TSTP Solution File: SET014+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET014+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 : n019.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 15:23:06 EDT 2023
% Result : Theorem 3.74s 1.34s
% Output : Proof 6.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n019.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 12:24:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.67/0.98 Prover 4: Preprocessing ...
% 1.67/0.98 Prover 1: Preprocessing ...
% 2.32/1.02 Prover 2: Preprocessing ...
% 2.32/1.02 Prover 6: Preprocessing ...
% 2.32/1.02 Prover 3: Preprocessing ...
% 2.32/1.02 Prover 0: Preprocessing ...
% 2.32/1.02 Prover 5: Preprocessing ...
% 2.91/1.18 Prover 3: Warning: ignoring some quantifiers
% 3.69/1.21 Prover 5: Proving ...
% 3.69/1.21 Prover 1: Warning: ignoring some quantifiers
% 3.69/1.21 Prover 3: Constructing countermodel ...
% 3.74/1.21 Prover 1: Constructing countermodel ...
% 3.74/1.22 Prover 2: Proving ...
% 3.74/1.22 Prover 4: Warning: ignoring some quantifiers
% 3.74/1.22 Prover 6: Proving ...
% 3.74/1.23 Prover 4: Constructing countermodel ...
% 3.74/1.23 Prover 0: Proving ...
% 3.74/1.34 Prover 0: proved (724ms)
% 3.74/1.34
% 3.74/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.74/1.34
% 3.74/1.34 Prover 3: stopped
% 3.74/1.34 Prover 5: stopped
% 3.74/1.34 Prover 6: stopped
% 3.74/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.74/1.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.74/1.37 Prover 2: stopped
% 3.74/1.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.74/1.37 Prover 10: Preprocessing ...
% 3.74/1.37 Prover 8: Preprocessing ...
% 3.74/1.37 Prover 7: Preprocessing ...
% 3.74/1.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.74/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.74/1.40 Prover 11: Preprocessing ...
% 3.74/1.40 Prover 13: Preprocessing ...
% 3.74/1.44 Prover 7: Warning: ignoring some quantifiers
% 3.74/1.45 Prover 10: Warning: ignoring some quantifiers
% 3.74/1.45 Prover 7: Constructing countermodel ...
% 3.74/1.45 Prover 13: Warning: ignoring some quantifiers
% 3.74/1.46 Prover 10: Constructing countermodel ...
% 3.74/1.46 Prover 8: Warning: ignoring some quantifiers
% 3.74/1.47 Prover 4: Found proof (size 47)
% 3.74/1.47 Prover 8: Constructing countermodel ...
% 3.74/1.47 Prover 13: Constructing countermodel ...
% 3.74/1.47 Prover 1: Found proof (size 37)
% 5.30/1.48 Prover 1: proved (851ms)
% 5.30/1.48 Prover 4: proved (843ms)
% 5.30/1.48 Prover 7: stopped
% 5.30/1.48 Prover 10: stopped
% 5.30/1.48 Prover 13: stopped
% 5.30/1.48 Prover 8: stopped
% 5.30/1.50 Prover 11: Warning: ignoring some quantifiers
% 5.30/1.50 Prover 11: Constructing countermodel ...
