TSTP Solution File: SET594+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 15:25:28 EDT 2023
% Result : Theorem 5.67s 1.59s
% Output : Proof 7.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 09:09:53 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.75/0.98 Prover 1: Preprocessing ...
% 1.75/0.98 Prover 4: Preprocessing ...
% 2.33/1.03 Prover 2: Preprocessing ...
% 2.33/1.03 Prover 3: Preprocessing ...
% 2.33/1.03 Prover 5: Preprocessing ...
% 2.33/1.03 Prover 0: Preprocessing ...
% 2.33/1.03 Prover 6: Preprocessing ...
% 4.23/1.34 Prover 1: Warning: ignoring some quantifiers
% 4.23/1.34 Prover 4: Warning: ignoring some quantifiers
% 4.23/1.34 Prover 3: Warning: ignoring some quantifiers
% 4.23/1.35 Prover 3: Constructing countermodel ...
% 4.23/1.35 Prover 6: Proving ...
% 4.23/1.35 Prover 5: Proving ...
% 4.23/1.35 Prover 2: Proving ...
% 4.23/1.35 Prover 1: Constructing countermodel ...
% 4.23/1.35 Prover 0: Proving ...
% 4.23/1.36 Prover 4: Constructing countermodel ...
% 5.67/1.58 Prover 0: proved (963ms)
% 5.67/1.59
% 5.67/1.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.59
% 5.67/1.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.67/1.59 Prover 5: stopped
% 5.67/1.59 Prover 2: stopped
% 5.67/1.60 Prover 6: stopped
% 5.67/1.60 Prover 3: stopped
% 5.67/1.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.67/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.30/1.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.30/1.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.30/1.63 Prover 8: Preprocessing ...
% 6.30/1.63 Prover 10: Preprocessing ...
% 6.30/1.64 Prover 13: Preprocessing ...
% 6.30/1.65 Prover 7: Preprocessing ...
% 6.30/1.65 Prover 11: Preprocessing ...
% 6.30/1.68 Prover 10: Warning: ignoring some quantifiers
% 6.90/1.70 Prover 7: Warning: ignoring some quantifiers
% 6.90/1.70 Prover 13: Warning: ignoring some quantifiers
% 6.90/1.70 Prover 7: Constructing countermodel ...
% 6.90/1.70 Prover 13: Constructing countermodel ...
% 6.90/1.71 Prover 10: Constructing countermodel ...
% 6.90/1.71 Prover 1: Found proof (size 43)
% 6.90/1.71 Prover 1: proved (1085ms)
% 6.90/1.72 Prover 7: stopped
% 6.90/1.72 Prover 8: Warning: ignoring some quantifiers
% 6.90/1.72 Prover 10: stopped
% 6.90/1.72 Prover 4: stopped
% 6.90/1.72 Prover 8: Constructing countermodel ...
% 6.90/1.72 Prover 13: stopped
% 6.90/1.73 Prover 8: stopped
% 6.90/1.75 Prover 11: Warning: ignoring some quantifiers
% 6.90/1.76 Prover 11: Constructing countermodel ...
% 6.90/1.76 Prover 11: stopped
% 6.90/1.76
% 6.90/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.90/1.76
% 6.90/1.77 % SZS output start Proof for theBenchmark
% 6.90/1.78 Assumptions after simplification:
% 6.90/1.78 ---------------------------------
% 6.90/1.78
% 6.90/1.78 (commutativity_of_intersection)
% 7.51/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 7.51/1.81 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 7.51/1.81
% 7.51/1.81 (commutativity_of_union)
% 7.51/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1)
% 7.51/1.81 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2)))
% 7.51/1.81
% 7.51/1.81 (intersection_defn)
% 7.55/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.55/1.82 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 7.55/1.82 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 7.55/1.82 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 7.55/1.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~
% 7.55/1.82 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) =
% 7.55/1.82 0 & member(v2, v0) = 0))
% 7.55/1.82
% 7.55/1.82 (prove_th53)
% 7.55/1.82 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.55/1.82 $i] : ? [v6: int] : ( ~ (v6 = 0) & intersection(v0, v2) = v4 &
% 7.55/1.82 intersection(v0, v1) = v3 & union(v3, v4) = v0 & union(v1, v2) = v5 &
% 7.55/1.82 subset(v0, v5) = v6 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.55/1.82
% 7.55/1.82 (subset_defn)
