TSTP Solution File: SET593+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET593+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 : n009.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 6.08s 1.53s
% Output : Proof 7.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET593+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:01:35 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.61/0.61 ________ _____
% 0.61/0.61 ___ __ \_________(_)________________________________
% 0.61/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.61
% 0.61/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.61 (2023-06-19)
% 0.61/0.61
% 0.61/0.61 (c) Philipp Rümmer, 2009-2023
% 0.61/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.61 Amanda Stjerna.
% 0.61/0.61 Free software under BSD-3-Clause.
% 0.61/0.61
% 0.61/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.61
% 0.61/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.62 Running up to 7 provers in parallel.
% 0.66/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.31/1.03 Prover 1: Preprocessing ...
% 2.31/1.03 Prover 4: Preprocessing ...
% 2.31/1.07 Prover 0: Preprocessing ...
% 2.31/1.07 Prover 2: Preprocessing ...
% 2.31/1.07 Prover 5: Preprocessing ...
% 2.31/1.08 Prover 6: Preprocessing ...
% 2.31/1.08 Prover 3: Preprocessing ...
% 3.84/1.27 Prover 5: Proving ...
% 3.84/1.27 Prover 3: Warning: ignoring some quantifiers
% 3.84/1.29 Prover 3: Constructing countermodel ...
% 3.84/1.30 Prover 2: Proving ...
% 3.84/1.30 Prover 1: Warning: ignoring some quantifiers
% 4.33/1.30 Prover 6: Proving ...
% 4.33/1.31 Prover 0: Proving ...
% 4.33/1.31 Prover 4: Warning: ignoring some quantifiers
% 4.33/1.31 Prover 1: Constructing countermodel ...
% 4.33/1.32 Prover 4: Constructing countermodel ...
% 6.04/1.53 Prover 0: proved (903ms)
% 6.04/1.53
% 6.08/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.08/1.53
% 6.08/1.54 Prover 3: stopped
% 6.08/1.55 Prover 2: stopped
% 6.08/1.55 Prover 5: stopped
% 6.08/1.55 Prover 6: stopped
% 6.08/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.08/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.08/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.08/1.55 Prover 7: Preprocessing ...
% 6.08/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.08/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.08/1.57 Prover 10: Preprocessing ...
% 6.08/1.58 Prover 8: Preprocessing ...
% 6.08/1.58 Prover 11: Preprocessing ...
% 6.08/1.59 Prover 13: Preprocessing ...
% 6.08/1.59 Prover 7: Warning: ignoring some quantifiers
% 6.08/1.60 Prover 7: Constructing countermodel ...
% 6.57/1.64 Prover 10: Warning: ignoring some quantifiers
% 6.57/1.64 Prover 1: Found proof (size 63)
% 6.57/1.64 Prover 1: proved (1006ms)
% 6.57/1.64 Prover 4: stopped
% 6.57/1.64 Prover 7: stopped
% 6.57/1.64 Prover 13: Warning: ignoring some quantifiers
% 6.57/1.64 Prover 10: Constructing countermodel ...
% 6.57/1.65 Prover 13: Constructing countermodel ...
% 6.57/1.65 Prover 10: stopped
% 6.57/1.65 Prover 11: Warning: ignoring some quantifiers
% 6.57/1.65 Prover 13: stopped
% 6.57/1.65 Prover 11: Constructing countermodel ...
% 6.57/1.65 Prover 8: Warning: ignoring some quantifiers
% 6.57/1.66 Prover 11: stopped
% 6.57/1.66 Prover 8: Constructing countermodel ...
