TSTP Solution File: SET585+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET585+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 : n024.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 15:25:25 EDT 2023
% Result : Theorem 5.70s 1.55s
% Output : Proof 7.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET585+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.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 12:31:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.65 ________ _____
% 0.19/0.65 ___ __ \_________(_)________________________________
% 0.19/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.65
% 0.19/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.65 (2023-06-19)
% 0.19/0.65
% 0.19/0.65 (c) Philipp Rümmer, 2009-2023
% 0.19/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.65 Amanda Stjerna.
% 0.19/0.65 Free software under BSD-3-Clause.
% 0.19/0.65
% 0.19/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.65
% 0.19/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.66 Running up to 7 provers in parallel.
% 0.65/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.93/1.01 Prover 4: Preprocessing ...
% 1.93/1.01 Prover 1: Preprocessing ...
% 2.55/1.07 Prover 5: Preprocessing ...
% 2.55/1.07 Prover 3: Preprocessing ...
% 2.55/1.07 Prover 6: Preprocessing ...
% 2.55/1.07 Prover 2: Preprocessing ...
% 2.55/1.07 Prover 0: Preprocessing ...
% 4.23/1.36 Prover 1: Warning: ignoring some quantifiers
% 4.23/1.36 Prover 5: Proving ...
% 4.64/1.37 Prover 6: Proving ...
% 4.64/1.37 Prover 3: Warning: ignoring some quantifiers
% 4.64/1.38 Prover 1: Constructing countermodel ...
% 4.64/1.39 Prover 3: Constructing countermodel ...
% 4.64/1.39 Prover 2: Proving ...
% 4.64/1.40 Prover 4: Warning: ignoring some quantifiers
% 4.64/1.41 Prover 0: Proving ...
% 4.64/1.41 Prover 4: Constructing countermodel ...
% 5.70/1.55 Prover 2: proved (878ms)
% 5.70/1.55
% 5.70/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.70/1.55
% 5.70/1.55 Prover 6: stopped
% 5.70/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.70/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.70/1.56 Prover 5: stopped
% 5.70/1.56 Prover 3: stopped
% 5.90/1.57 Prover 0: stopped
% 5.90/1.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.90/1.58 Prover 7: Preprocessing ...
% 5.90/1.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.90/1.58 Prover 8: Preprocessing ...
% 5.90/1.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.90/1.60 Prover 13: Preprocessing ...
% 5.90/1.61 Prover 10: Preprocessing ...
% 5.90/1.63 Prover 11: Preprocessing ...
% 6.38/1.64 Prover 1: Found proof (size 27)
% 6.38/1.64 Prover 1: proved (970ms)
% 6.38/1.64 Prover 4: stopped
% 6.38/1.66 Prover 11: stopped
% 6.38/1.66 Prover 7: Warning: ignoring some quantifiers
% 6.38/1.67 Prover 10: Warning: ignoring some quantifiers
% 6.38/1.67 Prover 13: Warning: ignoring some quantifiers
% 6.69/1.67 Prover 7: Constructing countermodel ...
% 6.69/1.67 Prover 10: Constructing countermodel ...
% 6.69/1.68 Prover 8: Warning: ignoring some quantifiers
% 6.69/1.68 Prover 7: stopped
% 6.69/1.68 Prover 13: Constructing countermodel ...
% 6.69/1.68 Prover 10: stopped
% 6.69/1.68 Prover 8: Constructing countermodel ...
% 6.69/1.69 Prover 13: stopped
% 6.69/1.69 Prover 8: stopped
% 6.69/1.69
% 6.69/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.69/1.69
% 6.69/1.69 % SZS output start Proof for theBenchmark
% 6.69/1.70 Assumptions after simplification:
% 6.69/1.70 ---------------------------------
% 6.69/1.70
% 6.69/1.70 (commutativity_of_intersection)
% 6.69/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 6.69/1.73 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 6.69/1.73
% 6.69/1.73 (commutativity_of_union)
% 6.69/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1)
% 6.69/1.73 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2)))
% 6.69/1.73
% 6.69/1.73 (intersection_defn)
% 6.69/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 6.69/1.73 | ~ (member(v2, v3) = v4) | ~ (intersection(v0, v1) = v3) | ~ $i(v2) | ~
% 6.69/1.73 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 6.69/1.73 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 6.69/1.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (member(v2, v3) = 0) | ~
% 6.69/1.73 (intersection(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 6.69/1.73 (member(v2, v1) = 0 & member(v2, v0) = 0))
% 6.69/1.74
% 7.07/1.74 (prove_intersection_subset_of_union)
% 7.07/1.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.07/1.74 int] : ( ~ (v5 = 0) & intersection(v0, v1) = v3 & union(v0, v2) = v4 &
% 7.07/1.74 subset(v3, v4) = v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.07/1.74
% 7.07/1.74 (subset_defn)
