TSTP Solution File: SET162+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET162+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 : n012.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 15:24:06 EDT 2023
% Result : Theorem 6.26s 1.58s
% Output : Proof 8.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET162+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n012.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sat Aug 26 16:27:40 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.35/1.02 Prover 4: Preprocessing ...
% 2.35/1.02 Prover 1: Preprocessing ...
% 2.73/1.06 Prover 2: Preprocessing ...
% 2.73/1.06 Prover 6: Preprocessing ...
% 2.73/1.06 Prover 5: Preprocessing ...
% 2.73/1.06 Prover 0: Preprocessing ...
% 2.73/1.06 Prover 3: Preprocessing ...
% 4.95/1.37 Prover 6: Proving ...
% 4.95/1.39 Prover 1: Constructing countermodel ...
% 4.95/1.42 Prover 5: Proving ...
% 4.95/1.42 Prover 3: Constructing countermodel ...
% 4.95/1.44 Prover 4: Constructing countermodel ...
% 5.63/1.49 Prover 0: Proving ...
% 5.63/1.49 Prover 2: Proving ...
% 6.26/1.58 Prover 3: proved (947ms)
% 6.26/1.58
% 6.26/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.26/1.58
% 6.26/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.26/1.58 Prover 5: stopped
% 6.26/1.58 Prover 0: stopped
% 6.26/1.59 Prover 6: stopped
% 6.65/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.65/1.59 Prover 2: stopped
% 6.65/1.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.65/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.65/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.65/1.63 Prover 13: Preprocessing ...
% 6.65/1.63 Prover 8: Preprocessing ...
% 6.65/1.63 Prover 10: Preprocessing ...
% 6.65/1.63 Prover 11: Preprocessing ...
% 6.65/1.63 Prover 7: Preprocessing ...
% 7.13/1.70 Prover 1: Found proof (size 48)
% 7.13/1.70 Prover 1: proved (1073ms)
% 7.13/1.70 Prover 11: stopped
% 7.51/1.71 Prover 4: stopped
% 7.51/1.72 Prover 7: Warning: ignoring some quantifiers
% 7.51/1.72 Prover 10: Warning: ignoring some quantifiers
% 7.51/1.73 Prover 7: Constructing countermodel ...
% 7.51/1.73 Prover 10: Constructing countermodel ...
% 7.51/1.74 Prover 13: Warning: ignoring some quantifiers
% 7.51/1.74 Prover 7: stopped
% 7.51/1.74 Prover 10: stopped
% 7.82/1.75 Prover 13: Constructing countermodel ...
% 7.82/1.76 Prover 13: stopped
% 7.82/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.82/1.78 Prover 8: Constructing countermodel ...
% 7.82/1.79 Prover 8: stopped
% 7.82/1.79
% 7.82/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.82/1.79
% 7.82/1.80 % SZS output start Proof for theBenchmark
% 7.82/1.80 Assumptions after simplification:
% 7.82/1.80 ---------------------------------
% 7.82/1.80
% 7.82/1.80 (empty_set)
% 7.82/1.82 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 7.82/1.82
% 7.82/1.82 (equal_set)
% 7.82/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 7.82/1.83 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 7.82/1.83 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 7.82/1.83 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.82/1.83 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 7.82/1.83
% 7.82/1.83 (subset)
% 7.82/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.82/1.83 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.82/1.83 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.82/1.83 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.82/1.83 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.82/1.83
% 7.82/1.83 (thI18)
% 7.82/1.83 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 7.82/1.83 union(v0, empty_set) = v1 & equal_set(v1, v0) = v2 & $i(v1) & $i(v0))
% 7.82/1.83
% 7.82/1.83 (union)
% 7.82/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.82/1.83 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 7.82/1.83 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 7.82/1.83 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 7.82/1.83 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 7.82/1.83 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.82/1.83 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 7.82/1.83
% 7.82/1.83 (function-axioms)