% 6.57/1.67 Prover 8: stopped
% 6.57/1.67
% 6.57/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.57/1.67
% 7.04/1.68 % SZS output start Proof for theBenchmark
% 7.04/1.68 Assumptions after simplification:
% 7.04/1.68 ---------------------------------
% 7.04/1.68
% 7.04/1.68 (commutativity_of_union)
% 7.04/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1)
% 7.04/1.71 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2)))
% 7.04/1.71
% 7.04/1.71 (difference_defn)
% 7.04/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.04/1.72 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 7.04/1.72 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 7.04/1.72 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 7.04/1.72 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2,
% 7.04/1.72 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 7.04/1.72 0) & member(v2, v1) = v4 & member(v2, v0) = 0))
% 7.04/1.72
% 7.04/1.72 (prove_th52)
% 7.04/1.72 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.04/1.72 any] : ? [v6: $i] : ? [v7: any] : (subset(v6, v1) = v7 & subset(v4, v2) =
% 7.04/1.72 v5 & subset(v0, v3) = 0 & difference(v0, v2) = v6 & difference(v0, v1) = v4
% 7.04/1.72 & union(v1, v2) = v3 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 7.04/1.72 ( ~ (v7 = 0) | ~ (v5 = 0)))
% 7.04/1.72
% 7.04/1.72 (subset_defn)
% 7.04/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.04/1.72 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.04/1.72 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.04/1.72 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.04/1.72 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.04/1.72
% 7.04/1.72 (union_defn)
% 7.04/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.04/1.73 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 7.04/1.73 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 7.04/1.73 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 7.04/1.73 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0)
% 7.04/1.73 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.04/1.73 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 7.04/1.73
% 7.04/1.73 (function-axioms)
% 7.04/1.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.04/1.73 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 7.04/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.04/1.73 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 7.04/1.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 7.04/1.73 (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.04/1.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3,
% 7.04/1.73 v2) = v1) | ~ (member(v3, v2) = v0))
% 7.04/1.73
% 7.04/1.73 Further assumptions not needed in the proof:
% 7.04/1.73 --------------------------------------------
% 7.04/1.73 equal_member_defn, reflexivity_of_subset
% 7.04/1.73
% 7.04/1.73 Those formulas are unsatisfiable:
% 7.04/1.73 ---------------------------------
% 7.04/1.73
% 7.04/1.73 Begin of proof
% 7.04/1.73 |
% 7.04/1.73 | ALPHA: (union_defn) implies:
% 7.04/1.74 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0,
% 7.04/1.74 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.04/1.74 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 &
% 7.04/1.74 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 7.04/1.74 |
% 7.04/1.74 | ALPHA: (difference_defn) implies:
% 7.04/1.74 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.04/1.74 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~
% 7.04/1.74 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) =
% 7.04/1.74 | v4 & member(v2, v0) = 0))
% 7.04/1.74 |
% 7.04/1.74 | ALPHA: (subset_defn) implies:
% 7.04/1.74 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 7.04/1.74 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 7.04/1.74 | member(v2, v1) = 0))