% 5.30/1.51 Prover 11: stopped
% 5.30/1.51
% 5.30/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.30/1.51
% 5.30/1.52 % SZS output start Proof for theBenchmark
% 5.30/1.52 Assumptions after simplification:
% 5.30/1.52 ---------------------------------
% 5.30/1.52
% 5.30/1.52 (commutativity_of_union)
% 5.30/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1)
% 5.30/1.55 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 5.30/1.55 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0)
% 5.30/1.55 = v2 & $i(v2)))
% 5.30/1.55
% 5.30/1.55 (prove_union_subset)
% 5.30/1.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 5.30/1.56 = 0) & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 &
% 5.30/1.56 union(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.30/1.56
% 5.30/1.56 (subset_defn)
% 6.02/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.02/1.56 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.02/1.56 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 6.02/1.56 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 6.02/1.56 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 6.02/1.56 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 6.02/1.56 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 6.02/1.56 ~ $i(v0) | member(v2, v1) = 0)
% 6.02/1.56
% 6.02/1.56 (union_defn)
% 6.02/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 6.02/1.57 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 6.02/1.57 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 6.02/1.57 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 6.02/1.57 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0)
% 6.02/1.57 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 6.02/1.57 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 6.02/1.57
% 6.02/1.57 (function-axioms)
% 6.02/1.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.02/1.57 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 6.02/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.02/1.57 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 6.02/1.57 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.02/1.57 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.02/1.57
% 6.02/1.57 Further assumptions not needed in the proof:
% 6.02/1.57 --------------------------------------------
% 6.02/1.57 equal_member_defn, reflexivity_of_subset
% 6.02/1.57
% 6.02/1.57 Those formulas are unsatisfiable:
% 6.02/1.57 ---------------------------------
% 6.02/1.57
% 6.02/1.57 Begin of proof
% 6.02/1.57 |
% 6.02/1.57 | ALPHA: (union_defn) implies:
% 6.02/1.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0,
% 6.02/1.58 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 6.02/1.58 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 &
% 6.02/1.58 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 6.02/1.58 |
% 6.02/1.58 | ALPHA: (subset_defn) implies:
% 6.02/1.58 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 6.02/1.58 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 6.02/1.58 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 6.02/1.58 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.02/1.58 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~
% 6.02/1.58 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) =
% 6.02/1.58 | v4))
% 6.02/1.58 |
% 6.02/1.58 | ALPHA: (commutativity_of_union) implies:
% 6.02/1.58 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~
% 6.02/1.58 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2)))
% 6.02/1.58 |
% 6.02/1.58 | ALPHA: (function-axioms) implies:
% 6.02/1.58 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.02/1.58 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 6.02/1.58 | = v0))
% 6.02/1.58 |
% 6.02/1.58 | DELTA: instantiating (prove_union_subset) with fresh symbols all_7_0, all_7_1,
% 6.02/1.58 | all_7_2, all_7_3, all_7_4 gives:
% 6.02/1.59 | (6) ~ (all_7_0 = 0) & subset(all_7_1, all_7_3) = all_7_0 & subset(all_7_2,
% 6.02/1.59 | all_7_3) = 0 & subset(all_7_4, all_7_3) = 0 & union(all_7_4, all_7_2)
% 6.02/1.59 | = all_7_1 & $i(all_7_1) & $i(all_7_2) & $i(all_7_3) & $i(all_7_4)
% 6.02/1.59 |
% 6.02/1.59 | ALPHA: (6) implies:
% 6.02/1.59 | (7) ~ (all_7_0 = 0)
% 6.02/1.59 | (8) $i(all_7_4)
% 6.02/1.59 | (9) $i(all_7_3)
% 6.02/1.59 | (10) $i(all_7_2)
% 6.02/1.59 | (11) union(all_7_4, all_7_2) = all_7_1
% 6.02/1.59 | (12) subset(all_7_4, all_7_3) = 0
% 6.02/1.59 | (13) subset(all_7_2, all_7_3) = 0
% 6.02/1.59 | (14) subset(all_7_1, all_7_3) = all_7_0
% 6.02/1.59 |
% 6.02/1.59 | GROUND_INST: instantiating (4) with all_7_2, all_7_4, all_7_1, simplifying
% 6.02/1.59 | with (8), (10), (11) gives:
% 6.02/1.59 | (15) union(all_7_2, all_7_4) = all_7_1 & $i(all_7_1)
% 6.02/1.59 |
% 6.02/1.59 | ALPHA: (15) implies:
% 6.02/1.59 | (16) $i(all_7_1)
% 6.02/1.59 | (17) union(all_7_2, all_7_4) = all_7_1
% 6.02/1.59 |
% 6.02/1.59 | GROUND_INST: instantiating (2) with all_7_1, all_7_3, all_7_0, simplifying
% 6.02/1.59 | with (9), (14), (16) gives:
% 6.02/1.59 | (18) all_7_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 6.02/1.59 | all_7_1) = 0 & member(v0, all_7_3) = v1 & $i(v0))
% 6.02/1.59 |
% 6.02/1.59 | BETA: splitting (18) gives:
% 6.02/1.59 |
% 6.02/1.59 | Case 1:
% 6.02/1.59 | |
% 6.02/1.59 | | (19) all_7_0 = 0
% 6.02/1.59 | |
% 6.02/1.59 | | REDUCE: (7), (19) imply:
% 6.02/1.59 | | (20) $false
% 6.02/1.59 | |
% 6.02/1.59 | | CLOSE: (20) is inconsistent.
