TSTP Solution File: NUM842+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM842+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 11:50:20 EDT 2023
% Result : Theorem 10.68s 2.18s
% Output : Proof 13.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : NUM842+1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.31 % Computer : n023.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Fri Aug 25 08:10:27 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.16/0.57 ________ _____
% 0.16/0.57 ___ __ \_________(_)________________________________
% 0.16/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.57
% 0.16/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.57 (2023-06-19)
% 0.16/0.57
% 0.16/0.57 (c) Philipp Rümmer, 2009-2023
% 0.16/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.57 Amanda Stjerna.
% 0.16/0.57 Free software under BSD-3-Clause.
% 0.16/0.57
% 0.16/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.57
% 0.16/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.58 Running up to 7 provers in parallel.
% 0.65/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.78/1.08 Prover 4: Preprocessing ...
% 2.78/1.08 Prover 1: Preprocessing ...
% 3.22/1.12 Prover 0: Preprocessing ...
% 3.22/1.12 Prover 5: Preprocessing ...
% 3.22/1.12 Prover 2: Preprocessing ...
% 3.22/1.12 Prover 6: Preprocessing ...
% 3.22/1.12 Prover 3: Preprocessing ...
% 6.37/1.53 Prover 1: Warning: ignoring some quantifiers
% 6.52/1.58 Prover 1: Constructing countermodel ...
% 6.52/1.58 Prover 6: Proving ...
% 6.52/1.58 Prover 5: Proving ...
% 6.52/1.58 Prover 3: Warning: ignoring some quantifiers
% 6.52/1.60 Prover 3: Constructing countermodel ...
% 7.10/1.63 Prover 2: Proving ...
% 7.10/1.67 Prover 4: Warning: ignoring some quantifiers
% 7.63/1.73 Prover 4: Constructing countermodel ...
% 8.26/1.79 Prover 0: Proving ...
% 10.68/2.18 Prover 3: proved (1588ms)
% 10.68/2.18
% 10.68/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.68/2.18
% 10.68/2.18 Prover 6: proved (1587ms)
% 10.68/2.18
% 10.68/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.68/2.18
% 10.68/2.18 Prover 5: stopped
% 10.68/2.18 Prover 2: stopped
% 10.68/2.20 Prover 0: stopped
% 10.68/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.68/2.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.68/2.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.68/2.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.68/2.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.68/2.23 Prover 8: Preprocessing ...
% 11.49/2.26 Prover 7: Preprocessing ...
% 11.49/2.26 Prover 11: Preprocessing ...
% 11.49/2.26 Prover 10: Preprocessing ...
% 11.49/2.27 Prover 13: Preprocessing ...
% 12.30/2.33 Prover 1: Found proof (size 200)
% 12.30/2.33 Prover 1: proved (1740ms)
% 12.30/2.33 Prover 4: stopped
% 12.30/2.33 Prover 13: stopped
% 12.30/2.34 Prover 10: Warning: ignoring some quantifiers
% 12.30/2.35 Prover 10: Constructing countermodel ...
% 12.30/2.35 Prover 8: Warning: ignoring some quantifiers
% 12.30/2.36 Prover 7: Warning: ignoring some quantifiers
% 12.30/2.36 Prover 10: stopped
% 12.30/2.37 Prover 7: Constructing countermodel ...
% 12.30/2.37 Prover 8: Constructing countermodel ...
% 12.30/2.38 Prover 7: stopped
% 12.30/2.38 Prover 8: stopped
% 12.30/2.39 Prover 11: Warning: ignoring some quantifiers
% 12.30/2.40 Prover 11: Constructing countermodel ...
% 12.89/2.41 Prover 11: stopped
% 12.89/2.41
% 12.89/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.89/2.41
% 12.89/2.43 % SZS output start Proof for theBenchmark
% 12.89/2.43 Assumptions after simplification:
% 12.89/2.43 ---------------------------------
% 12.89/2.43
% 12.89/2.43 (ass(cond(209, 0), 0))
% 12.89/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.89/2.46 $i] : ! [v6: int] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) =
% 12.89/2.46 v4) | ~ (greater(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.89/2.46 $i(v0) | ? [v7: any] : ? [v8: any] : (greater(v2, v3) = v7 & greater(v0,
% 12.89/2.46 v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 12.89/2.46
% 12.89/2.46 (ass(cond(61, 0), 0))
% 12.89/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1)
% 12.89/2.46 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2)))
% 12.89/2.46
% 12.89/2.46 (ass(cond(goal(193), 0), 2))
% 12.89/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.89/2.46 int] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~
% 12.89/2.46 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] :
% 12.89/2.46 ( ~ (v6 = 0) & greater(v0, v1) = v6))
% 12.89/2.46
% 12.89/2.46 (def(cond(conseq(axiom(3)), 16), 1))
% 12.89/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) = v2) |
% 12.89/2.46 ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) &
% 12.89/2.46 greater(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 12.89/2.46 (geq(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | greater(v1, v0) = 0)
% 12.89/2.46
% 12.89/2.46 (dis(antec(218)))
% 12.89/2.47 $i(vd356) & $i(vd354) & $i(vd355) & $i(vd353) & ? [v0: any] : ? [v1: any] :
% 12.89/2.47 ? [v2: any] : ? [v3: any] : (geq(vd355, vd356) = v2 & geq(vd353, vd354) = v1
% 12.89/2.47 & greater(vd355, vd356) = v0 & greater(vd353, vd354) = v3 & ((v3 = 0 & v2 =
% 12.89/2.47 0) | (v1 = 0 & v0 = 0)))
% 12.89/2.47
% 12.89/2.47 (holds(conseq(218), 361, 0))
% 12.89/2.47 $i(vd356) & $i(vd354) & $i(vd355) & $i(vd353) & ? [v0: $i] : ? [v1: $i] : ?
