TSTP Solution File: NUM839+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM839+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 : 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 11:50:18 EDT 2023
% Result : Theorem 10.04s 2.09s
% Output : Proof 13.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : NUM839+2 : TPTP v8.1.2. Released v4.1.0.
% 0.02/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.31 % Computer : n023.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Aug 25 15:55:41 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.54/0.57 ________ _____
% 0.54/0.57 ___ __ \_________(_)________________________________
% 0.54/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.54/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.54/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.57 (2023-06-19)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2023
% 0.54/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.57 Amanda Stjerna.
% 0.54/0.57 Free software under BSD-3-Clause.
% 0.54/0.57
% 0.54/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.57
% 0.54/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.59 Running up to 7 provers in parallel.
% 0.54/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.54/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.54/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.54/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.54/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.54/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.54/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.69/1.12 Prover 4: Preprocessing ...
% 2.69/1.12 Prover 1: Preprocessing ...
% 3.18/1.17 Prover 0: Preprocessing ...
% 3.18/1.17 Prover 3: Preprocessing ...
% 3.18/1.17 Prover 2: Preprocessing ...
% 3.18/1.17 Prover 6: Preprocessing ...
% 3.18/1.17 Prover 5: Preprocessing ...
% 7.16/1.71 Prover 1: Warning: ignoring some quantifiers
% 7.88/1.79 Prover 3: Warning: ignoring some quantifiers
% 7.88/1.79 Prover 1: Constructing countermodel ...
% 7.88/1.80 Prover 5: Proving ...
% 7.88/1.80 Prover 6: Proving ...
% 7.88/1.81 Prover 3: Constructing countermodel ...
% 8.32/1.87 Prover 4: Warning: ignoring some quantifiers
% 8.32/1.89 Prover 2: Proving ...
% 8.89/1.95 Prover 4: Constructing countermodel ...
% 9.32/1.99 Prover 0: Proving ...
% 10.04/2.09 Prover 3: proved (1487ms)
% 10.04/2.09
% 10.04/2.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.04/2.09
% 10.04/2.09 Prover 6: stopped
% 10.04/2.09 Prover 5: stopped
% 10.04/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.04/2.10 Prover 0: stopped
% 10.04/2.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.04/2.11 Prover 2: stopped
% 10.31/2.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.31/2.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.31/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.63/2.16 Prover 7: Preprocessing ...
% 10.63/2.18 Prover 10: Preprocessing ...
% 10.63/2.20 Prover 8: Preprocessing ...
% 10.63/2.20 Prover 11: Preprocessing ...
% 10.63/2.20 Prover 13: Preprocessing ...
% 11.68/2.35 Prover 1: Found proof (size 42)
% 11.68/2.35 Prover 1: proved (1755ms)
% 11.68/2.35 Prover 4: stopped
% 11.68/2.35 Prover 11: stopped
% 12.04/2.37 Prover 10: Warning: ignoring some quantifiers
% 12.04/2.38 Prover 13: Warning: ignoring some quantifiers
% 12.04/2.39 Prover 10: Constructing countermodel ...
% 12.04/2.40 Prover 13: Constructing countermodel ...
% 12.04/2.40 Prover 10: stopped
% 12.04/2.40 Prover 8: Warning: ignoring some quantifiers
% 12.04/2.41 Prover 13: stopped
% 12.04/2.41 Prover 7: Warning: ignoring some quantifiers
% 12.04/2.42 Prover 8: Constructing countermodel ...
% 12.04/2.43 Prover 7: Constructing countermodel ...