% 7.04/1.74 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.04/1.74 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.04/1.74 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.04/1.74 |
% 7.04/1.74 | ALPHA: (function-axioms) implies:
% 7.04/1.74 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.04/1.74 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.04/1.74 | = v0))
% 7.04/1.74 |
% 7.04/1.74 | DELTA: instantiating (prove_th52) with fresh symbols all_9_0, all_9_1,
% 7.04/1.74 | all_9_2, all_9_3, all_9_4, all_9_5, all_9_6, all_9_7 gives:
% 7.04/1.74 | (6) subset(all_9_1, all_9_6) = all_9_0 & subset(all_9_3, all_9_5) = all_9_2
% 7.04/1.74 | & subset(all_9_7, all_9_4) = 0 & difference(all_9_7, all_9_5) = all_9_1
% 7.04/1.74 | & difference(all_9_7, all_9_6) = all_9_3 & union(all_9_6, all_9_5) =
% 7.04/1.74 | all_9_4 & $i(all_9_1) & $i(all_9_3) & $i(all_9_4) & $i(all_9_5) &
% 7.04/1.74 | $i(all_9_6) & $i(all_9_7) & ( ~ (all_9_0 = 0) | ~ (all_9_2 = 0))
% 7.04/1.74 |
% 7.04/1.74 | ALPHA: (6) implies:
% 7.04/1.75 | (7) $i(all_9_7)
% 7.04/1.75 | (8) $i(all_9_6)
% 7.04/1.75 | (9) $i(all_9_5)
% 7.04/1.75 | (10) $i(all_9_3)
% 7.04/1.75 | (11) $i(all_9_1)
% 7.04/1.75 | (12) union(all_9_6, all_9_5) = all_9_4
% 7.04/1.75 | (13) difference(all_9_7, all_9_6) = all_9_3
% 7.04/1.75 | (14) difference(all_9_7, all_9_5) = all_9_1
% 7.04/1.75 | (15) subset(all_9_7, all_9_4) = 0
% 7.04/1.75 | (16) subset(all_9_3, all_9_5) = all_9_2
% 7.04/1.75 | (17) subset(all_9_1, all_9_6) = all_9_0
% 7.04/1.75 | (18) ~ (all_9_0 = 0) | ~ (all_9_2 = 0)
% 7.04/1.75 |
% 7.04/1.75 | GROUND_INST: instantiating (commutativity_of_union) with all_9_6, all_9_5,
% 7.04/1.75 | all_9_4, simplifying with (8), (9), (12) gives:
% 7.04/1.75 | (19) union(all_9_5, all_9_6) = all_9_4 & $i(all_9_4)
% 7.04/1.75 |
% 7.04/1.75 | ALPHA: (19) implies:
% 7.04/1.75 | (20) $i(all_9_4)
% 7.04/1.75 | (21) union(all_9_5, all_9_6) = all_9_4
% 7.04/1.75 |
% 7.04/1.75 | GROUND_INST: instantiating (3) with all_9_7, all_9_4, simplifying with (7),
% 7.04/1.75 | (15), (20) gives:
% 7.04/1.75 | (22) ! [v0: $i] : ( ~ (member(v0, all_9_7) = 0) | ~ $i(v0) | member(v0,
% 7.04/1.75 | all_9_4) = 0)
% 7.04/1.75 |
% 7.04/1.75 | GROUND_INST: instantiating (4) with all_9_3, all_9_5, all_9_2, simplifying
% 7.04/1.75 | with (9), (10), (16) gives:
% 7.04/1.75 | (23) all_9_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.04/1.75 | all_9_3) = 0 & member(v0, all_9_5) = v1 & $i(v0))
% 7.04/1.75 |
% 7.04/1.75 | GROUND_INST: instantiating (4) with all_9_1, all_9_6, all_9_0, simplifying
% 7.04/1.75 | with (8), (11), (17) gives:
% 7.04/1.75 | (24) all_9_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.04/1.75 | all_9_1) = 0 & member(v0, all_9_6) = v1 & $i(v0))
% 7.04/1.75 |
% 7.04/1.75 | BETA: splitting (18) gives:
% 7.04/1.75 |
% 7.04/1.75 | Case 1:
% 7.04/1.75 | |
% 7.04/1.75 | | (25) ~ (all_9_0 = 0)
% 7.04/1.75 | |
% 7.04/1.75 | | BETA: splitting (24) gives:
% 7.04/1.75 | |
% 7.04/1.75 | | Case 1:
% 7.04/1.75 | | |
% 7.04/1.75 | | | (26) all_9_0 = 0
% 7.04/1.75 | | |
% 7.04/1.75 | | | REDUCE: (25), (26) imply:
% 7.04/1.76 | | | (27) $false
% 7.04/1.76 | | |
% 7.04/1.76 | | | CLOSE: (27) is inconsistent.
% 7.04/1.76 | | |
% 7.04/1.76 | | Case 2:
% 7.04/1.76 | | |
% 7.04/1.76 | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_9_1) =
% 7.04/1.76 | | | 0 & member(v0, all_9_6) = v1 & $i(v0))
% 7.04/1.76 | | |
% 7.04/1.76 | | | DELTA: instantiating (28) with fresh symbols all_36_0, all_36_1 gives:
% 7.04/1.76 | | | (29) ~ (all_36_0 = 0) & member(all_36_1, all_9_1) = 0 &
% 7.04/1.76 | | | member(all_36_1, all_9_6) = all_36_0 & $i(all_36_1)
% 7.04/1.76 | | |
% 7.04/1.76 | | | ALPHA: (29) implies:
% 7.04/1.76 | | | (30) ~ (all_36_0 = 0)
