 14.27/2.86 | | | (29) greater(vd519, vd520) = all_143_1
% 14.27/2.86 | | |
% 14.27/2.86 | | | GROUND_INST: instantiating (6) with all_64_0, all_143_0, vd518, vd517,
% 14.27/2.86 | | | simplifying with (15), (28) gives:
% 14.27/2.86 | | | (30) all_143_0 = all_64_0
% 14.27/2.86 | | |
% 14.27/2.86 | | | GROUND_INST: instantiating (6) with all_133_1, all_143_0, vd518, vd517,
% 14.27/2.86 | | | simplifying with (21), (28) gives:
% 14.27/2.86 | | | (31) all_143_0 = all_133_1
% 14.27/2.86 | | |
% 14.27/2.86 | | | GROUND_INST: instantiating (6) with all_133_0, all_143_1, vd520, vd519,
% 14.27/2.86 | | | simplifying with (22), (29) gives:
% 14.27/2.86 | | | (32) all_143_1 = all_133_0
% 14.27/2.86 | | |
% 14.27/2.86 | | | GROUND_INST: instantiating (6) with 0, all_143_1, vd520, vd519,
% 14.27/2.86 | | | simplifying with (13), (29) gives:
% 14.27/2.86 | | | (33) all_143_1 = 0
% 14.27/2.86 | | |
% 14.27/2.86 | | | COMBINE_EQS: (30), (31) imply:
% 14.27/2.86 | | | (34) all_133_1 = all_64_0
% 14.27/2.86 | | |
% 14.27/2.86 | | | COMBINE_EQS: (32), (33) imply:
% 14.27/2.86 | | | (35) all_133_0 = 0
% 14.27/2.86 | | |
% 14.27/2.86 | | | SIMP: (35) implies:
% 14.27/2.86 | | | (36) all_133_0 = 0
% 14.27/2.86 | | |
% 14.27/2.86 | | | BETA: splitting (23) gives:
% 14.27/2.86 | | |
% 14.27/2.86 | | | Case 1:
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | (37) ~ (all_133_0 = 0)
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | REDUCE: (36), (37) imply:
% 14.27/2.86 | | | | (38) $false
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | CLOSE: (38) is inconsistent.
% 14.27/2.86 | | | |
% 14.27/2.86 | | | Case 2:
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | (39) ~ (all_133_1 = 0)
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | REDUCE: (34), (39) imply:
% 14.27/2.86 | | | | (40) ~ (all_64_0 = 0)
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | GROUND_INST: instantiating (16) with vd518, vd517, simplifying with (7),
% 14.27/2.86 | | | | (11), (12) gives:
% 14.27/2.86 | | | | (41) vd518 = vd517 | greater(vd517, vd518) = 0
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | BETA: splitting (41) gives:
% 14.27/2.86 | | | |
% 14.27/2.86 | | | | Case 1:
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | (42) greater(vd517, vd518) = 0
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | GROUND_INST: instantiating (6) with all_64_0, 0, vd518, vd517,
% 14.27/2.86 | | | | | simplifying with (15), (42) gives:
% 14.27/2.86 | | | | | (43) all_64_0 = 0
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | REDUCE: (40), (43) imply:
% 14.27/2.86 | | | | | (44) $false
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | CLOSE: (44) is inconsistent.
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | Case 2:
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | (45) vd518 = vd517
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | REDUCE: (2), (45) imply:
% 14.27/2.86 | | | | | (46) vmul(vd520, vd517) = all_60_1
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | GROUND_INST: instantiating (1) with vd517, vd519, vd520, all_60_2,
% 14.27/2.86 | | | | | all_60_1, all_60_0, simplifying with (4), (9), (10),
% 14.27/2.86 | | | | | (12), (14), (46) gives:
% 14.27/2.86 | | | | | (47) all_60_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd519,
% 14.27/2.86 | | | | | vd520) = v0)
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | BETA: splitting (47) gives:
% 14.27/2.86 | | | | |
% 14.27/2.86 | | | | | Case 1:
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | (48) all_60_0 = 0
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | REDUCE: (8), (48) imply:
% 14.27/2.86 | | | | | | (49) $false
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | CLOSE: (49) is inconsistent.