% 7.82/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.82/1.84 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.82/1.84 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.82/1.84 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 7.82/1.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 7.82/1.84 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.82/1.84 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 7.82/1.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.82/1.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 7.82/1.84 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.82/1.84 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 7.82/1.84 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.82/1.84 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.82/1.84 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 7.82/1.84 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 7.82/1.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 7.82/1.84 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 7.82/1.84 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 7.82/1.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 8.29/1.84 (power_set(v2) = v0))
% 8.29/1.84
% 8.29/1.84 Further assumptions not needed in the proof:
% 8.29/1.84 --------------------------------------------
% 8.29/1.84 difference, intersection, power_set, product, singleton, sum, unordered_pair
% 8.29/1.84
% 8.29/1.84 Those formulas are unsatisfiable:
% 8.29/1.84 ---------------------------------
% 8.29/1.84
% 8.29/1.84 Begin of proof
% 8.29/1.84 |
% 8.29/1.84 | ALPHA: (subset) implies:
% 8.29/1.84 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.29/1.84 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.29/1.84 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.29/1.84 |
% 8.29/1.84 | ALPHA: (equal_set) implies:
% 8.29/1.84 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 8.29/1.84 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.29/1.84 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 8.29/1.84 | 0))))
% 8.29/1.84 |
% 8.29/1.84 | ALPHA: (union) implies:
% 8.29/1.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 8.29/1.85 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 8.29/1.85 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 8.29/1.85 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 8.29/1.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.29/1.85 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 8.29/1.85 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 8.29/1.85 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 8.29/1.85 | v5))
% 8.29/1.85 |
% 8.29/1.85 | ALPHA: (empty_set) implies:
% 8.29/1.85 | (5) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 8.29/1.85 |
% 8.29/1.85 | ALPHA: (thI18) implies:
% 8.29/1.85 | (6) $i(empty_set)
% 8.29/1.85 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & union(v0,
% 8.29/1.85 | empty_set) = v1 & equal_set(v1, v0) = v2 & $i(v1) & $i(v0))
% 8.29/1.85 |
% 8.29/1.85 | ALPHA: (function-axioms) implies:
% 8.29/1.85 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.29/1.85 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 8.29/1.85 | = v0))
% 8.29/1.85 |
% 8.29/1.85 | DELTA: instantiating (7) with fresh symbols all_15_0, all_15_1, all_15_2
% 8.29/1.85 | gives:
% 8.29/1.85 | (9) ~ (all_15_0 = 0) & union(all_15_2, empty_set) = all_15_1 &
% 8.29/1.85 | equal_set(all_15_1, all_15_2) = all_15_0 & $i(all_15_1) & $i(all_15_2)
% 8.29/1.85 |
% 8.29/1.85 | ALPHA: (9) implies:
% 8.29/1.85 | (10) ~ (all_15_0 = 0)
% 8.29/1.85 | (11) $i(all_15_2)
% 8.29/1.85 | (12) $i(all_15_1)
% 8.29/1.85 | (13) equal_set(all_15_1, all_15_2) = all_15_0
% 8.29/1.85 | (14) union(all_15_2, empty_set) = all_15_1
% 8.29/1.85 |
% 8.29/1.85 | GROUND_INST: instantiating (2) with all_15_1, all_15_2, all_15_0, simplifying
% 8.29/1.85 | with (11), (12), (13) gives:
% 8.29/1.85 | (15) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 8.29/1.85 | all_15_2) = v0 & subset(all_15_2, all_15_1) = v1 & ( ~ (v1 = 0) |
% 8.29/1.85 | ~ (v0 = 0)))
% 8.29/1.85 |
% 8.29/1.85 | BETA: splitting (15) gives:
% 8.29/1.85 |
% 8.29/1.86 | Case 1:
% 8.29/1.86 | |
% 8.29/1.86 | | (16) all_15_0 = 0
% 8.29/1.86 | |
% 8.29/1.86 | | REDUCE: (10), (16) imply:
% 8.29/1.86 | | (17) $false
% 8.29/1.86 | |
% 8.29/1.86 | | CLOSE: (17) is inconsistent.