% 7.55/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.55/1.83 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.55/1.83 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.55/1.83 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.55/1.83 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.55/1.83
% 7.55/1.83 (union_defn)
% 7.55/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.55/1.83 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 7.55/1.83 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 7.55/1.83 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 7.55/1.83 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0)
% 7.55/1.83 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.55/1.83 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 7.55/1.83
% 7.55/1.83 (function-axioms)
% 7.55/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.55/1.83 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: $i]
% 7.55/1.83 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1)
% 7.55/1.83 | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.55/1.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 7.55/1.83 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.55/1.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.55/1.84 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 7.55/1.84
% 7.55/1.84 Further assumptions not needed in the proof:
% 7.55/1.84 --------------------------------------------
% 7.55/1.84 equal_defn, equal_member_defn, reflexivity_of_subset
% 7.55/1.84
% 7.55/1.84 Those formulas are unsatisfiable:
% 7.55/1.84 ---------------------------------
% 7.55/1.84
% 7.55/1.84 Begin of proof
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (subset_defn) implies:
% 7.55/1.84 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.55/1.84 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.55/1.84 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (union_defn) implies:
% 7.55/1.84 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0,
% 7.55/1.84 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.55/1.84 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 &
% 7.55/1.84 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 7.55/1.84 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 7.55/1.84 | (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~
% 7.55/1.84 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 7.55/1.84 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) =
% 7.55/1.84 | v5))
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (intersection_defn) implies:
% 7.55/1.84 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.55/1.84 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) |
% 7.55/1.84 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 7.55/1.84 |
% 7.55/1.84 | ALPHA: (function-axioms) implies:
% 7.55/1.84 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.55/1.84 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.55/1.84 | = v0))
% 7.55/1.84 |
% 7.55/1.85 | DELTA: instantiating (prove_th53) with fresh symbols all_11_0, all_11_1,
% 7.55/1.85 | all_11_2, all_11_3, all_11_4, all_11_5, all_11_6 gives:
% 7.55/1.85 | (6) ~ (all_11_0 = 0) & intersection(all_11_6, all_11_4) = all_11_2 &
% 7.55/1.85 | intersection(all_11_6, all_11_5) = all_11_3 & union(all_11_3, all_11_2)
% 7.55/1.85 | = all_11_6 & union(all_11_5, all_11_4) = all_11_1 & subset(all_11_6,
% 7.55/1.85 | all_11_1) = all_11_0 & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) &
% 7.55/1.85 | $i(all_11_4) & $i(all_11_5) & $i(all_11_6)
% 7.55/1.85 |
% 7.55/1.85 | ALPHA: (6) implies:
% 7.55/1.85 | (7) ~ (all_11_0 = 0)
% 7.55/1.85 | (8) $i(all_11_6)
% 7.55/1.85 | (9) $i(all_11_5)
% 7.55/1.85 | (10) $i(all_11_4)
% 7.55/1.85 | (11) $i(all_11_3)
% 7.55/1.85 | (12) $i(all_11_2)
% 7.55/1.85 | (13) $i(all_11_1)
% 7.55/1.85 | (14) subset(all_11_6, all_11_1) = all_11_0
% 7.55/1.85 | (15) union(all_11_5, all_11_4) = all_11_1
% 7.55/1.85 | (16) union(all_11_3, all_11_2) = all_11_6
% 7.55/1.85 | (17) intersection(all_11_6, all_11_5) = all_11_3
