TSTP Solution File: SET688+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET688+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 15:26:00 EDT 2023
% Result : Theorem 6.58s 1.70s
% Output : Proof 8.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET688+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:23:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.46/1.03 Prover 4: Preprocessing ...
% 2.46/1.04 Prover 1: Preprocessing ...
% 2.46/1.08 Prover 5: Preprocessing ...
% 2.46/1.08 Prover 6: Preprocessing ...
% 2.46/1.08 Prover 0: Preprocessing ...
% 2.46/1.08 Prover 2: Preprocessing ...
% 2.46/1.08 Prover 3: Preprocessing ...
% 5.34/1.46 Prover 6: Proving ...
% 5.34/1.48 Prover 3: Constructing countermodel ...
% 5.34/1.49 Prover 5: Proving ...
% 5.34/1.50 Prover 1: Constructing countermodel ...
% 5.34/1.51 Prover 4: Constructing countermodel ...
% 5.34/1.52 Prover 0: Proving ...
% 5.34/1.52 Prover 2: Proving ...
% 6.58/1.70 Prover 3: proved (1072ms)
% 6.58/1.70
% 6.58/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.58/1.70
% 6.58/1.70 Prover 0: stopped
% 6.58/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.58/1.70 Prover 2: stopped
% 6.58/1.70 Prover 6: stopped
% 7.06/1.73 Prover 5: stopped
% 7.06/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.06/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.06/1.73 Prover 7: Preprocessing ...
% 7.06/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.06/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.06/1.75 Prover 10: Preprocessing ...
% 7.43/1.76 Prover 8: Preprocessing ...
% 7.43/1.77 Prover 11: Preprocessing ...
% 7.43/1.78 Prover 1: Found proof (size 36)
% 7.43/1.78 Prover 1: proved (1161ms)
% 7.43/1.78 Prover 4: stopped
% 7.43/1.78 Prover 10: stopped
% 7.43/1.79 Prover 13: Preprocessing ...
% 7.43/1.80 Prover 7: Warning: ignoring some quantifiers
% 7.43/1.81 Prover 7: Constructing countermodel ...
% 7.43/1.81 Prover 11: stopped
% 7.43/1.82 Prover 7: stopped
% 7.43/1.83 Prover 13: stopped
% 8.06/1.86 Prover 8: Warning: ignoring some quantifiers
% 8.06/1.87 Prover 8: Constructing countermodel ...
% 8.06/1.88 Prover 8: stopped
% 8.06/1.88
% 8.06/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.06/1.88
% 8.06/1.88 % SZS output start Proof for theBenchmark
% 8.06/1.89 Assumptions after simplification:
% 8.06/1.89 ---------------------------------
% 8.06/1.89
% 8.06/1.89 (equal_set)
% 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 8.24/1.92 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 8.24/1.92 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 8.24/1.92 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.24/1.92 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.24/1.92
% 8.24/1.92 (subset)
% 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.24/1.92 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.24/1.92 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.24/1.92 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.24/1.92 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.24/1.92
% 8.24/1.92 (thI04)
% 8.24/1.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~
% 8.24/1.92 (v4 = 0) & ~ (v3 = 0) & equal_set(v1, v2) = v4 & equal_set(v0, v2) = 0 &
% 8.24/1.92 equal_set(v0, v1) = v3 & subset(v1, v2) = 0 & subset(v0, v1) = 0 & $i(v2) &
% 8.24/1.92 $i(v1) & $i(v0))
% 8.24/1.92
% 8.24/1.92 (function-axioms)
% 8.24/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.24/1.93 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.24/1.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.24/1.93 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 8.24/1.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 8.24/1.93 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.24/1.93 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 8.24/1.93 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.24/1.93 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 8.24/1.93 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.24/1.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 8.24/1.93 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 8.24/1.93 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.24/1.93 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 8.24/1.93 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 8.24/1.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 8.24/1.93 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 8.24/1.93 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 8.24/1.93 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 8.24/1.93 (power_set(v2) = v0))
% 8.24/1.93
% 8.24/1.93 Further assumptions not needed in the proof:
% 8.24/1.93 --------------------------------------------
% 8.24/1.93 difference, empty_set, intersection, power_set, product, singleton, sum, union,