% 8.29/1.86 | |
% 8.29/1.86 | Case 2:
% 8.29/1.86 | |
% 8.29/1.86 | | (18) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v0 &
% 8.29/1.86 | | subset(all_15_2, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.29/1.86 | |
% 8.29/1.86 | | DELTA: instantiating (18) with fresh symbols all_24_0, all_24_1 gives:
% 8.29/1.86 | | (19) subset(all_15_1, all_15_2) = all_24_1 & subset(all_15_2, all_15_1) =
% 8.29/1.86 | | all_24_0 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0))
% 8.29/1.86 | |
% 8.29/1.86 | | ALPHA: (19) implies:
% 8.29/1.86 | | (20) subset(all_15_2, all_15_1) = all_24_0
% 8.29/1.86 | | (21) subset(all_15_1, all_15_2) = all_24_1
% 8.29/1.86 | | (22) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 8.29/1.86 | |
% 8.29/1.86 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_0,
% 8.29/1.86 | | simplifying with (11), (12), (20) gives:
% 8.29/1.86 | | (23) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.29/1.86 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 8.29/1.86 | |
% 8.29/1.86 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_1,
% 8.29/1.86 | | simplifying with (11), (12), (21) gives:
% 8.29/1.86 | | (24) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.29/1.86 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 8.29/1.86 | |
% 8.29/1.86 | | BETA: splitting (22) gives:
% 8.29/1.86 | |
% 8.29/1.86 | | Case 1:
% 8.29/1.86 | | |
% 8.29/1.86 | | | (25) ~ (all_24_0 = 0)
% 8.29/1.86 | | |
% 8.29/1.86 | | | BETA: splitting (23) gives:
% 8.29/1.86 | | |
% 8.29/1.86 | | | Case 1:
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | (26) all_24_0 = 0
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | REDUCE: (25), (26) imply:
% 8.29/1.86 | | | | (27) $false
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | CLOSE: (27) is inconsistent.
% 8.29/1.86 | | | |
% 8.29/1.86 | | | Case 2:
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.29/1.86 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | DELTA: instantiating (28) with fresh symbols all_37_0, all_37_1 gives:
% 8.29/1.86 | | | | (29) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 8.29/1.86 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1)
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | ALPHA: (29) implies:
% 8.29/1.86 | | | | (30) ~ (all_37_0 = 0)
% 8.29/1.86 | | | | (31) $i(all_37_1)
% 8.29/1.86 | | | | (32) member(all_37_1, all_15_2) = 0
% 8.29/1.86 | | | | (33) member(all_37_1, all_15_1) = all_37_0
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_2, empty_set,
% 8.29/1.86 | | | | all_15_1, all_37_0, simplifying with (6), (11), (14), (31),
% 8.29/1.86 | | | | (33) gives:
% 8.29/1.86 | | | | (34) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 8.29/1.86 | | | | (v0 = 0) & member(all_37_1, all_15_2) = v0 & member(all_37_1,
% 8.29/1.86 | | | | empty_set) = v1)
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | BETA: splitting (34) gives:
% 8.29/1.86 | | | |
% 8.29/1.86 | | | | Case 1:
% 8.29/1.86 | | | | |
% 8.29/1.86 | | | | | (35) all_37_0 = 0
% 8.29/1.86 | | | | |
% 8.29/1.86 | | | | | REDUCE: (30), (35) imply:
% 8.29/1.86 | | | | | (36) $false
% 8.29/1.86 | | | | |
% 8.29/1.86 | | | | | CLOSE: (36) is inconsistent.
% 8.29/1.86 | | | | |
% 8.29/1.87 | | | | Case 2:
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | (37) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 8.29/1.87 | | | | | member(all_37_1, all_15_2) = v0 & member(all_37_1,
% 8.29/1.87 | | | | | empty_set) = v1)
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | DELTA: instantiating (37) with fresh symbols all_52_0, all_52_1 gives:
% 8.29/1.87 | | | | | (38) ~ (all_52_0 = 0) & ~ (all_52_1 = 0) & member(all_37_1,
% 8.29/1.87 | | | | | all_15_2) = all_52_1 & member(all_37_1, empty_set) =
% 8.29/1.87 | | | | | all_52_0
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | ALPHA: (38) implies:
% 8.29/1.87 | | | | | (39) ~ (all_52_1 = 0)
% 8.29/1.87 | | | | | (40) member(all_37_1, all_15_2) = all_52_1
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | GROUND_INST: instantiating (8) with 0, all_52_1, all_15_2, all_37_1,
% 8.29/1.87 | | | | | simplifying with (32), (40) gives:
% 8.29/1.87 | | | | | (41) all_52_1 = 0
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | REDUCE: (39), (41) imply:
% 8.29/1.87 | | | | | (42) $false
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | CLOSE: (42) is inconsistent.