% 12.89/2.47 [v2: int] : ( ~ (v2 = 0) & vplus(vd354, vd356) = v1 & vplus(vd353, vd355) = v0
% 12.89/2.47 & greater(v0, v1) = v2 & $i(v1) & $i(v0))
% 12.89/2.47
% 12.89/2.47 (function-axioms)
% 12.89/2.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.89/2.47 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 12.89/2.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.89/2.47 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] :
% 12.89/2.47 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) |
% 12.89/2.47 ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.89/2.47 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (geq(v3, v2)
% 12.89/2.47 = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.89/2.47 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3,
% 12.89/2.47 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 12.89/2.47 [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & !
% 12.89/2.47 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~
% 12.89/2.47 (vsucc(v2) = v0))
% 12.89/2.47
% 12.89/2.47 Further assumptions not needed in the proof:
% 12.89/2.47 --------------------------------------------
% 12.89/2.48 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 12.89/2.48 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 12.89/2.48 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0),
% 12.89/2.48 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(73, 0), 0), ass(cond(81,
% 12.89/2.48 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1),
% 12.89/2.48 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0),
% 12.89/2.48 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 12.89/2.48 ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0),
% 12.89/2.48 2), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88),
% 12.89/2.48 0), 2), ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 12.89/2.48 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 17), 1),
% 12.89/2.48 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3),
% 12.89/2.48 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 12.89/2.48 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))
% 12.89/2.48
% 12.89/2.48 Those formulas are unsatisfiable:
% 12.89/2.48 ---------------------------------
% 12.89/2.48
% 12.89/2.48 Begin of proof
% 12.89/2.48 |
% 12.89/2.48 | ALPHA: (dis(antec(218))) implies:
% 12.89/2.48 | (1) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : (geq(vd355,
% 12.89/2.48 | vd356) = v2 & geq(vd353, vd354) = v1 & greater(vd355, vd356) = v0 &
% 12.89/2.48 | greater(vd353, vd354) = v3 & ((v3 = 0 & v2 = 0) | (v1 = 0 & v0 = 0)))
% 12.89/2.48 |
% 12.89/2.48 | ALPHA: (def(cond(conseq(axiom(3)), 16), 1)) implies:
% 12.89/2.48 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1)
% 12.89/2.48 | | ~ $i(v0) | greater(v1, v0) = 0)
% 12.89/2.48 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) =
% 12.89/2.48 | v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~
% 12.89/2.48 | (v3 = 0) & greater(v1, v0) = v3)))
% 12.89/2.48 |
% 12.89/2.48 | ALPHA: (holds(conseq(218), 361, 0)) implies:
% 12.89/2.48 | (4) $i(vd353)
% 12.89/2.48 | (5) $i(vd355)
% 12.89/2.48 | (6) $i(vd354)
% 13.26/2.48 | (7) $i(vd356)
% 13.26/2.48 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vplus(vd354,
% 13.26/2.48 | vd356) = v1 & vplus(vd353, vd355) = v0 & greater(v0, v1) = v2 &
% 13.26/2.48 | $i(v1) & $i(v0))
% 13.26/2.48 |
% 13.26/2.48 | ALPHA: (function-axioms) implies:
% 13.26/2.49 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.26/2.49 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 13.26/2.49 | v2) = v0))
% 13.26/2.49 |
% 13.26/2.49 | DELTA: instantiating (8) with fresh symbols all_42_0, all_42_1, all_42_2
% 13.26/2.49 | gives:
% 13.26/2.49 | (10) ~ (all_42_0 = 0) & vplus(vd354, vd356) = all_42_1 & vplus(vd353,
% 13.26/2.49 | vd355) = all_42_2 & greater(all_42_2, all_42_1) = all_42_0 &
% 13.26/2.49 | $i(all_42_1) & $i(all_42_2)
% 13.26/2.49 |
% 13.26/2.49 | ALPHA: (10) implies:
% 13.26/2.49 | (11) ~ (all_42_0 = 0)
% 13.26/2.49 | (12) greater(all_42_2, all_42_1) = all_42_0
% 13.26/2.49 | (13) vplus(vd353, vd355) = all_42_2
% 13.26/2.49 | (14) vplus(vd354, vd356) = all_42_1
% 13.26/2.49 |
% 13.26/2.49 | DELTA: instantiating (1) with fresh symbols all_46_0, all_46_1, all_46_2,
% 13.26/2.49 | all_46_3 gives:
% 13.26/2.49 | (15) geq(vd355, vd356) = all_46_1 & geq(vd353, vd354) = all_46_2 &
% 13.26/2.49 | greater(vd355, vd356) = all_46_3 & greater(vd353, vd354) = all_46_0 &
% 13.26/2.49 | ((all_46_0 = 0 & all_46_1 = 0) | (all_46_2 = 0 & all_46_3 = 0))
% 13.26/2.49 |
% 13.26/2.49 | ALPHA: (15) implies:
% 13.26/2.49 | (16) greater(vd353, vd354) = all_46_0
% 13.26/2.49 | (17) greater(vd355, vd356) = all_46_3
% 13.26/2.49 | (18) geq(vd353, vd354) = all_46_2
% 13.26/2.49 | (19) geq(vd355, vd356) = all_46_1
% 13.26/2.49 | (20) (all_46_0 = 0 & all_46_1 = 0) | (all_46_2 = 0 & all_46_3 = 0)
% 13.26/2.49 |
% 13.26/2.49 | GROUND_INST: instantiating (3) with vd354, vd353, all_46_2, simplifying with
% 13.26/2.49 | (4), (6), (18) gives:
% 13.26/2.49 | (21) all_46_2 = 0 | ( ~ (vd354 = vd353) & ? [v0: int] : ( ~ (v0 = 0) &
% 13.26/2.49 | greater(vd353, vd354) = v0))
% 13.26/2.49 |
% 13.26/2.49 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd353, vd355, all_42_2,
% 13.26/2.49 | simplifying with (4), (5), (13) gives:
% 13.26/2.49 | (22) vplus(vd355, vd353) = all_42_2 & $i(all_42_2)
% 13.26/2.49 |
% 13.26/2.49 | ALPHA: (22) implies:
% 13.26/2.49 | (23) vplus(vd355, vd353) = all_42_2
% 13.26/2.49 |
% 13.26/2.49 | GROUND_INST: instantiating (ass(cond(209, 0), 0)) with vd353, vd354, vd355,
% 13.26/2.49 | vd356, all_42_2, all_42_1, all_42_0, simplifying with (4), (5),
% 13.26/2.49 | (6), (7), (12), (13), (14) gives:
% 13.26/2.50 | (24) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) =
% 13.26/2.50 | v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.50 |
% 13.26/2.50 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd354, vd356, all_42_1,
% 13.26/2.50 | simplifying with (6), (7), (14) gives:
% 13.26/2.50 | (25) vplus(vd356, vd354) = all_42_1 & $i(all_42_1)
% 13.26/2.50 |
% 13.26/2.50 | ALPHA: (25) implies:
% 13.26/2.50 | (26) vplus(vd356, vd354) = all_42_1
% 13.26/2.50 |
% 13.26/2.50 | GROUND_INST: instantiating (ass(cond(209, 0), 0)) with vd355, vd356, vd353,
% 13.26/2.50 | vd354, all_42_2, all_42_1, all_42_0, simplifying with (4), (5),
% 13.26/2.50 | (6), (7), (12), (23), (26) gives:
% 13.26/2.50 | (27) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) =
% 13.26/2.50 | v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.50 |
% 13.26/2.50 | BETA: splitting (20) gives:
% 13.26/2.50 |
% 13.26/2.50 | Case 1:
% 13.26/2.50 | |
% 13.26/2.50 | | (28) all_46_0 = 0 & all_46_1 = 0
% 13.26/2.50 | |
% 13.26/2.50 | | ALPHA: (28) implies:
% 13.26/2.50 | | (29) all_46_1 = 0
% 13.26/2.50 | | (30) all_46_0 = 0
% 13.26/2.50 | |
% 13.26/2.50 | | REDUCE: (19), (29) imply:
% 13.26/2.50 | | (31) geq(vd355, vd356) = 0
% 13.26/2.50 | |
% 13.26/2.50 | | REDUCE: (16), (30) imply:
% 13.26/2.50 | | (32) greater(vd353, vd354) = 0
% 13.26/2.50 | |
% 13.26/2.50 | | BETA: splitting (21) gives:
% 13.26/2.50 | |
% 13.26/2.50 | | Case 1:
% 13.26/2.50 | | |
% 13.26/2.50 | | | (33) all_46_2 = 0
% 13.26/2.50 | | |
% 13.26/2.50 | | | REDUCE: (18), (33) imply:
% 13.26/2.50 | | | (34) geq(vd353, vd354) = 0
% 13.26/2.50 | | |
% 13.26/2.50 | | | GROUND_INST: instantiating (2) with vd356, vd355, simplifying with (5),
% 13.26/2.50 | | | (7), (31) gives:
% 13.26/2.50 | | | (35) vd356 = vd355 | greater(vd355, vd356) = 0
% 13.26/2.50 | | |
% 13.26/2.50 | | | BETA: splitting (35) gives:
% 13.26/2.50 | | |
% 13.26/2.50 | | | Case 1:
% 13.26/2.50 | | | |
% 13.26/2.50 | | | | (36) greater(vd355, vd356) = 0
% 13.26/2.50 | | | |
% 13.26/2.50 | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23), (24),
% 13.26/2.50 | | | | (26), (27), (34), (36), (ass(cond(goal(193), 0), 2)) are
% 13.26/2.50 | | | | inconsistent by sub-proof #2.