% 7.55/1.85 | (18) intersection(all_11_6, all_11_4) = all_11_2
% 7.55/1.85 |
% 7.55/1.85 | GROUND_INST: instantiating (1) with all_11_6, all_11_1, all_11_0, simplifying
% 7.55/1.85 | with (8), (13), (14) gives:
% 7.55/1.85 | (19) all_11_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.55/1.85 | all_11_1) = v1 & member(v0, all_11_6) = 0 & $i(v0))
% 7.55/1.85 |
% 7.55/1.85 | GROUND_INST: instantiating (commutativity_of_union) with all_11_5, all_11_4,
% 7.55/1.85 | all_11_1, simplifying with (9), (10), (15) gives:
% 7.55/1.85 | (20) union(all_11_4, all_11_5) = all_11_1 & $i(all_11_1)
% 7.55/1.85 |
% 7.55/1.85 | ALPHA: (20) implies:
% 7.55/1.85 | (21) union(all_11_4, all_11_5) = all_11_1
% 7.55/1.85 |
% 7.55/1.85 | GROUND_INST: instantiating (commutativity_of_union) with all_11_3, all_11_2,
% 7.55/1.85 | all_11_6, simplifying with (11), (12), (16) gives:
% 7.55/1.85 | (22) union(all_11_2, all_11_3) = all_11_6 & $i(all_11_6)
% 7.55/1.85 |
% 7.55/1.85 | ALPHA: (22) implies:
% 7.55/1.85 | (23) union(all_11_2, all_11_3) = all_11_6
% 7.55/1.85 |
% 7.55/1.85 | GROUND_INST: instantiating (commutativity_of_intersection) with all_11_6,
% 7.55/1.85 | all_11_5, all_11_3, simplifying with (8), (9), (17) gives:
% 7.55/1.85 | (24) intersection(all_11_5, all_11_6) = all_11_3 & $i(all_11_3)
% 7.55/1.85 |
% 7.55/1.86 | GROUND_INST: instantiating (commutativity_of_intersection) with all_11_6,
% 7.55/1.86 | all_11_4, all_11_2, simplifying with (8), (10), (18) gives:
% 7.55/1.86 | (25) intersection(all_11_4, all_11_6) = all_11_2 & $i(all_11_2)
% 7.55/1.86 |
% 7.55/1.86 | BETA: splitting (19) gives:
% 7.55/1.86 |
% 7.55/1.86 | Case 1:
% 7.55/1.86 | |
% 7.55/1.86 | | (26) all_11_0 = 0
% 7.55/1.86 | |
% 7.55/1.86 | | REDUCE: (7), (26) imply:
% 7.55/1.86 | | (27) $false
% 7.55/1.86 | |
% 7.55/1.86 | | CLOSE: (27) is inconsistent.
% 7.55/1.86 | |
% 7.55/1.86 | Case 2:
% 7.55/1.86 | |
% 7.55/1.86 | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_11_1) =
% 7.55/1.86 | | v1 & member(v0, all_11_6) = 0 & $i(v0))
% 7.55/1.86 | |
% 7.55/1.86 | | DELTA: instantiating (28) with fresh symbols all_23_0, all_23_1 gives:
% 7.55/1.86 | | (29) ~ (all_23_0 = 0) & member(all_23_1, all_11_1) = all_23_0 &
% 7.55/1.86 | | member(all_23_1, all_11_6) = 0 & $i(all_23_1)
% 7.55/1.86 | |
% 7.55/1.86 | | ALPHA: (29) implies:
% 7.55/1.86 | | (30) ~ (all_23_0 = 0)
% 7.55/1.86 | | (31) $i(all_23_1)
% 7.55/1.86 | | (32) member(all_23_1, all_11_6) = 0
% 7.55/1.86 | | (33) member(all_23_1, all_11_1) = all_23_0
% 7.55/1.86 | |
% 7.55/1.86 | | GROUND_INST: instantiating (3) with all_11_4, all_11_5, all_23_1, all_11_1,
% 7.55/1.86 | | all_23_0, simplifying with (9), (10), (21), (31), (33) gives:
% 7.55/1.86 | | (34) all_23_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 7.55/1.86 | | 0) & member(all_23_1, all_11_4) = v0 & member(all_23_1,
% 7.55/1.86 | | all_11_5) = v1)
% 7.55/1.86 | |
% 7.55/1.86 | | GROUND_INST: instantiating (2) with all_11_2, all_11_3, all_23_1, all_11_6,
% 7.55/1.86 | | simplifying with (11), (12), (23), (31), (32) gives:
% 7.55/1.86 | | (35) ? [v0: any] : ? [v1: any] : (member(all_23_1, all_11_2) = v0 &
% 7.55/1.86 | | member(all_23_1, all_11_3) = v1 & (v1 = 0 | v0 = 0))
% 7.55/1.86 | |
% 7.55/1.86 | | DELTA: instantiating (35) with fresh symbols all_30_0, all_30_1 gives:
% 7.55/1.86 | | (36) member(all_23_1, all_11_2) = all_30_1 & member(all_23_1, all_11_3) =
% 7.55/1.86 | | all_30_0 & (all_30_0 = 0 | all_30_1 = 0)
% 7.55/1.86 | |
% 7.55/1.86 | | ALPHA: (36) implies:
% 7.55/1.86 | | (37) member(all_23_1, all_11_3) = all_30_0
% 7.55/1.86 | | (38) member(all_23_1, all_11_2) = all_30_1
% 7.55/1.86 | | (39) all_30_0 = 0 | all_30_1 = 0
% 7.55/1.86 | |
% 7.55/1.86 | | BETA: splitting (34) gives:
% 7.55/1.86 | |
% 7.55/1.86 | | Case 1:
% 7.55/1.86 | | |
% 7.55/1.86 | | | (40) all_23_0 = 0
% 7.55/1.87 | | |
% 7.55/1.87 | | | REDUCE: (30), (40) imply:
% 7.55/1.87 | | | (41) $false
% 7.55/1.87 | | |
% 7.55/1.87 | | | CLOSE: (41) is inconsistent.