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | End of split
% 8.29/1.87 | | | |
% 8.29/1.87 | | | End of split
% 8.29/1.87 | | |
% 8.29/1.87 | | Case 2:
% 8.29/1.87 | | |
% 8.29/1.87 | | | (43) ~ (all_24_1 = 0)
% 8.29/1.87 | | |
% 8.29/1.87 | | | BETA: splitting (24) gives:
% 8.29/1.87 | | |
% 8.29/1.87 | | | Case 1:
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | (44) all_24_1 = 0
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | REDUCE: (43), (44) imply:
% 8.29/1.87 | | | | (45) $false
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | CLOSE: (45) is inconsistent.
% 8.29/1.87 | | | |
% 8.29/1.87 | | | Case 2:
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | (46) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 8.29/1.87 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | DELTA: instantiating (46) with fresh symbols all_37_0, all_37_1 gives:
% 8.29/1.87 | | | | (47) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 8.29/1.87 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1)
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | ALPHA: (47) implies:
% 8.29/1.87 | | | | (48) ~ (all_37_0 = 0)
% 8.29/1.87 | | | | (49) $i(all_37_1)
% 8.29/1.87 | | | | (50) member(all_37_1, all_15_2) = all_37_0
% 8.29/1.87 | | | | (51) member(all_37_1, all_15_1) = 0
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_2, empty_set,
% 8.29/1.87 | | | | all_15_1, simplifying with (6), (11), (14), (49), (51)
% 8.29/1.87 | | | | gives:
% 8.29/1.87 | | | | (52) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_2) = v0 &
% 8.29/1.87 | | | | member(all_37_1, empty_set) = v1 & (v1 = 0 | v0 = 0))
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | DELTA: instantiating (52) with fresh symbols all_45_0, all_45_1 gives:
% 8.29/1.87 | | | | (53) member(all_37_1, all_15_2) = all_45_1 & member(all_37_1,
% 8.29/1.87 | | | | empty_set) = all_45_0 & (all_45_0 = 0 | all_45_1 = 0)
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | ALPHA: (53) implies:
% 8.29/1.87 | | | | (54) member(all_37_1, empty_set) = all_45_0
% 8.29/1.87 | | | | (55) member(all_37_1, all_15_2) = all_45_1
% 8.29/1.87 | | | | (56) all_45_0 = 0 | all_45_1 = 0
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | GROUND_INST: instantiating (8) with all_37_0, all_45_1, all_15_2,
% 8.29/1.87 | | | | all_37_1, simplifying with (50), (55) gives:
% 8.29/1.87 | | | | (57) all_45_1 = all_37_0
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | BETA: splitting (56) gives:
% 8.29/1.87 | | | |
% 8.29/1.87 | | | | Case 1:
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | (58) all_45_0 = 0
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | REDUCE: (54), (58) imply:
% 8.29/1.87 | | | | | (59) member(all_37_1, empty_set) = 0
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | GROUND_INST: instantiating (5) with all_37_1, simplifying with (49),
% 8.29/1.87 | | | | | (59) gives:
% 8.29/1.87 | | | | | (60) $false
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | CLOSE: (60) is inconsistent.
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | Case 2:
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | (61) all_45_1 = 0
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | COMBINE_EQS: (57), (61) imply:
% 8.29/1.87 | | | | | (62) all_37_0 = 0
% 8.29/1.87 | | | | |
% 8.29/1.87 | | | | | REDUCE: (48), (62) imply:
% 8.29/1.87 | | | | | (63) $false
% 8.29/1.88 | | | | |
% 8.29/1.88 | | | | | CLOSE: (63) is inconsistent.
% 8.29/1.88 | | | | |
% 8.29/1.88 | | | | End of split
% 8.29/1.88 | | | |
% 8.29/1.88 | | | End of split
% 8.29/1.88 | | |
% 8.29/1.88 | | End of split
% 8.29/1.88 | |
% 8.29/1.88 | End of split
% 8.29/1.88 |
% 8.29/1.88 End of proof
% 8.29/1.88 % SZS output end Proof for theBenchmark
% 8.29/1.88
% 8.29/1.88 1266ms
%------------------------------------------------------------------------------