% 13.26/2.50 | | | |
% 13.26/2.50 | | | Case 2:
% 13.26/2.50 | | | |
% 13.26/2.50 | | | | (37) vd356 = vd355
% 13.26/2.50 | | | |
% 13.26/2.50 | | | | REDUCE: (14), (37) imply:
% 13.26/2.50 | | | | (38) vplus(vd354, vd355) = all_42_1
% 13.26/2.50 | | | |
% 13.26/2.50 | | | | GROUND_INST: instantiating (ass(cond(goal(193), 0), 2)) with vd353,
% 13.26/2.50 | | | | vd354, vd355, all_42_2, all_42_1, all_42_0, simplifying
% 13.26/2.50 | | | | with (4), (5), (6), (12), (13), (38) gives:
% 13.26/2.51 | | | | (39) all_42_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd353,
% 13.26/2.51 | | | | vd354) = v0)
% 13.26/2.51 | | | |
% 13.26/2.51 | | | | BETA: splitting (39) gives:
% 13.26/2.51 | | | |
% 13.26/2.51 | | | | Case 1:
% 13.26/2.51 | | | | |
% 13.26/2.51 | | | | | (40) all_42_0 = 0
% 13.26/2.51 | | | | |
% 13.26/2.51 | | | | | REDUCE: (11), (40) imply:
% 13.26/2.51 | | | | | (41) $false
% 13.26/2.51 | | | | |
% 13.26/2.51 | | | | | CLOSE: (41) is inconsistent.
% 13.26/2.51 | | | | |
% 13.26/2.51 | | | | Case 2:
% 13.26/2.51 | | | | |
% 13.26/2.51 | | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0)
% 13.26/2.51 | | | | |
% 13.26/2.51 | | | | | REF_CLOSE: (9), (11), (24), (27), (32), (42) are inconsistent by
% 13.26/2.51 | | | | | sub-proof #1.
% 13.26/2.51 | | | | |
% 13.26/2.51 | | | | End of split
% 13.26/2.51 | | | |
% 13.26/2.51 | | | End of split
% 13.26/2.51 | | |
% 13.26/2.51 | | Case 2:
% 13.26/2.51 | | |
% 13.26/2.51 | | | (43) ~ (vd354 = vd353) & ? [v0: int] : ( ~ (v0 = 0) & greater(vd353,
% 13.26/2.51 | | | vd354) = v0)
% 13.26/2.51 | | |
% 13.26/2.51 | | | ALPHA: (43) implies:
% 13.26/2.51 | | | (44) ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0)
% 13.26/2.51 | | |
% 13.26/2.51 | | | REF_CLOSE: (9), (11), (24), (27), (32), (44) are inconsistent by sub-proof
% 13.26/2.51 | | | #1.
% 13.26/2.51 | | |
% 13.26/2.51 | | End of split
% 13.26/2.51 | |
% 13.26/2.51 | Case 2:
% 13.26/2.51 | |
% 13.26/2.51 | | (45) all_46_2 = 0 & all_46_3 = 0
% 13.26/2.51 | |
% 13.26/2.51 | | ALPHA: (45) implies:
% 13.26/2.51 | | (46) all_46_3 = 0
% 13.26/2.51 | | (47) all_46_2 = 0
% 13.26/2.51 | |
% 13.26/2.51 | | REDUCE: (18), (47) imply:
% 13.26/2.51 | | (48) geq(vd353, vd354) = 0
% 13.26/2.51 | |
% 13.26/2.51 | | REDUCE: (17), (46) imply:
% 13.26/2.51 | | (49) greater(vd355, vd356) = 0
% 13.26/2.51 | |
% 13.26/2.51 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23), (24), (26),
% 13.26/2.51 | | (27), (48), (49), (ass(cond(goal(193), 0), 2)) are inconsistent
% 13.26/2.51 | | by sub-proof #2.