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | Case 2:
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & greater(vd519, vd520) = v0)
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | DELTA: instantiating (50) with fresh symbol all_139_0 gives:
% 14.27/2.86 | | | | | | (51) ~ (all_139_0 = 0) & greater(vd519, vd520) = all_139_0
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | ALPHA: (51) implies:
% 14.27/2.86 | | | | | | (52) ~ (all_139_0 = 0)
% 14.27/2.86 | | | | | | (53) greater(vd519, vd520) = all_139_0
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | BETA: splitting (3) gives:
% 14.27/2.86 | | | | | |
% 14.27/2.86 | | | | | | Case 1:
% 14.27/2.86 | | | | | | |
% 14.27/2.86 | | | | | | | (54) all_60_0 = 0
% 14.27/2.86 | | | | | | |
% 14.27/2.86 | | | | | | | REDUCE: (8), (54) imply:
% 14.27/2.86 | | | | | | | (55) $false
% 14.27/2.86 | | | | | | |
% 14.27/2.86 | | | | | | | CLOSE: (55) is inconsistent.
% 14.27/2.86 | | | | | | |
% 14.27/2.87 | | | | | | Case 2:
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | DELTA: instantiating (26) with fresh symbols all_145_0, all_145_1
% 14.27/2.87 | | | | | | | gives:
% 14.27/2.87 | | | | | | | (56) greater(vd519, vd520) = all_145_1 & greater(vd517, vd518)
% 14.27/2.87 | | | | | | | = all_145_0 & ( ~ (all_145_0 = 0) | ~ (all_145_1 = 0))
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | ALPHA: (56) implies:
% 14.27/2.87 | | | | | | | (57) greater(vd519, vd520) = all_145_1
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | GROUND_INST: instantiating (6) with all_133_0, all_139_0, vd520,
% 14.27/2.87 | | | | | | | vd519, simplifying with (22), (53) gives:
% 14.27/2.87 | | | | | | | (58) all_139_0 = all_133_0
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | GROUND_INST: instantiating (6) with all_139_0, all_145_1, vd520,
% 14.27/2.87 | | | | | | | vd519, simplifying with (53), (57) gives:
% 14.27/2.87 | | | | | | | (59) all_145_1 = all_139_0
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | GROUND_INST: instantiating (6) with 0, all_145_1, vd520, vd519,
% 14.27/2.87 | | | | | | | simplifying with (13), (57) gives:
% 14.27/2.87 | | | | | | | (60) all_145_1 = 0
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | COMBINE_EQS: (59), (60) imply:
% 14.27/2.87 | | | | | | | (61) all_139_0 = 0
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | SIMP: (61) implies:
% 14.27/2.87 | | | | | | | (62) all_139_0 = 0
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | REDUCE: (52), (62) imply:
% 14.27/2.87 | | | | | | | (63) $false
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | | CLOSE: (63) is inconsistent.
% 14.27/2.87 | | | | | | |
% 14.27/2.87 | | | | | | End of split
% 14.27/2.87 | | | | | |
% 14.27/2.87 | | | | | End of split
% 14.27/2.87 | | | | |
% 14.27/2.87 | | | | End of split
% 14.27/2.87 | | | |
% 14.27/2.87 | | | End of split
% 14.27/2.87 | | |
% 14.27/2.87 | | End of split
% 14.27/2.87 | |
% 14.27/2.87 | End of split
% 14.27/2.87 |
% 14.27/2.87 End of proof
% 14.27/2.87 % SZS output end Proof for theBenchmark
% 14.27/2.87
% 14.27/2.87 2246ms
%------------------------------------------------------------------------------