% 7.55/1.87 | | |
% 7.55/1.87 | | Case 2:
% 7.55/1.87 | | |
% 7.55/1.87 | | | (42) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 7.55/1.87 | | | member(all_23_1, all_11_4) = v0 & member(all_23_1, all_11_5) =
% 7.55/1.87 | | | v1)
% 7.55/1.87 | | |
% 7.55/1.87 | | | DELTA: instantiating (42) with fresh symbols all_38_0, all_38_1 gives:
% 7.55/1.87 | | | (43) ~ (all_38_0 = 0) & ~ (all_38_1 = 0) & member(all_23_1, all_11_4)
% 7.55/1.87 | | | = all_38_1 & member(all_23_1, all_11_5) = all_38_0
% 7.55/1.87 | | |
% 7.55/1.87 | | | ALPHA: (43) implies:
% 7.55/1.87 | | | (44) ~ (all_38_1 = 0)
% 7.55/1.87 | | | (45) ~ (all_38_0 = 0)
% 7.55/1.87 | | | (46) member(all_23_1, all_11_5) = all_38_0
% 7.55/1.87 | | | (47) member(all_23_1, all_11_4) = all_38_1
% 7.55/1.87 | | |
% 7.55/1.87 | | | BETA: splitting (39) gives:
% 7.55/1.87 | | |
% 7.55/1.87 | | | Case 1:
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | (48) all_30_0 = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | REDUCE: (37), (48) imply:
% 7.55/1.87 | | | | (49) member(all_23_1, all_11_3) = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | GROUND_INST: instantiating (4) with all_11_6, all_11_5, all_23_1,
% 7.55/1.87 | | | | all_11_3, simplifying with (8), (9), (17), (31), (49)
% 7.55/1.87 | | | | gives:
% 7.55/1.87 | | | | (50) member(all_23_1, all_11_5) = 0 & member(all_23_1, all_11_6) = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | ALPHA: (50) implies:
% 7.55/1.87 | | | | (51) member(all_23_1, all_11_5) = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | GROUND_INST: instantiating (5) with all_38_0, 0, all_11_5, all_23_1,
% 7.55/1.87 | | | | simplifying with (46), (51) gives:
% 7.55/1.87 | | | | (52) all_38_0 = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | REDUCE: (45), (52) imply:
% 7.55/1.87 | | | | (53) $false
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | CLOSE: (53) is inconsistent.
% 7.55/1.87 | | | |
% 7.55/1.87 | | | Case 2:
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | (54) all_30_1 = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | REDUCE: (38), (54) imply:
% 7.55/1.87 | | | | (55) member(all_23_1, all_11_2) = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | GROUND_INST: instantiating (4) with all_11_6, all_11_4, all_23_1,
% 7.55/1.87 | | | | all_11_2, simplifying with (8), (10), (18), (31), (55)
% 7.55/1.87 | | | | gives:
% 7.55/1.87 | | | | (56) member(all_23_1, all_11_4) = 0 & member(all_23_1, all_11_6) = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | ALPHA: (56) implies:
% 7.55/1.87 | | | | (57) member(all_23_1, all_11_4) = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | GROUND_INST: instantiating (5) with all_38_1, 0, all_11_4, all_23_1,
% 7.55/1.87 | | | | simplifying with (47), (57) gives:
% 7.55/1.87 | | | | (58) all_38_1 = 0
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | REDUCE: (44), (58) imply:
% 7.55/1.87 | | | | (59) $false
% 7.55/1.87 | | | |
% 7.55/1.87 | | | | CLOSE: (59) is inconsistent.
% 7.55/1.87 | | | |
% 7.55/1.87 | | | End of split
% 7.55/1.87 | | |
% 7.55/1.87 | | End of split
% 7.55/1.87 | |
% 7.55/1.87 | End of split
% 7.55/1.87 |
% 7.55/1.87 End of proof
% 7.55/1.87 % SZS output end Proof for theBenchmark
% 7.55/1.88
% 7.55/1.88 1274ms
%------------------------------------------------------------------------------