% 8.24/1.93 unordered_pair
% 8.24/1.93
% 8.24/1.93 Those formulas are unsatisfiable:
% 8.24/1.93 ---------------------------------
% 8.24/1.93
% 8.24/1.93 Begin of proof
% 8.24/1.93 |
% 8.24/1.93 | ALPHA: (subset) implies:
% 8.24/1.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 8.24/1.94 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 8.24/1.94 | member(v2, v1) = 0))
% 8.24/1.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.24/1.94 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.24/1.94 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (equal_set) implies:
% 8.24/1.94 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) |
% 8.24/1.94 | ~ $i(v0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.24/1.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 8.24/1.94 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.24/1.94 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 8.24/1.94 | 0))))
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (function-axioms) implies:
% 8.24/1.94 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.24/1.94 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 8.24/1.94 | = v0))
% 8.24/1.94 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.24/1.94 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 8.24/1.94 | = v0))
% 8.24/1.94 |
% 8.24/1.94 | DELTA: instantiating (thI04) with fresh symbols all_15_0, all_15_1, all_15_2,
% 8.24/1.94 | all_15_3, all_15_4 gives:
% 8.24/1.94 | (7) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) & equal_set(all_15_3, all_15_2) =
% 8.24/1.94 | all_15_0 & equal_set(all_15_4, all_15_2) = 0 & equal_set(all_15_4,
% 8.24/1.94 | all_15_3) = all_15_1 & subset(all_15_3, all_15_2) = 0 &
% 8.24/1.94 | subset(all_15_4, all_15_3) = 0 & $i(all_15_2) & $i(all_15_3) &
% 8.24/1.94 | $i(all_15_4)
% 8.24/1.94 |
% 8.24/1.94 | ALPHA: (7) implies:
% 8.24/1.94 | (8) ~ (all_15_1 = 0)
% 8.24/1.94 | (9) ~ (all_15_0 = 0)
% 8.24/1.94 | (10) $i(all_15_4)
% 8.24/1.94 | (11) $i(all_15_3)
% 8.24/1.94 | (12) $i(all_15_2)
% 8.24/1.94 | (13) subset(all_15_4, all_15_3) = 0
% 8.24/1.94 | (14) subset(all_15_3, all_15_2) = 0
% 8.24/1.94 | (15) equal_set(all_15_4, all_15_3) = all_15_1
% 8.24/1.95 | (16) equal_set(all_15_4, all_15_2) = 0
% 8.24/1.95 | (17) equal_set(all_15_3, all_15_2) = all_15_0
% 8.24/1.95 |
% 8.24/1.95 | GROUND_INST: instantiating (1) with all_15_4, all_15_3, simplifying with (10),
% 8.24/1.95 | (11), (13) gives:
% 8.24/1.95 | (18) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) | member(v0,
% 8.24/1.95 | all_15_3) = 0)
% 8.24/1.95 |
% 8.24/1.95 | GROUND_INST: instantiating (4) with all_15_4, all_15_3, all_15_1, simplifying
% 8.24/1.95 | with (10), (11), (15) gives:
% 8.24/1.95 | (19) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_3,
% 8.24/1.95 | all_15_4) = v1 & subset(all_15_4, all_15_3) = v0 & ( ~ (v1 = 0) |
% 8.24/1.95 | ~ (v0 = 0)))
% 8.24/1.95 |
% 8.24/1.95 | GROUND_INST: instantiating (3) with all_15_4, all_15_2, simplifying with (10),
% 8.24/1.95 | (12), (16) gives:
% 8.24/1.95 | (20) subset(all_15_2, all_15_4) = 0 & subset(all_15_4, all_15_2) = 0
% 8.24/1.95 |
% 8.24/1.95 | ALPHA: (20) implies:
% 8.24/1.95 | (21) subset(all_15_2, all_15_4) = 0
% 8.24/1.95 |
% 8.24/1.95 | GROUND_INST: instantiating (4) with all_15_3, all_15_2, all_15_0, simplifying
% 8.24/1.95 | with (11), (12), (17) gives:
% 8.24/1.95 | (22) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_2,
% 8.24/1.95 | all_15_3) = v1 & subset(all_15_3, all_15_2) = v0 & ( ~ (v1 = 0) |
% 8.24/1.95 | ~ (v0 = 0)))
% 8.24/1.95 |
% 8.24/1.95 | BETA: splitting (22) gives:
% 8.24/1.95 |
% 8.24/1.95 | Case 1:
% 8.24/1.95 | |
% 8.24/1.95 | | (23) all_15_0 = 0
% 8.24/1.95 | |
% 8.24/1.95 | | REDUCE: (9), (23) imply:
% 8.24/1.95 | | (24) $false
% 8.24/1.95 | |
% 8.24/1.95 | | CLOSE: (24) is inconsistent.
% 8.24/1.95 | |
% 8.24/1.95 | Case 2:
% 8.24/1.95 | |
% 8.24/1.95 | | (25) ? [v0: any] : ? [v1: any] : (subset(all_15_2, all_15_3) = v1 &
% 8.24/1.95 | | subset(all_15_3, all_15_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.24/1.95 | |
% 8.24/1.95 | | DELTA: instantiating (25) with fresh symbols all_29_0, all_29_1 gives:
% 8.24/1.95 | | (26) subset(all_15_2, all_15_3) = all_29_0 & subset(all_15_3, all_15_2) =
% 8.24/1.95 | | all_29_1 & ( ~ (all_29_0 = 0) | ~ (all_29_1 = 0))
% 8.24/1.95 | |
% 8.24/1.95 | | ALPHA: (26) implies:
% 8.24/1.95 | | (27) subset(all_15_3, all_15_2) = all_29_1
% 8.24/1.96 | | (28) subset(all_15_2, all_15_3) = all_29_0
% 8.24/1.96 | | (29) ~ (all_29_0 = 0) | ~ (all_29_1 = 0)
% 8.24/1.96 | |
% 8.24/1.96 | | BETA: splitting (19) gives:
% 8.24/1.96 | |
% 8.24/1.96 | | Case 1:
% 8.24/1.96 | | |
% 8.24/1.96 | | | (30) all_15_1 = 0
% 8.24/1.96 | | |
% 8.24/1.96 | | | REDUCE: (8), (30) imply:
% 8.24/1.96 | | | (31) $false
% 8.24/1.96 | | |
% 8.24/1.96 | | | CLOSE: (31) is inconsistent.