% 13.26/2.51 | |
% 13.26/2.51 | End of split
% 13.26/2.51 |
% 13.26/2.51 End of proof
% 13.26/2.51
% 13.26/2.51 Sub-proof #1 shows that the following formulas are inconsistent:
% 13.26/2.51 ----------------------------------------------------------------
% 13.26/2.51 (1) ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0)
% 13.26/2.51 (2) ~ (all_42_0 = 0)
% 13.26/2.51 (3) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0
% 13.26/2.51 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.51 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.26/2.51 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) =
% 13.26/2.51 v0))
% 13.26/2.51 (5) greater(vd353, vd354) = 0
% 13.26/2.51 (6) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1
% 13.26/2.51 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.51
% 13.26/2.51 Begin of proof
% 13.26/2.51 |
% 13.26/2.51 | DELTA: instantiating (1) with fresh symbol all_121_0 gives:
% 13.26/2.52 | (7) ~ (all_121_0 = 0) & greater(vd353, vd354) = all_121_0
% 13.26/2.52 |
% 13.26/2.52 | ALPHA: (7) implies:
% 13.26/2.52 | (8) ~ (all_121_0 = 0)
% 13.26/2.52 | (9) greater(vd353, vd354) = all_121_0
% 13.26/2.52 |
% 13.26/2.52 | BETA: splitting (3) gives:
% 13.26/2.52 |
% 13.26/2.52 | Case 1:
% 13.26/2.52 | |
% 13.26/2.52 | | (10) all_42_0 = 0
% 13.26/2.52 | |
% 13.26/2.52 | | REDUCE: (2), (10) imply:
% 13.26/2.52 | | (11) $false
% 13.26/2.52 | |
% 13.26/2.52 | | CLOSE: (11) is inconsistent.
% 13.26/2.52 | |
% 13.26/2.52 | Case 2:
% 13.26/2.52 | |
% 13.26/2.52 | | (12) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0 &
% 13.26/2.52 | | greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.52 | |
% 13.26/2.52 | | DELTA: instantiating (12) with fresh symbols all_127_0, all_127_1 gives:
% 13.26/2.52 | | (13) greater(vd355, vd356) = all_127_1 & greater(vd353, vd354) =
% 13.26/2.52 | | all_127_0 & ( ~ (all_127_0 = 0) | ~ (all_127_1 = 0))
% 13.26/2.52 | |
% 13.26/2.52 | | ALPHA: (13) implies:
% 13.26/2.52 | | (14) greater(vd353, vd354) = all_127_0
% 13.26/2.52 | |
% 13.26/2.52 | | BETA: splitting (6) gives:
% 13.26/2.52 | |
% 13.26/2.52 | | Case 1:
% 13.26/2.52 | | |
% 13.26/2.52 | | | (15) all_42_0 = 0
% 13.26/2.52 | | |
% 13.26/2.52 | | | REDUCE: (2), (15) imply:
% 13.26/2.52 | | | (16) $false
% 13.26/2.52 | | |
% 13.26/2.52 | | | CLOSE: (16) is inconsistent.
% 13.26/2.52 | | |
% 13.26/2.52 | | Case 2:
% 13.26/2.52 | | |
% 13.26/2.52 | | | (17) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1 &
% 13.26/2.52 | | | greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.52 | | |
% 13.26/2.52 | | | DELTA: instantiating (17) with fresh symbols all_133_0, all_133_1 gives:
% 13.26/2.52 | | | (18) greater(vd355, vd356) = all_133_0 & greater(vd353, vd354) =
% 13.26/2.52 | | | all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0))
% 13.26/2.52 | | |
% 13.26/2.52 | | | ALPHA: (18) implies:
% 13.26/2.52 | | | (19) greater(vd353, vd354) = all_133_1
% 13.26/2.52 | | |
% 13.26/2.52 | | | GROUND_INST: instantiating (4) with 0, all_127_0, vd354, vd353,
% 13.26/2.52 | | | simplifying with (5), (14) gives:
% 13.26/2.52 | | | (20) all_127_0 = 0
% 13.26/2.52 | | |
% 13.26/2.52 | | | GROUND_INST: instantiating (4) with all_127_0, all_133_1, vd354, vd353,
% 13.26/2.52 | | | simplifying with (14), (19) gives:
% 13.26/2.52 | | | (21) all_133_1 = all_127_0
% 13.26/2.52 | | |
% 13.26/2.52 | | | GROUND_INST: instantiating (4) with all_121_0, all_133_1, vd354, vd353,
% 13.26/2.52 | | | simplifying with (9), (19) gives:
% 13.26/2.52 | | | (22) all_133_1 = all_121_0
% 13.26/2.52 | | |
% 13.26/2.52 | | | COMBINE_EQS: (21), (22) imply:
% 13.26/2.52 | | | (23) all_127_0 = all_121_0
% 13.26/2.52 | | |
% 13.26/2.52 | | | SIMP: (23) implies:
% 13.26/2.52 | | | (24) all_127_0 = all_121_0
% 13.26/2.52 | | |
% 13.26/2.52 | | | COMBINE_EQS: (20), (24) imply:
% 13.26/2.52 | | | (25) all_121_0 = 0
% 13.26/2.52 | | |
% 13.26/2.52 | | | SIMP: (25) implies:
% 13.26/2.52 | | | (26) all_121_0 = 0
% 13.26/2.52 | | |
% 13.26/2.52 | | | REDUCE: (8), (26) imply:
% 13.26/2.52 | | | (27) $false
% 13.26/2.52 | | |
% 13.26/2.52 | | | CLOSE: (27) is inconsistent.