% 12.04/2.44 Prover 8: stopped
% 12.04/2.45 Prover 7: stopped
% 12.04/2.45
% 12.04/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.04/2.45
% 12.67/2.46 % SZS output start Proof for theBenchmark
% 12.67/2.47 Assumptions after simplification:
% 12.67/2.47 ---------------------------------
% 12.67/2.47
% 12.67/2.47 (ass(cond(140, 0), 0))
% 12.85/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 12.85/2.51 | less(v1, v0) = 0)
% 12.85/2.51
% 12.85/2.51 (ass(cond(147, 0), 0))
% 12.85/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2)
% 12.85/2.52 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & less(v0, v1) = v3))
% 12.85/2.52
% 12.85/2.52 (ass(cond(61, 0), 0))
% 12.85/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1)
% 12.85/2.52 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2)))
% 12.85/2.52
% 12.85/2.52 (ass(cond(goal(130), 0), 0))
% 12.85/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (greater(v0,
% 12.85/2.52 v1) = v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0)
% 12.85/2.52
% 12.85/2.52 (ass(cond(goal(130), 0), 2))
% 12.85/2.53 ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 12.85/2.53 | ? [v2: int] : ( ~ (v2 = 0) & less(v0, v1) = v2))
% 12.85/2.53
% 12.85/2.53 (ass(cond(goal(193), 0), 0))
% 12.85/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.85/2.53 int] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~
% 12.85/2.53 (vplus(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : (
% 12.85/2.53 ~ (v6 = 0) & less(v0, v1) = v6))
% 12.85/2.53
% 12.85/2.53 (holds(antec(204), 331, 0))
% 13.06/2.53 $i(vd330) & $i(vd329) & $i(vd328) & ? [v0: $i] : ? [v1: $i] : (vplus(vd329,
% 13.06/2.53 vd330) = v1 & vplus(vd328, vd330) = v0 & greater(v0, v1) = 0 & $i(v1) &
% 13.06/2.53 $i(v0))
% 13.06/2.53
% 13.06/2.53 (holds(conseq(204), 332, 0))
% 13.06/2.54 $i(vd329) & $i(vd328) & ? [v0: int] : ( ~ (v0 = 0) & greater(vd328, vd329) =
% 13.06/2.54 v0)
% 13.06/2.54
% 13.06/2.54 (function-axioms)
% 13.09/2.54 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.09/2.54 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 13.09/2.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.09/2.55 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 13.09/2.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.09/2.55 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] :
% 13.09/2.55 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) |
% 13.09/2.55 ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.09/2.55 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3,
% 13.09/2.55 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.09/2.55 [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & !
% 13.09/2.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~
% 13.09/2.55 (vsucc(v2) = v0))
% 13.09/2.55
% 13.09/2.55 Further assumptions not needed in the proof:
% 13.09/2.55 --------------------------------------------
% 13.09/2.55 ass(cond(12, 0), 0), ass(cond(158, 0), 0), ass(cond(163, 0), 0), ass(cond(168,
% 13.09/2.55 0), 0), ass(cond(184, 0), 0), ass(cond(189, 0), 0), ass(cond(20, 0), 0),
% 13.09/2.55 ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0),
% 13.09/2.55 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 1),
% 13.09/2.55 ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0),
% 13.09/2.55 1), ass(cond(goal(193), 0), 2), ass(cond(goal(88), 0), 0), ass(cond(goal(88),
% 13.09/2.55 0), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3),
% 13.09/2.55 def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), 1),
% 13.09/2.55 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 13.09/2.55 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 13.09/2.55 holds(definiens(29), 44, 0)))
% 13.09/2.55
% 13.09/2.55 Those formulas are unsatisfiable:
% 13.09/2.55 ---------------------------------
% 13.09/2.55
% 13.09/2.55 Begin of proof
% 13.09/2.55 |
% 13.09/2.55 | ALPHA: (holds(antec(204), 331, 0)) implies:
% 13.09/2.55 | (1) $i(vd330)
% 13.09/2.55 | (2) ? [v0: $i] : ? [v1: $i] : (vplus(vd329, vd330) = v1 & vplus(vd328,
% 13.09/2.55 | vd330) = v0 & greater(v0, v1) = 0 & $i(v1) & $i(v0))
% 13.09/2.55 |
% 13.09/2.55 | ALPHA: (holds(conseq(204), 332, 0)) implies:
% 13.09/2.55 | (3) $i(vd328)