% 7.07/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.07/1.74 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.07/1.74 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.07/1.74 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.07/1.74 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.07/1.74
% 7.07/1.74 (union_defn)
% 7.07/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.07/1.75 | ~ (member(v2, v3) = v4) | ~ (union(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 7.07/1.75 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 7.07/1.75 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 7.07/1.75 ! [v2: $i] : ! [v3: $i] : ( ~ (member(v2, v3) = 0) | ~ (union(v0, v1) = v3)
% 7.07/1.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.07/1.75 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 7.07/1.75
% 7.07/1.75 (function-axioms)
% 7.07/1.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.07/1.75 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) &
% 7.07/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.07/1.75 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: $i]
% 7.07/1.75 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1)
% 7.07/1.75 | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.07/1.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 7.07/1.75 v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.07/1.75
% 7.07/1.75 Further assumptions not needed in the proof:
% 7.07/1.75 --------------------------------------------
% 7.07/1.75 equal_member_defn, intersection_is_subset, reflexivity_of_subset,
% 7.07/1.75 subset_of_union, transitivity_of_subset
% 7.07/1.75
% 7.07/1.75 Those formulas are unsatisfiable:
% 7.07/1.75 ---------------------------------
% 7.07/1.75
% 7.07/1.75 Begin of proof
% 7.07/1.75 |
% 7.07/1.76 | ALPHA: (union_defn) implies:
% 7.07/1.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 7.07/1.76 | (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (union(v0, v1) = v3) | ~
% 7.07/1.76 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 7.07/1.76 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) =
% 7.07/1.76 | v5))
% 7.07/1.76 |
% 7.07/1.76 | ALPHA: (intersection_defn) implies:
% 7.07/1.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (member(v2,
% 7.07/1.76 | v3) = 0) | ~ (intersection(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 7.07/1.76 | | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 7.07/1.76 |
% 7.07/1.76 | ALPHA: (subset_defn) implies:
% 7.07/1.76 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.07/1.76 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.07/1.76 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.07/1.76 |
% 7.07/1.76 | ALPHA: (function-axioms) implies:
% 7.21/1.77 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.21/1.77 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.21/1.77 | = v0))
% 7.21/1.77 |
% 7.21/1.77 | DELTA: instantiating (prove_intersection_subset_of_union) with fresh symbols
% 7.21/1.77 | all_12_0, all_12_1, all_12_2, all_12_3, all_12_4, all_12_5 gives:
% 7.21/1.77 | (5) ~ (all_12_0 = 0) & intersection(all_12_5, all_12_4) = all_12_2 &
% 7.21/1.77 | union(all_12_5, all_12_3) = all_12_1 & subset(all_12_2, all_12_1) =
% 7.21/1.77 | all_12_0 & $i(all_12_1) & $i(all_12_2) & $i(all_12_3) & $i(all_12_4) &
% 7.21/1.77 | $i(all_12_5)
% 7.21/1.77 |
% 7.21/1.77 | ALPHA: (5) implies:
% 7.21/1.77 | (6) ~ (all_12_0 = 0)
% 7.21/1.77 | (7) $i(all_12_5)
% 7.21/1.77 | (8) $i(all_12_4)
% 7.21/1.77 | (9) $i(all_12_3)
% 7.21/1.77 | (10) $i(all_12_2)
% 7.21/1.77 | (11) $i(all_12_1)
% 7.21/1.77 | (12) subset(all_12_2, all_12_1) = all_12_0
% 7.21/1.77 | (13) union(all_12_5, all_12_3) = all_12_1
% 7.21/1.77 | (14) intersection(all_12_5, all_12_4) = all_12_2
% 7.21/1.77 |
% 7.21/1.77 | GROUND_INST: instantiating (3) with all_12_2, all_12_1, all_12_0, simplifying
% 7.21/1.77 | with (10), (11), (12) gives:
% 7.21/1.77 | (15) all_12_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.21/1.77 | all_12_1) = v1 & member(v0, all_12_2) = 0 & $i(v0))
% 7.21/1.77 |
% 7.21/1.78 | GROUND_INST: instantiating (commutativity_of_union) with all_12_5, all_12_3,
% 7.21/1.78 | all_12_1, simplifying with (7), (9), (13) gives:
% 7.21/1.78 | (16) union(all_12_3, all_12_5) = all_12_1 & $i(all_12_1)
% 7.21/1.78 |
% 7.21/1.78 | ALPHA: (16) implies:
% 7.21/1.78 | (17) union(all_12_3, all_12_5) = all_12_1
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (commutativity_of_intersection) with all_12_5,
% 7.21/1.78 | all_12_4, all_12_2, simplifying with (7), (8), (14) gives:
% 7.21/1.78 | (18) intersection(all_12_4, all_12_5) = all_12_2 & $i(all_12_2)
% 7.21/1.78 |
% 7.21/1.78 | ALPHA: (18) implies:
% 7.21/1.78 | (19) intersection(all_12_4, all_12_5) = all_12_2
% 7.21/1.78 |
% 7.21/1.78 | BETA: splitting (15) gives:
% 7.21/1.78 |
% 7.21/1.78 | Case 1:
% 7.21/1.78 | |
% 7.21/1.78 | | (20) all_12_0 = 0
% 7.21/1.78 | |
% 7.21/1.78 | | REDUCE: (6), (20) imply:
% 7.21/1.78 | | (21) $false
% 7.21/1.78 | |
% 7.21/1.78 | | CLOSE: (21) is inconsistent.