% 13.26/2.52 | | |
% 13.26/2.52 | | End of split
% 13.26/2.52 | |
% 13.26/2.52 | End of split
% 13.26/2.52 |
% 13.26/2.52 End of proof
% 13.26/2.52
% 13.26/2.52 Sub-proof #2 shows that the following formulas are inconsistent:
% 13.26/2.52 ----------------------------------------------------------------
% 13.26/2.52 (1) geq(vd353, vd354) = 0
% 13.26/2.52 (2) $i(vd356)
% 13.26/2.52 (3) greater(vd355, vd356) = 0
% 13.26/2.52 (4) $i(vd354)
% 13.26/2.52 (5) vplus(vd355, vd353) = all_42_2
% 13.26/2.52 (6) ~ (all_42_0 = 0)
% 13.26/2.52 (7) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0
% 13.26/2.52 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.52 (8) $i(vd355)
% 13.26/2.52 (9) vplus(vd356, vd354) = all_42_1
% 13.26/2.52 (10) $i(vd353)
% 13.26/2.52 (11) greater(vd353, vd354) = all_46_0
% 13.26/2.52 (12) greater(all_42_2, all_42_1) = all_42_0
% 13.26/2.52 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.26/2.52 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2)
% 13.26/2.52 = v0))
% 13.26/2.53 (14) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1)
% 13.26/2.53 | ~ $i(v0) | greater(v1, v0) = 0)
% 13.26/2.53 (15) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1
% 13.26/2.53 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.53 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 13.26/2.53 [v5: int] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3)
% 13.26/2.53 | ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 13.26/2.53 [v6: int] : ( ~ (v6 = 0) & greater(v0, v1) = v6))
% 13.26/2.53
% 13.26/2.53 Begin of proof
% 13.26/2.53 |
% 13.26/2.53 | BETA: splitting (7) gives:
% 13.26/2.53 |
% 13.26/2.53 | Case 1:
% 13.26/2.53 | |
% 13.26/2.53 | | (17) all_42_0 = 0
% 13.26/2.53 | |
% 13.26/2.53 | | REDUCE: (6), (17) imply:
% 13.26/2.53 | | (18) $false
% 13.26/2.53 | |
% 13.26/2.53 | | CLOSE: (18) is inconsistent.
% 13.26/2.53 | |
% 13.26/2.53 | Case 2:
% 13.26/2.53 | |
% 13.26/2.53 | | (19) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0 &
% 13.26/2.53 | | greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.53 | |
% 13.26/2.53 | | DELTA: instantiating (19) with fresh symbols all_125_0, all_125_1 gives:
% 13.26/2.53 | | (20) greater(vd355, vd356) = all_125_1 & greater(vd353, vd354) =
% 13.26/2.53 | | all_125_0 & ( ~ (all_125_0 = 0) | ~ (all_125_1 = 0))
% 13.26/2.53 | |
% 13.26/2.53 | | ALPHA: (20) implies:
% 13.26/2.53 | | (21) greater(vd353, vd354) = all_125_0
% 13.26/2.53 | | (22) greater(vd355, vd356) = all_125_1
% 13.26/2.53 | |
% 13.26/2.53 | | BETA: splitting (15) gives:
% 13.26/2.53 | |
% 13.26/2.53 | | Case 1:
% 13.26/2.53 | | |
% 13.26/2.53 | | | (23) all_42_0 = 0
% 13.26/2.53 | | |
% 13.26/2.53 | | | REDUCE: (6), (23) imply:
% 13.26/2.53 | | | (24) $false
% 13.26/2.53 | | |
% 13.26/2.53 | | | CLOSE: (24) is inconsistent.