% 13.09/2.55 | (4) $i(vd329)
% 13.09/2.56 | (5) ? [v0: int] : ( ~ (v0 = 0) & greater(vd328, vd329) = v0)
% 13.09/2.56 |
% 13.09/2.56 | ALPHA: (function-axioms) implies:
% 13.09/2.56 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.09/2.56 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 13.09/2.56 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.09/2.56 | ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) =
% 13.09/2.56 | v0))
% 13.09/2.56 |
% 13.09/2.56 | DELTA: instantiating (5) with fresh symbol all_31_0 gives:
% 13.09/2.56 | (8) ~ (all_31_0 = 0) & greater(vd328, vd329) = all_31_0
% 13.09/2.56 |
% 13.09/2.56 | ALPHA: (8) implies:
% 13.09/2.56 | (9) ~ (all_31_0 = 0)
% 13.09/2.56 | (10) greater(vd328, vd329) = all_31_0
% 13.09/2.56 |
% 13.09/2.56 | DELTA: instantiating (2) with fresh symbols all_35_0, all_35_1 gives:
% 13.09/2.56 | (11) vplus(vd329, vd330) = all_35_0 & vplus(vd328, vd330) = all_35_1 &
% 13.09/2.56 | greater(all_35_1, all_35_0) = 0 & $i(all_35_0) & $i(all_35_1)
% 13.09/2.56 |
% 13.09/2.56 | ALPHA: (11) implies:
% 13.09/2.56 | (12) $i(all_35_1)
% 13.09/2.56 | (13) $i(all_35_0)
% 13.09/2.56 | (14) greater(all_35_1, all_35_0) = 0
% 13.09/2.56 | (15) vplus(vd328, vd330) = all_35_1
% 13.09/2.56 | (16) vplus(vd329, vd330) = all_35_0
% 13.09/2.56 |
% 13.09/2.57 | GROUND_INST: instantiating (ass(cond(goal(130), 0), 0)) with vd328, vd329,
% 13.09/2.57 | all_31_0, simplifying with (3), (4), (10) gives:
% 13.09/2.57 | (17) all_31_0 = 0 | vd329 = vd328 | less(vd328, vd329) = 0
% 13.09/2.57 |
% 13.09/2.57 | GROUND_INST: instantiating (ass(cond(147, 0), 0)) with vd329, vd328, all_31_0,
% 13.09/2.57 | simplifying with (3), (4), (10) gives:
% 13.09/2.57 | (18) all_31_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less(vd329, vd328) = v0)
% 13.09/2.57 |
% 13.09/2.57 | GROUND_INST: instantiating (ass(cond(140, 0), 0)) with all_35_1, all_35_0,
% 13.09/2.57 | simplifying with (12), (13), (14) gives:
% 13.09/2.57 | (19) less(all_35_0, all_35_1) = 0
% 13.09/2.57 |
% 13.09/2.57 | GROUND_INST: instantiating (ass(cond(goal(130), 0), 2)) with all_35_1,
% 13.09/2.57 | all_35_0, simplifying with (12), (13), (14) gives:
% 13.09/2.57 | (20) ? [v0: int] : ( ~ (v0 = 0) & less(all_35_1, all_35_0) = v0)
% 13.09/2.57 |
% 13.09/2.57 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd328, vd330, all_35_1,
% 13.09/2.57 | simplifying with (1), (3), (15) gives:
% 13.09/2.57 | (21) vplus(vd330, vd328) = all_35_1 & $i(all_35_1)
% 13.09/2.57 |
% 13.09/2.57 | ALPHA: (21) implies:
% 13.09/2.57 | (22) vplus(vd330, vd328) = all_35_1
% 13.09/2.57 |
% 13.09/2.57 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd329, vd330, all_35_0,
% 13.09/2.57 | simplifying with (1), (4), (16) gives:
% 13.09/2.57 | (23) vplus(vd330, vd329) = all_35_0 & $i(all_35_0)
% 13.09/2.57 |
% 13.09/2.57 | ALPHA: (23) implies:
% 13.09/2.57 | (24) vplus(vd330, vd329) = all_35_0
% 13.09/2.57 |
% 13.09/2.57 | DELTA: instantiating (20) with fresh symbol all_50_0 gives:
% 13.09/2.57 | (25) ~ (all_50_0 = 0) & less(all_35_1, all_35_0) = all_50_0
% 13.09/2.57 |
% 13.09/2.57 | ALPHA: (25) implies:
% 13.09/2.57 | (26) ~ (all_50_0 = 0)
% 13.09/2.57 | (27) less(all_35_1, all_35_0) = all_50_0
% 13.09/2.57 |
% 13.09/2.57 | BETA: splitting (18) gives:
% 13.09/2.57 |
% 13.09/2.58 | Case 1:
% 13.09/2.58 | |
% 13.09/2.58 | | (28) all_31_0 = 0
% 13.09/2.58 | |
% 13.09/2.58 | | REDUCE: (9), (28) imply:
% 13.09/2.58 | | (29) $false
% 13.09/2.58 | |
% 13.09/2.58 | | CLOSE: (29) is inconsistent.
% 13.09/2.58 | |
% 13.09/2.58 | Case 2:
% 13.09/2.58 | |
% 13.09/2.58 | |
% 13.09/2.58 | | GROUND_INST: instantiating (ass(cond(goal(193), 0), 0)) with vd328, vd329,
% 13.09/2.58 | | vd330, all_35_1, all_35_0, all_50_0, simplifying with (1), (3),
% 13.09/2.58 | | (4), (15), (16), (27) gives:
% 13.09/2.58 | | (30) all_50_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less(vd328, vd329) =
% 13.09/2.58 | | v0)
% 13.09/2.58 | |
% 13.09/2.58 | | BETA: splitting (30) gives:
% 13.09/2.58 | |
% 13.09/2.58 | | Case 1:
% 13.09/2.58 | | |
% 13.09/2.58 | | | (31) all_50_0 = 0
% 13.09/2.58 | | |
% 13.09/2.58 | | | REDUCE: (26), (31) imply:
% 13.09/2.58 | | | (32) $false
% 13.09/2.58 | | |
% 13.09/2.58 | | | CLOSE: (32) is inconsistent.