% 7.21/1.78 | |
% 7.21/1.78 | Case 2:
% 7.21/1.78 | |
% 7.21/1.78 | | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_12_1) =
% 7.21/1.78 | | v1 & member(v0, all_12_2) = 0 & $i(v0))
% 7.21/1.78 | |
% 7.21/1.78 | | DELTA: instantiating (22) with fresh symbols all_25_0, all_25_1 gives:
% 7.21/1.78 | | (23) ~ (all_25_0 = 0) & member(all_25_1, all_12_1) = all_25_0 &
% 7.21/1.78 | | member(all_25_1, all_12_2) = 0 & $i(all_25_1)
% 7.21/1.78 | |
% 7.21/1.78 | | ALPHA: (23) implies:
% 7.21/1.78 | | (24) ~ (all_25_0 = 0)
% 7.21/1.78 | | (25) $i(all_25_1)
% 7.21/1.78 | | (26) member(all_25_1, all_12_2) = 0
% 7.21/1.78 | | (27) member(all_25_1, all_12_1) = all_25_0
% 7.21/1.78 | |
% 7.21/1.78 | | GROUND_INST: instantiating (2) with all_12_4, all_12_5, all_25_1, all_12_2,
% 7.21/1.78 | | simplifying with (7), (8), (19), (25), (26) gives:
% 7.21/1.78 | | (28) member(all_25_1, all_12_4) = 0 & member(all_25_1, all_12_5) = 0
% 7.21/1.78 | |
% 7.21/1.78 | | ALPHA: (28) implies:
% 7.21/1.78 | | (29) member(all_25_1, all_12_5) = 0
% 7.21/1.78 | |
% 7.21/1.79 | | GROUND_INST: instantiating (1) with all_12_3, all_12_5, all_25_1, all_12_1,
% 7.21/1.79 | | all_25_0, simplifying with (7), (9), (17), (25), (27) gives:
% 7.21/1.79 | | (30) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 7.21/1.79 | | 0) & member(all_25_1, all_12_3) = v0 & member(all_25_1,
% 7.21/1.79 | | all_12_5) = v1)
% 7.21/1.79 | |
% 7.21/1.79 | | BETA: splitting (30) gives:
% 7.21/1.79 | |
% 7.21/1.79 | | Case 1:
% 7.21/1.79 | | |
% 7.21/1.79 | | | (31) all_25_0 = 0
% 7.21/1.79 | | |
% 7.21/1.79 | | | REDUCE: (24), (31) imply:
% 7.21/1.79 | | | (32) $false
% 7.21/1.79 | | |
% 7.21/1.79 | | | CLOSE: (32) is inconsistent.
% 7.21/1.79 | | |
% 7.21/1.79 | | Case 2:
% 7.21/1.79 | | |
% 7.21/1.79 | | | (33) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 7.21/1.79 | | | member(all_25_1, all_12_3) = v0 & member(all_25_1, all_12_5) =
% 7.21/1.79 | | | v1)
% 7.21/1.79 | | |
% 7.21/1.79 | | | DELTA: instantiating (33) with fresh symbols all_37_0, all_37_1 gives:
% 7.21/1.79 | | | (34) ~ (all_37_0 = 0) & ~ (all_37_1 = 0) & member(all_25_1, all_12_3)
% 7.21/1.79 | | | = all_37_1 & member(all_25_1, all_12_5) = all_37_0
% 7.21/1.79 | | |
% 7.21/1.79 | | | ALPHA: (34) implies:
% 7.21/1.79 | | | (35) ~ (all_37_0 = 0)
% 7.21/1.79 | | | (36) member(all_25_1, all_12_5) = all_37_0
% 7.21/1.79 | | |
% 7.21/1.79 | | | GROUND_INST: instantiating (4) with 0, all_37_0, all_12_5, all_25_1,
% 7.21/1.79 | | | simplifying with (29), (36) gives:
% 7.21/1.79 | | | (37) all_37_0 = 0
% 7.21/1.79 | | |
% 7.21/1.79 | | | REDUCE: (35), (37) imply:
% 7.21/1.79 | | | (38) $false
% 7.21/1.79 | | |
% 7.21/1.79 | | | CLOSE: (38) is inconsistent.
% 7.21/1.79 | | |
% 7.21/1.79 | | End of split
% 7.21/1.79 | |
% 7.21/1.79 | End of split
% 7.21/1.79 |
% 7.21/1.79 End of proof
% 7.21/1.79 % SZS output end Proof for theBenchmark
% 7.21/1.79
% 7.21/1.79 1144ms
%------------------------------------------------------------------------------