% 7.04/1.76 | | | (31) $i(all_36_1)
% 7.04/1.76 | | | (32) member(all_36_1, all_9_6) = all_36_0
% 7.04/1.76 | | | (33) member(all_36_1, all_9_1) = 0
% 7.04/1.76 | | |
% 7.04/1.76 | | | GROUND_INST: instantiating (2) with all_9_7, all_9_5, all_36_1, all_9_1,
% 7.04/1.76 | | | simplifying with (7), (9), (14), (31), (33) gives:
% 7.04/1.76 | | | (34) ? [v0: int] : ( ~ (v0 = 0) & member(all_36_1, all_9_5) = v0 &
% 7.04/1.76 | | | member(all_36_1, all_9_7) = 0)
% 7.04/1.76 | | |
% 7.04/1.76 | | | DELTA: instantiating (34) with fresh symbol all_43_0 gives:
% 7.04/1.76 | | | (35) ~ (all_43_0 = 0) & member(all_36_1, all_9_5) = all_43_0 &
% 7.04/1.76 | | | member(all_36_1, all_9_7) = 0
% 7.04/1.76 | | |
% 7.04/1.76 | | | ALPHA: (35) implies:
% 7.04/1.76 | | | (36) ~ (all_43_0 = 0)
% 7.04/1.76 | | | (37) member(all_36_1, all_9_7) = 0
% 7.04/1.76 | | | (38) member(all_36_1, all_9_5) = all_43_0
% 7.04/1.76 | | |
% 7.04/1.76 | | | GROUND_INST: instantiating (22) with all_36_1, simplifying with (31), (37)
% 7.04/1.76 | | | gives:
% 7.04/1.76 | | | (39) member(all_36_1, all_9_4) = 0
% 7.04/1.76 | | |
% 7.04/1.76 | | | GROUND_INST: instantiating (1) with all_9_5, all_9_6, all_36_1, all_9_4,
% 7.04/1.76 | | | simplifying with (8), (9), (21), (31), (39) gives:
% 7.04/1.76 | | | (40) ? [v0: any] : ? [v1: any] : (member(all_36_1, all_9_5) = v0 &
% 7.04/1.76 | | | member(all_36_1, all_9_6) = v1 & (v1 = 0 | v0 = 0))
% 7.04/1.76 | | |
% 7.04/1.76 | | | GROUND_INST: instantiating (1) with all_9_6, all_9_5, all_36_1, all_9_4,
% 7.04/1.76 | | | simplifying with (8), (9), (12), (31), (39) gives:
% 7.04/1.76 | | | (41) ? [v0: any] : ? [v1: any] : (member(all_36_1, all_9_5) = v1 &
% 7.04/1.76 | | | member(all_36_1, all_9_6) = v0 & (v1 = 0 | v0 = 0))
% 7.04/1.76 | | |
% 7.04/1.76 | | | DELTA: instantiating (41) with fresh symbols all_56_0, all_56_1 gives:
% 7.04/1.76 | | | (42) member(all_36_1, all_9_5) = all_56_0 & member(all_36_1, all_9_6) =
% 7.04/1.76 | | | all_56_1 & (all_56_0 = 0 | all_56_1 = 0)
% 7.04/1.76 | | |
% 7.04/1.76 | | | ALPHA: (42) implies:
% 7.04/1.77 | | | (43) member(all_36_1, all_9_6) = all_56_1
% 7.04/1.77 | | |
% 7.04/1.77 | | | DELTA: instantiating (40) with fresh symbols all_58_0, all_58_1 gives:
% 7.04/1.77 | | | (44) member(all_36_1, all_9_5) = all_58_1 & member(all_36_1, all_9_6) =
% 7.04/1.77 | | | all_58_0 & (all_58_0 = 0 | all_58_1 = 0)
% 7.04/1.77 | | |
% 7.04/1.77 | | | ALPHA: (44) implies:
% 7.04/1.77 | | | (45) member(all_36_1, all_9_6) = all_58_0
% 7.04/1.77 | | | (46) member(all_36_1, all_9_5) = all_58_1
% 7.04/1.77 | | | (47) all_58_0 = 0 | all_58_1 = 0
% 7.04/1.77 | | |
% 7.04/1.77 | | | GROUND_INST: instantiating (5) with all_36_0, all_58_0, all_9_6, all_36_1,
% 7.04/1.77 | | | simplifying with (32), (45) gives:
% 7.04/1.77 | | | (48) all_58_0 = all_36_0
% 7.04/1.77 | | |
% 7.04/1.77 | | | GROUND_INST: instantiating (5) with all_56_1, all_58_0, all_9_6, all_36_1,
% 7.04/1.77 | | | simplifying with (43), (45) gives:
% 7.04/1.77 | | | (49) all_58_0 = all_56_1
% 7.04/1.77 | | |
% 7.04/1.77 | | | GROUND_INST: instantiating (5) with all_43_0, all_58_1, all_9_5, all_36_1,
% 7.04/1.77 | | | simplifying with (38), (46) gives:
% 7.04/1.77 | | | (50) all_58_1 = all_43_0
% 7.04/1.77 | | |
% 7.04/1.77 | | | COMBINE_EQS: (48), (49) imply:
% 7.04/1.77 | | | (51) all_56_1 = all_36_0
% 7.04/1.77 | | |
% 7.04/1.77 | | | BETA: splitting (47) gives:
% 7.04/1.77 | | |
% 7.04/1.77 | | | Case 1:
% 7.04/1.77 | | | |
% 7.04/1.77 | | | | (52) all_58_0 = 0
% 7.04/1.77 | | | |
% 7.04/1.77 | | | | COMBINE_EQS: (48), (52) imply:
% 7.04/1.77 | | | | (53) all_36_0 = 0
% 7.04/1.77 | | | |
% 7.04/1.77 | | | | REDUCE: (30), (53) imply:
% 7.04/1.77 | | | | (54) $false
% 7.04/1.77 | | | |
% 7.04/1.77 | | | | CLOSE: (54) is inconsistent.