% 13.09/2.58 | | |
% 13.09/2.58 | | Case 2:
% 13.09/2.58 | | |
% 13.09/2.58 | | | (33) ? [v0: int] : ( ~ (v0 = 0) & less(vd328, vd329) = v0)
% 13.09/2.58 | | |
% 13.09/2.58 | | | DELTA: instantiating (33) with fresh symbol all_86_0 gives:
% 13.09/2.58 | | | (34) ~ (all_86_0 = 0) & less(vd328, vd329) = all_86_0
% 13.09/2.58 | | |
% 13.09/2.58 | | | ALPHA: (34) implies:
% 13.09/2.58 | | | (35) ~ (all_86_0 = 0)
% 13.09/2.58 | | | (36) less(vd328, vd329) = all_86_0
% 13.09/2.58 | | |
% 13.09/2.58 | | | BETA: splitting (17) gives:
% 13.09/2.58 | | |
% 13.09/2.58 | | | Case 1:
% 13.09/2.58 | | | |
% 13.09/2.58 | | | | (37) less(vd328, vd329) = 0
% 13.09/2.58 | | | |
% 13.09/2.58 | | | | GROUND_INST: instantiating (7) with 0, all_86_0, vd329, vd328,
% 13.09/2.58 | | | | simplifying with (36), (37) gives:
% 13.09/2.58 | | | | (38) all_86_0 = 0
% 13.09/2.58 | | | |
% 13.09/2.58 | | | | REDUCE: (35), (38) imply:
% 13.09/2.58 | | | | (39) $false
% 13.09/2.58 | | | |
% 13.09/2.58 | | | | CLOSE: (39) is inconsistent.
% 13.09/2.58 | | | |
% 13.09/2.58 | | | Case 2:
% 13.09/2.58 | | | |
% 13.09/2.58 | | | | (40) all_31_0 = 0 | vd329 = vd328
% 13.09/2.58 | | | |
% 13.09/2.58 | | | | BETA: splitting (40) gives:
% 13.09/2.58 | | | |
% 13.09/2.58 | | | | Case 1:
% 13.09/2.58 | | | | |
% 13.09/2.59 | | | | | (41) vd329 = vd328
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | REDUCE: (24), (41) imply:
% 13.09/2.59 | | | | | (42) vplus(vd330, vd328) = all_35_0
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | GROUND_INST: instantiating (6) with all_35_1, all_35_0, vd328, vd330,
% 13.09/2.59 | | | | | simplifying with (22), (42) gives:
% 13.09/2.59 | | | | | (43) all_35_0 = all_35_1
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | REDUCE: (19), (43) imply:
% 13.09/2.59 | | | | | (44) less(all_35_1, all_35_1) = 0
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | REDUCE: (27), (43) imply:
% 13.09/2.59 | | | | | (45) less(all_35_1, all_35_1) = all_50_0
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | GROUND_INST: instantiating (7) with 0, all_50_0, all_35_1, all_35_1,
% 13.09/2.59 | | | | | simplifying with (44), (45) gives:
% 13.09/2.59 | | | | | (46) all_50_0 = 0
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | REDUCE: (26), (46) imply:
% 13.09/2.59 | | | | | (47) $false
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | CLOSE: (47) is inconsistent.
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | Case 2:
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | (48) all_31_0 = 0
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | REDUCE: (9), (48) imply:
% 13.09/2.59 | | | | | (49) $false
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | | CLOSE: (49) is inconsistent.
% 13.09/2.59 | | | | |
% 13.09/2.59 | | | | End of split
% 13.09/2.59 | | | |
% 13.09/2.59 | | | End of split
% 13.09/2.59 | | |
% 13.09/2.59 | | End of split
% 13.09/2.59 | |
% 13.09/2.59 | End of split
% 13.09/2.59 |
% 13.09/2.59 End of proof
% 13.09/2.59 % SZS output end Proof for theBenchmark
% 13.09/2.59
% 13.09/2.59 2015ms
%------------------------------------------------------------------------------