% 6.02/1.59 | |
% 6.02/1.59 | Case 2:
% 6.02/1.59 | |
% 6.02/1.59 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_7_1) = 0
% 6.02/1.59 | | & member(v0, all_7_3) = v1 & $i(v0))
% 6.02/1.60 | |
% 6.02/1.60 | | DELTA: instantiating (21) with fresh symbols all_20_0, all_20_1 gives:
% 6.02/1.60 | | (22) ~ (all_20_0 = 0) & member(all_20_1, all_7_1) = 0 & member(all_20_1,
% 6.02/1.60 | | all_7_3) = all_20_0 & $i(all_20_1)
% 6.02/1.60 | |
% 6.02/1.60 | | ALPHA: (22) implies:
% 6.02/1.60 | | (23) ~ (all_20_0 = 0)
% 6.02/1.60 | | (24) $i(all_20_1)
% 6.02/1.60 | | (25) member(all_20_1, all_7_3) = all_20_0
% 6.02/1.60 | | (26) member(all_20_1, all_7_1) = 0
% 6.02/1.60 | |
% 6.02/1.60 | | GROUND_INST: instantiating (3) with all_7_2, all_7_3, all_20_1, all_20_0,
% 6.02/1.60 | | simplifying with (9), (10), (13), (24), (25) gives:
% 6.02/1.60 | | (27) all_20_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1,
% 6.02/1.60 | | all_7_2) = v0)
% 6.02/1.60 | |
% 6.02/1.60 | | GROUND_INST: instantiating (3) with all_7_4, all_7_3, all_20_1, all_20_0,
% 6.02/1.60 | | simplifying with (8), (9), (12), (24), (25) gives:
% 6.02/1.60 | | (28) all_20_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1,
% 6.02/1.60 | | all_7_4) = v0)
% 6.02/1.60 | |
% 6.02/1.60 | | GROUND_INST: instantiating (1) with all_7_4, all_7_2, all_20_1, all_7_1,
% 6.02/1.60 | | simplifying with (8), (10), (11), (24), (26) gives:
% 6.02/1.60 | | (29) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_7_2) = v1 &
% 6.02/1.60 | | member(all_20_1, all_7_4) = v0 & (v1 = 0 | v0 = 0))
% 6.02/1.60 | |
% 6.02/1.60 | | GROUND_INST: instantiating (1) with all_7_2, all_7_4, all_20_1, all_7_1,
% 6.02/1.60 | | simplifying with (8), (10), (17), (24), (26) gives:
% 6.02/1.60 | | (30) ? [v0: any] : ? [v1: any] : (member(all_20_1, all_7_2) = v0 &
% 6.02/1.60 | | member(all_20_1, all_7_4) = v1 & (v1 = 0 | v0 = 0))
% 6.02/1.60 | |
% 6.02/1.60 | | DELTA: instantiating (30) with fresh symbols all_27_0, all_27_1 gives:
% 6.02/1.60 | | (31) member(all_20_1, all_7_2) = all_27_1 & member(all_20_1, all_7_4) =
% 6.02/1.60 | | all_27_0 & (all_27_0 = 0 | all_27_1 = 0)
% 6.02/1.60 | |
% 6.02/1.60 | | ALPHA: (31) implies:
% 6.02/1.60 | | (32) member(all_20_1, all_7_4) = all_27_0
% 6.02/1.60 | | (33) member(all_20_1, all_7_2) = all_27_1
% 6.02/1.60 | | (34) all_27_0 = 0 | all_27_1 = 0
% 6.02/1.60 | |
% 6.02/1.60 | | DELTA: instantiating (29) with fresh symbols all_29_0, all_29_1 gives:
% 6.02/1.61 | | (35) member(all_20_1, all_7_2) = all_29_0 & member(all_20_1, all_7_4) =
% 6.02/1.61 | | all_29_1 & (all_29_0 = 0 | all_29_1 = 0)
% 6.02/1.61 | |
% 6.02/1.61 | | ALPHA: (35) implies:
% 6.02/1.61 | | (36) member(all_20_1, all_7_4) = all_29_1
% 6.02/1.61 | | (37) member(all_20_1, all_7_2) = all_29_0
% 6.02/1.61 | |
% 6.02/1.61 | | BETA: splitting (27) gives:
% 6.02/1.61 | |
% 6.02/1.61 | | Case 1:
% 6.02/1.61 | | |
% 6.02/1.61 | | | (38) all_20_0 = 0
% 6.02/1.61 | | |
% 6.02/1.61 | | | REDUCE: (23), (38) imply:
% 6.02/1.61 | | | (39) $false
% 6.02/1.61 | | |
% 6.02/1.61 | | | CLOSE: (39) is inconsistent.