% 13.26/2.53 | | |
% 13.26/2.53 | | Case 2:
% 13.26/2.53 | | |
% 13.26/2.53 | | | (25) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1 &
% 13.26/2.53 | | | greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.26/2.53 | | |
% 13.26/2.53 | | | DELTA: instantiating (25) with fresh symbols all_131_0, all_131_1 gives:
% 13.26/2.53 | | | (26) greater(vd355, vd356) = all_131_0 & greater(vd353, vd354) =
% 13.26/2.53 | | | all_131_1 & ( ~ (all_131_0 = 0) | ~ (all_131_1 = 0))
% 13.26/2.53 | | |
% 13.26/2.53 | | | ALPHA: (26) implies:
% 13.26/2.53 | | | (27) greater(vd353, vd354) = all_131_1
% 13.26/2.53 | | | (28) greater(vd355, vd356) = all_131_0
% 13.26/2.53 | | | (29) ~ (all_131_0 = 0) | ~ (all_131_1 = 0)
% 13.26/2.53 | | |
% 13.26/2.53 | | | GROUND_INST: instantiating (13) with all_46_0, all_131_1, vd354, vd353,
% 13.26/2.53 | | | simplifying with (11), (27) gives:
% 13.26/2.53 | | | (30) all_131_1 = all_46_0
% 13.26/2.53 | | |
% 13.26/2.53 | | | GROUND_INST: instantiating (13) with all_125_0, all_131_1, vd354, vd353,
% 13.26/2.53 | | | simplifying with (21), (27) gives:
% 13.26/2.53 | | | (31) all_131_1 = all_125_0
% 13.26/2.53 | | |
% 13.26/2.53 | | | GROUND_INST: instantiating (13) with all_125_1, all_131_0, vd356, vd355,
% 13.26/2.53 | | | simplifying with (22), (28) gives:
% 13.26/2.53 | | | (32) all_131_0 = all_125_1
% 13.26/2.53 | | |
% 13.26/2.53 | | | GROUND_INST: instantiating (13) with 0, all_131_0, vd356, vd355,
% 13.26/2.53 | | | simplifying with (3), (28) gives:
% 13.26/2.53 | | | (33) all_131_0 = 0
% 13.26/2.53 | | |
% 13.26/2.53 | | | COMBINE_EQS: (32), (33) imply:
% 13.26/2.53 | | | (34) all_125_1 = 0
% 13.26/2.53 | | |
% 13.26/2.53 | | | SIMP: (34) implies:
% 13.26/2.53 | | | (35) all_125_1 = 0
% 13.26/2.53 | | |
% 13.26/2.53 | | | COMBINE_EQS: (30), (31) imply:
% 13.26/2.53 | | | (36) all_125_0 = all_46_0
% 13.26/2.53 | | |
% 13.26/2.53 | | | SIMP: (36) implies:
% 13.26/2.53 | | | (37) all_125_0 = all_46_0
% 13.26/2.53 | | |
% 13.26/2.53 | | | BETA: splitting (29) gives:
% 13.26/2.53 | | |
% 13.26/2.53 | | | Case 1:
% 13.26/2.53 | | | |
% 13.26/2.53 | | | | (38) ~ (all_131_0 = 0)
% 13.26/2.53 | | | |
% 13.26/2.54 | | | | REDUCE: (33), (38) imply:
% 13.26/2.54 | | | | (39) $false
% 13.26/2.54 | | | |
% 13.26/2.54 | | | | CLOSE: (39) is inconsistent.
% 13.26/2.54 | | | |
% 13.26/2.54 | | | Case 2:
% 13.26/2.54 | | | |
% 13.26/2.54 | | | | (40) ~ (all_131_1 = 0)
% 13.26/2.54 | | | |
% 13.26/2.54 | | | | REDUCE: (30), (40) imply:
% 13.26/2.54 | | | | (41) ~ (all_46_0 = 0)
% 13.26/2.54 | | | |
% 13.26/2.54 | | | | GROUND_INST: instantiating (14) with vd354, vd353, simplifying with (1),
% 13.26/2.54 | | | | (4), (10) gives:
% 13.26/2.54 | | | | (42) vd354 = vd353 | greater(vd353, vd354) = 0
% 13.26/2.54 | | | |
% 13.26/2.54 | | | | BETA: splitting (42) gives:
% 13.26/2.54 | | | |
% 13.26/2.54 | | | | Case 1:
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | (43) greater(vd353, vd354) = 0
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | GROUND_INST: instantiating (13) with all_46_0, 0, vd354, vd353,
% 13.26/2.54 | | | | | simplifying with (11), (43) gives:
% 13.26/2.54 | | | | | (44) all_46_0 = 0
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | REDUCE: (41), (44) imply:
% 13.26/2.54 | | | | | (45) $false
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | CLOSE: (45) is inconsistent.
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | Case 2:
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | (46) vd354 = vd353
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | REDUCE: (9), (46) imply:
% 13.26/2.54 | | | | | (47) vplus(vd356, vd353) = all_42_1
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | GROUND_INST: instantiating (16) with vd355, vd356, vd353, all_42_2,
% 13.26/2.54 | | | | | all_42_1, all_42_0, simplifying with (2), (5), (8), (10),
% 13.26/2.54 | | | | | (12), (47) gives:
% 13.26/2.54 | | | | | (48) all_42_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd355,
% 13.26/2.54 | | | | | vd356) = v0)
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | BETA: splitting (48) gives:
% 13.26/2.54 | | | | |
% 13.26/2.54 | | | | | Case 1:
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | (49) all_42_0 = 0
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | REDUCE: (6), (49) imply:
% 13.26/2.54 | | | | | | (50) $false
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | CLOSE: (50) is inconsistent.