% 8.24/1.96 | | |
% 8.24/1.96 | | Case 2:
% 8.24/1.96 | | |
% 8.24/1.96 | | |
% 8.24/1.96 | | | GROUND_INST: instantiating (6) with 0, all_29_1, all_15_2, all_15_3,
% 8.24/1.96 | | | simplifying with (14), (27) gives:
% 8.24/1.96 | | | (32) all_29_1 = 0
% 8.24/1.96 | | |
% 8.24/1.96 | | | BETA: splitting (29) gives:
% 8.24/1.96 | | |
% 8.24/1.96 | | | Case 1:
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | (33) ~ (all_29_0 = 0)
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | GROUND_INST: instantiating (1) with all_15_2, all_15_4, simplifying with
% 8.24/1.96 | | | | (10), (12), (21) gives:
% 8.24/1.96 | | | | (34) ! [v0: $i] : ( ~ (member(v0, all_15_2) = 0) | ~ $i(v0) |
% 8.24/1.96 | | | | member(v0, all_15_4) = 0)
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | GROUND_INST: instantiating (2) with all_15_2, all_15_3, all_29_0,
% 8.24/1.96 | | | | simplifying with (11), (12), (28) gives:
% 8.24/1.96 | | | | (35) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.24/1.96 | | | | member(v0, all_15_2) = 0 & member(v0, all_15_3) = v1 & $i(v0))
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | BETA: splitting (35) gives:
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | Case 1:
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | (36) all_29_0 = 0
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | REDUCE: (33), (36) imply:
% 8.24/1.96 | | | | | (37) $false
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | CLOSE: (37) is inconsistent.
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | Case 2:
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 8.24/1.96 | | | | | all_15_2) = 0 & member(v0, all_15_3) = v1 & $i(v0))
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | DELTA: instantiating (38) with fresh symbols all_58_0, all_58_1 gives:
% 8.24/1.96 | | | | | (39) ~ (all_58_0 = 0) & member(all_58_1, all_15_2) = 0 &
% 8.24/1.96 | | | | | member(all_58_1, all_15_3) = all_58_0 & $i(all_58_1)
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | ALPHA: (39) implies:
% 8.24/1.96 | | | | | (40) ~ (all_58_0 = 0)
% 8.24/1.96 | | | | | (41) $i(all_58_1)
% 8.24/1.96 | | | | | (42) member(all_58_1, all_15_3) = all_58_0
% 8.24/1.96 | | | | | (43) member(all_58_1, all_15_2) = 0
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | GROUND_INST: instantiating (34) with all_58_1, simplifying with (41),
% 8.24/1.96 | | | | | (43) gives:
% 8.24/1.96 | | | | | (44) member(all_58_1, all_15_4) = 0
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | GROUND_INST: instantiating (18) with all_58_1, simplifying with (41),
% 8.24/1.96 | | | | | (44) gives:
% 8.24/1.96 | | | | | (45) member(all_58_1, all_15_3) = 0
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | GROUND_INST: instantiating (5) with all_58_0, 0, all_15_3, all_58_1,
% 8.24/1.96 | | | | | simplifying with (42), (45) gives:
% 8.24/1.96 | | | | | (46) all_58_0 = 0
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | REDUCE: (40), (46) imply:
% 8.24/1.96 | | | | | (47) $false
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | | CLOSE: (47) is inconsistent.
% 8.24/1.96 | | | | |
% 8.24/1.96 | | | | End of split
% 8.24/1.96 | | | |
% 8.24/1.96 | | | Case 2:
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | (48) ~ (all_29_1 = 0)
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | REDUCE: (32), (48) imply:
% 8.24/1.96 | | | | (49) $false
% 8.24/1.96 | | | |
% 8.24/1.96 | | | | CLOSE: (49) is inconsistent.
% 8.24/1.96 | | | |
% 8.24/1.96 | | | End of split
% 8.24/1.96 | | |
% 8.24/1.96 | | End of split
% 8.24/1.96 | |
% 8.24/1.96 | End of split
% 8.24/1.96 |
% 8.24/1.96 End of proof
% 8.24/1.96 % SZS output end Proof for theBenchmark
% 8.24/1.96
% 8.24/1.96 1361ms
%------------------------------------------------------------------------------