% 6.02/1.61 | | |
% 6.02/1.61 | | Case 2:
% 6.02/1.61 | | |
% 6.02/1.61 | | | (40) ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, all_7_2) = v0)
% 6.02/1.61 | | |
% 6.02/1.61 | | | DELTA: instantiating (40) with fresh symbol all_35_0 gives:
% 6.02/1.61 | | | (41) ~ (all_35_0 = 0) & member(all_20_1, all_7_2) = all_35_0
% 6.02/1.61 | | |
% 6.02/1.61 | | | ALPHA: (41) implies:
% 6.02/1.61 | | | (42) ~ (all_35_0 = 0)
% 6.02/1.61 | | | (43) member(all_20_1, all_7_2) = all_35_0
% 6.02/1.61 | | |
% 6.02/1.61 | | | BETA: splitting (28) gives:
% 6.02/1.61 | | |
% 6.02/1.61 | | | Case 1:
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | (44) all_20_0 = 0
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | REDUCE: (23), (44) imply:
% 6.02/1.61 | | | | (45) $false
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | CLOSE: (45) is inconsistent.
% 6.02/1.61 | | | |
% 6.02/1.61 | | | Case 2:
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & member(all_20_1, all_7_4) = v0)
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | DELTA: instantiating (46) with fresh symbol all_41_0 gives:
% 6.02/1.61 | | | | (47) ~ (all_41_0 = 0) & member(all_20_1, all_7_4) = all_41_0
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | ALPHA: (47) implies:
% 6.02/1.61 | | | | (48) ~ (all_41_0 = 0)
% 6.02/1.61 | | | | (49) member(all_20_1, all_7_4) = all_41_0
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | GROUND_INST: instantiating (5) with all_29_1, all_41_0, all_7_4,
% 6.02/1.61 | | | | all_20_1, simplifying with (36), (49) gives:
% 6.02/1.61 | | | | (50) all_41_0 = all_29_1
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | GROUND_INST: instantiating (5) with all_27_0, all_41_0, all_7_4,
% 6.02/1.61 | | | | all_20_1, simplifying with (32), (49) gives:
% 6.02/1.61 | | | | (51) all_41_0 = all_27_0
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | GROUND_INST: instantiating (5) with all_29_0, all_35_0, all_7_2,
% 6.02/1.61 | | | | all_20_1, simplifying with (37), (43) gives:
% 6.02/1.61 | | | | (52) all_35_0 = all_29_0
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | GROUND_INST: instantiating (5) with all_27_1, all_35_0, all_7_2,
% 6.02/1.61 | | | | all_20_1, simplifying with (33), (43) gives:
% 6.02/1.61 | | | | (53) all_35_0 = all_27_1
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | COMBINE_EQS: (50), (51) imply:
% 6.02/1.61 | | | | (54) all_29_1 = all_27_0
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | COMBINE_EQS: (52), (53) imply:
% 6.02/1.61 | | | | (55) all_29_0 = all_27_1
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | REDUCE: (48), (51) imply:
% 6.02/1.61 | | | | (56) ~ (all_27_0 = 0)
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | REDUCE: (42), (53) imply:
% 6.02/1.61 | | | | (57) ~ (all_27_1 = 0)
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | BETA: splitting (34) gives:
% 6.02/1.61 | | | |
% 6.02/1.61 | | | | Case 1:
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | | (58) all_27_0 = 0
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | | REDUCE: (56), (58) imply:
% 6.02/1.61 | | | | | (59) $false
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | | CLOSE: (59) is inconsistent.
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | Case 2:
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | | (60) all_27_1 = 0
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | | REDUCE: (57), (60) imply:
% 6.02/1.61 | | | | | (61) $false
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | | CLOSE: (61) is inconsistent.
% 6.02/1.61 | | | | |
% 6.02/1.61 | | | | End of split
% 6.02/1.61 | | | |
% 6.02/1.61 | | | End of split
% 6.02/1.61 | | |
% 6.02/1.61 | | End of split
% 6.02/1.61 | |
% 6.02/1.61 | End of split
% 6.02/1.61 |
% 6.02/1.61 End of proof
% 6.02/1.62 % SZS output end Proof for theBenchmark
% 6.02/1.62
% 6.02/1.62 1016ms
%------------------------------------------------------------------------------