% 7.04/1.77 | | | |
% 7.04/1.77 | | | Case 2:
% 7.04/1.77 | | | |
% 7.04/1.77 | | | | (55) all_58_1 = 0
% 7.04/1.77 | | | |
% 7.04/1.77 | | | | COMBINE_EQS: (50), (55) imply:
% 7.53/1.77 | | | | (56) all_43_0 = 0
% 7.53/1.77 | | | |
% 7.53/1.77 | | | | SIMP: (56) implies:
% 7.53/1.77 | | | | (57) all_43_0 = 0
% 7.53/1.77 | | | |
% 7.53/1.77 | | | | REDUCE: (36), (57) imply:
% 7.53/1.77 | | | | (58) $false
% 7.53/1.77 | | | |
% 7.53/1.77 | | | | CLOSE: (58) is inconsistent.
% 7.53/1.77 | | | |
% 7.53/1.77 | | | End of split
% 7.53/1.77 | | |
% 7.53/1.77 | | End of split
% 7.53/1.77 | |
% 7.53/1.77 | Case 2:
% 7.53/1.77 | |
% 7.53/1.77 | | (59) ~ (all_9_2 = 0)
% 7.53/1.77 | |
% 7.53/1.77 | | BETA: splitting (23) gives:
% 7.53/1.77 | |
% 7.53/1.77 | | Case 1:
% 7.53/1.77 | | |
% 7.53/1.77 | | | (60) all_9_2 = 0
% 7.53/1.77 | | |
% 7.53/1.77 | | | REDUCE: (59), (60) imply:
% 7.53/1.77 | | | (61) $false
% 7.53/1.77 | | |
% 7.53/1.77 | | | CLOSE: (61) is inconsistent.
% 7.53/1.77 | | |
% 7.53/1.77 | | Case 2:
% 7.53/1.77 | | |
% 7.53/1.77 | | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_9_3) =
% 7.53/1.77 | | | 0 & member(v0, all_9_5) = v1 & $i(v0))
% 7.53/1.77 | | |
% 7.53/1.77 | | | DELTA: instantiating (62) with fresh symbols all_36_0, all_36_1 gives:
% 7.53/1.77 | | | (63) ~ (all_36_0 = 0) & member(all_36_1, all_9_3) = 0 &
% 7.53/1.77 | | | member(all_36_1, all_9_5) = all_36_0 & $i(all_36_1)
% 7.53/1.77 | | |
% 7.53/1.77 | | | ALPHA: (63) implies:
% 7.53/1.77 | | | (64) ~ (all_36_0 = 0)
% 7.53/1.77 | | | (65) $i(all_36_1)
% 7.53/1.77 | | | (66) member(all_36_1, all_9_5) = all_36_0
% 7.53/1.77 | | | (67) member(all_36_1, all_9_3) = 0
% 7.53/1.77 | | |
% 7.53/1.77 | | | GROUND_INST: instantiating (2) with all_9_7, all_9_6, all_36_1, all_9_3,
% 7.53/1.77 | | | simplifying with (7), (8), (13), (65), (67) gives:
% 7.53/1.78 | | | (68) ? [v0: int] : ( ~ (v0 = 0) & member(all_36_1, all_9_6) = v0 &
% 7.53/1.78 | | | member(all_36_1, all_9_7) = 0)
% 7.53/1.78 | | |
% 7.53/1.78 | | | DELTA: instantiating (68) with fresh symbol all_44_0 gives:
% 7.53/1.78 | | | (69) ~ (all_44_0 = 0) & member(all_36_1, all_9_6) = all_44_0 &
% 7.53/1.78 | | | member(all_36_1, all_9_7) = 0
% 7.53/1.78 | | |
% 7.53/1.78 | | | ALPHA: (69) implies:
% 7.53/1.78 | | | (70) ~ (all_44_0 = 0)
% 7.53/1.78 | | | (71) member(all_36_1, all_9_7) = 0
% 7.53/1.78 | | | (72) member(all_36_1, all_9_6) = all_44_0
% 7.53/1.78 | | |
% 7.53/1.78 | | | GROUND_INST: instantiating (22) with all_36_1, simplifying with (65), (71)
% 7.53/1.78 | | | gives:
% 7.53/1.78 | | | (73) member(all_36_1, all_9_4) = 0