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | Case 2:
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0)
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | DELTA: instantiating (51) with fresh symbol all_121_0 gives:
% 13.26/2.54 | | | | | | (52) ~ (all_121_0 = 0) & greater(vd355, vd356) = all_121_0
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | ALPHA: (52) implies:
% 13.26/2.54 | | | | | | (53) ~ (all_121_0 = 0)
% 13.26/2.54 | | | | | | (54) greater(vd355, vd356) = all_121_0
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | BETA: splitting (7) gives:
% 13.26/2.54 | | | | | |
% 13.26/2.54 | | | | | | Case 1:
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | | (55) all_42_0 = 0
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | | REDUCE: (6), (55) imply:
% 13.26/2.54 | | | | | | | (56) $false
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | | CLOSE: (56) is inconsistent.
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | Case 2:
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | | DELTA: instantiating (19) with fresh symbols all_127_0, all_127_1
% 13.26/2.54 | | | | | | | gives:
% 13.26/2.54 | | | | | | | (57) greater(vd355, vd356) = all_127_1 & greater(vd353, vd354)
% 13.26/2.54 | | | | | | | = all_127_0 & ( ~ (all_127_0 = 0) | ~ (all_127_1 = 0))
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | | ALPHA: (57) implies:
% 13.26/2.54 | | | | | | | (58) greater(vd355, vd356) = all_127_1
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | | BETA: splitting (15) gives:
% 13.26/2.54 | | | | | | |
% 13.26/2.54 | | | | | | | Case 1:
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | | (59) all_42_0 = 0
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | | REDUCE: (6), (59) imply:
% 13.26/2.54 | | | | | | | | (60) $false
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | | CLOSE: (60) is inconsistent.
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | Case 2:
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | | DELTA: instantiating (25) with fresh symbols all_138_0,
% 13.26/2.54 | | | | | | | | all_138_1 gives:
% 13.26/2.54 | | | | | | | | (61) greater(vd355, vd356) = all_138_0 & greater(vd353,
% 13.26/2.54 | | | | | | | | vd354) = all_138_1 & ( ~ (all_138_0 = 0) | ~
% 13.26/2.54 | | | | | | | | (all_138_1 = 0))
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | | ALPHA: (61) implies:
% 13.26/2.54 | | | | | | | | (62) greater(vd355, vd356) = all_138_0
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | | GROUND_INST: instantiating (13) with all_121_0, all_127_1,
% 13.26/2.54 | | | | | | | | vd356, vd355, simplifying with (54), (58) gives:
% 13.26/2.54 | | | | | | | | (63) all_127_1 = all_121_0
% 13.26/2.54 | | | | | | | |
% 13.26/2.54 | | | | | | | | GROUND_INST: instantiating (13) with all_127_1, all_138_0,
% 13.26/2.54 | | | | | | | | vd356, vd355, simplifying with (58), (62) gives:
% 13.26/2.54 | | | | | | | | (64) all_138_0 = all_127_1
% 13.26/2.54 | | | | | | | |
% 13.26/2.55 | | | | | | | | GROUND_INST: instantiating (13) with 0, all_138_0, vd356, vd355,
% 13.26/2.55 | | | | | | | | simplifying with (3), (62) gives:
% 13.26/2.55 | | | | | | | | (65) all_138_0 = 0
% 13.26/2.55 | | | | | | | |
% 13.26/2.55 | | | | | | | | COMBINE_EQS: (64), (65) imply:
% 13.26/2.55 | | | | | | | | (66) all_127_1 = 0
% 13.26/2.55 | | | | | | | |
% 13.26/2.55 | | | | | | | | SIMP: (66) implies:
% 13.26/2.55 | | | | | | | | (67) all_127_1 = 0
% 13.26/2.55 | | | | | | | |
% 13.26/2.55 | | | | | | | | COMBINE_EQS: (63), (67) imply:
% 13.26/2.55 | | | | | | | | (68) all_121_0 = 0
% 13.26/2.55 | | | | | | | |
% 13.26/2.55 | | | | | | | | SIMP: (68) implies:
% 13.26/2.55 | | | | | | | | (69) all_121_0 = 0
% 13.26/2.55 | | | | | | | |
% 13.26/2.55 | | | | | | | | REDUCE: (53), (69) imply:
% 13.26/2.55 | | | | | | | | (70) $false
% 13.26/2.55 | | | | | | | |
% 13.26/2.55 | | | | | | | | CLOSE: (70) is inconsistent.
% 13.26/2.55 | | | | | | | |
% 13.26/2.55 | | | | | | | End of split
% 13.26/2.55 | | | | | | |
% 13.26/2.55 | | | | | | End of split
% 13.26/2.55 | | | | | |
% 13.26/2.55 | | | | | End of split
% 13.26/2.55 | | | | |
% 13.26/2.55 | | | | End of split
% 13.26/2.55 | | | |
% 13.26/2.55 | | | End of split
% 13.26/2.55 | | |
% 13.26/2.55 | | End of split
% 13.26/2.55 | |
% 13.26/2.55 | End of split
% 13.26/2.55 |
% 13.26/2.55 End of proof
% 13.26/2.55 % SZS output end Proof for theBenchmark
% 13.26/2.55
% 13.26/2.55 1977ms
%------------------------------------------------------------------------------