% 7.53/1.78 | | |
% 7.53/1.78 | | | GROUND_INST: instantiating (1) with all_9_5, all_9_6, all_36_1, all_9_4,
% 7.53/1.78 | | | simplifying with (8), (9), (21), (65), (73) gives:
% 7.53/1.78 | | | (74) ? [v0: any] : ? [v1: any] : (member(all_36_1, all_9_5) = v0 &
% 7.53/1.78 | | | member(all_36_1, all_9_6) = v1 & (v1 = 0 | v0 = 0))
% 7.53/1.78 | | |
% 7.53/1.78 | | | DELTA: instantiating (74) with fresh symbols all_59_0, all_59_1 gives:
% 7.53/1.78 | | | (75) member(all_36_1, all_9_5) = all_59_1 & member(all_36_1, all_9_6) =
% 7.53/1.78 | | | all_59_0 & (all_59_0 = 0 | all_59_1 = 0)
% 7.53/1.78 | | |
% 7.53/1.78 | | | ALPHA: (75) implies:
% 7.53/1.78 | | | (76) member(all_36_1, all_9_6) = all_59_0
% 7.53/1.78 | | | (77) member(all_36_1, all_9_5) = all_59_1
% 7.53/1.78 | | | (78) all_59_0 = 0 | all_59_1 = 0
% 7.53/1.78 | | |
% 7.53/1.78 | | | GROUND_INST: instantiating (5) with all_44_0, all_59_0, all_9_6, all_36_1,
% 7.53/1.78 | | | simplifying with (72), (76) gives:
% 7.53/1.78 | | | (79) all_59_0 = all_44_0
% 7.53/1.78 | | |
% 7.53/1.78 | | | GROUND_INST: instantiating (5) with all_36_0, all_59_1, all_9_5, all_36_1,
% 7.53/1.78 | | | simplifying with (66), (77) gives:
% 7.53/1.78 | | | (80) all_59_1 = all_36_0
% 7.53/1.78 | | |
% 7.53/1.78 | | | BETA: splitting (78) gives:
% 7.53/1.78 | | |
% 7.53/1.78 | | | Case 1:
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | (81) all_59_0 = 0
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | COMBINE_EQS: (79), (81) imply:
% 7.53/1.78 | | | | (82) all_44_0 = 0
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | REDUCE: (70), (82) imply:
% 7.53/1.78 | | | | (83) $false
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | CLOSE: (83) is inconsistent.
% 7.53/1.78 | | | |
% 7.53/1.78 | | | Case 2:
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | (84) all_59_1 = 0
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | COMBINE_EQS: (80), (84) imply:
% 7.53/1.78 | | | | (85) all_36_0 = 0
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | SIMP: (85) implies:
% 7.53/1.78 | | | | (86) all_36_0 = 0
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | REDUCE: (64), (86) imply:
% 7.53/1.78 | | | | (87) $false
% 7.53/1.78 | | | |
% 7.53/1.78 | | | | CLOSE: (87) is inconsistent.
% 7.53/1.78 | | | |
% 7.53/1.78 | | | End of split
% 7.53/1.78 | | |
% 7.53/1.78 | | End of split
% 7.53/1.78 | |
% 7.53/1.78 | End of split
% 7.53/1.78 |
% 7.53/1.78 End of proof
% 7.53/1.78 % SZS output end Proof for theBenchmark
% 7.53/1.78
% 7.53/1.78 1172ms
%------------------------------------------------------------------------------