TSTP Solution File: SET352+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET352+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 : 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 15:24:42 EDT 2023
% Result : Theorem 10.44s 2.35s
% Output : Proof 13.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET352+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 08:41:13 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.17/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.19/1.15 Prover 4: Preprocessing ...
% 2.19/1.16 Prover 1: Preprocessing ...
% 3.00/1.20 Prover 6: Preprocessing ...
% 3.00/1.20 Prover 0: Preprocessing ...
% 3.00/1.20 Prover 5: Preprocessing ...
% 3.00/1.20 Prover 3: Preprocessing ...
% 3.00/1.20 Prover 2: Preprocessing ...
% 6.21/1.70 Prover 6: Proving ...
% 6.50/1.72 Prover 1: Constructing countermodel ...
% 6.62/1.76 Prover 5: Proving ...
% 6.62/1.78 Prover 4: Constructing countermodel ...
% 6.62/1.78 Prover 2: Proving ...
% 6.62/1.81 Prover 3: Constructing countermodel ...
% 7.24/1.88 Prover 0: Proving ...
% 10.44/2.35 Prover 3: proved (1685ms)
% 10.44/2.35
% 10.44/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.44/2.35
% 10.44/2.35 Prover 2: stopped
% 10.44/2.35 Prover 0: stopped
% 10.44/2.36 Prover 6: stopped
% 10.44/2.36 Prover 5: stopped
% 10.44/2.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.44/2.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.44/2.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.44/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.44/2.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.13/2.41 Prover 11: Preprocessing ...
% 11.13/2.43 Prover 13: Preprocessing ...
% 11.13/2.43 Prover 10: Preprocessing ...
% 11.13/2.44 Prover 8: Preprocessing ...
% 11.13/2.44 Prover 1: Found proof (size 69)
% 11.13/2.44 Prover 1: proved (1787ms)
% 11.13/2.44 Prover 7: Preprocessing ...
% 11.13/2.44 Prover 4: stopped
% 11.13/2.48 Prover 7: stopped
% 11.79/2.49 Prover 10: stopped
% 11.79/2.49 Prover 13: stopped
% 11.79/2.50 Prover 11: stopped
% 11.99/2.57 Prover 8: Warning: ignoring some quantifiers
% 11.99/2.58 Prover 8: Constructing countermodel ...
% 11.99/2.59 Prover 8: stopped
% 11.99/2.59
% 11.99/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.99/2.59
% 11.99/2.61 % SZS output start Proof for theBenchmark
% 11.99/2.61 Assumptions after simplification:
% 11.99/2.61 ---------------------------------
% 11.99/2.61
% 11.99/2.61 (equal_set)
% 12.46/2.65 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 12.46/2.65 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 12.46/2.65 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 12.46/2.65 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 12.46/2.65 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 12.46/2.65
% 12.46/2.65 (subset)
% 12.46/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 12.46/2.66 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 12.46/2.66 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 12.46/2.66 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 12.46/2.66 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 12.46/2.66
% 12.46/2.66 (sum)
% 12.46/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (sum(v1)
% 12.46/2.66 = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : (
% 12.46/2.66 ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 12.46/2.66 member(v4, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 12.46/2.66 (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 12.46/2.66 $i] : (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3)))
% 12.46/2.66
% 12.46/2.67 (thI40)
% 12.46/2.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 12.46/2.67 int] : ( ~ (v5 = 0) & sum(v2) = v3 & unordered_pair(v0, v1) = v2 & union(v0,
% 12.46/2.67 v1) = v4 & equal_set(v3, v4) = v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 12.46/2.67 $i(v0))
% 12.46/2.67
% 12.46/2.67 (union)
% 12.46/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 12.46/2.67 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 12.46/2.67 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 12.46/2.67 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 12.46/2.67 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 12.46/2.67 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 12.46/2.67 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 12.46/2.67
% 12.46/2.67 (unordered_pair)
% 12.46/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 12.46/2.68 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) |
% 12.46/2.68 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) & ! [v0: $i] : !
% 12.46/2.68 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | ~
% 12.46/2.68 (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~
% 12.46/2.68 $i(v1) | ~ $i(v0))
% 12.46/2.68
% 12.46/2.68 (function-axioms)
% 12.46/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.46/2.69 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 12.46/2.69 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.46/2.69 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 12.46/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 12.46/2.69 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.46/2.69 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 12.46/2.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.46/2.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 12.46/2.69 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.46/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 12.46/2.69 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.46/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.46/2.69 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 12.46/2.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 12.46/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 12.46/2.69 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 12.46/2.69 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 12.46/2.69 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 12.46/2.69 (power_set(v2) = v0))
% 12.46/2.69
% 12.46/2.69 Further assumptions not needed in the proof:
% 12.46/2.69 --------------------------------------------
% 12.46/2.69 difference, empty_set, intersection, power_set, product, singleton
% 12.46/2.69
% 12.46/2.69 Those formulas are unsatisfiable:
% 12.46/2.69 ---------------------------------
% 12.46/2.69
% 12.46/2.69 Begin of proof
% 12.46/2.69 |
% 12.46/2.69 | ALPHA: (subset) implies:
% 12.46/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 12.46/2.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 12.46/2.69 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 12.88/2.69 |
% 12.88/2.69 | ALPHA: (equal_set) implies:
% 12.88/2.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 12.88/2.70 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 12.88/2.70 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 12.88/2.70 | 0))))
% 12.88/2.70 |
% 12.88/2.70 | ALPHA: (union) implies:
% 12.88/2.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1,
% 12.88/2.70 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 12.88/2.70 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 &
% 12.88/2.70 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 12.88/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.88/2.70 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 12.88/2.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 12.88/2.70 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 12.88/2.70 | v5))
% 12.88/2.70 |
% 12.88/2.70 | ALPHA: (unordered_pair) implies:
% 12.88/2.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 12.88/2.70 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~
% 12.88/2.70 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 12.88/2.70 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.88/2.70 | (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 12.88/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0)))
% 12.88/2.70 |
% 12.88/2.70 | ALPHA: (sum) implies:
% 12.88/2.70 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1) = v2) | ~
% 12.88/2.70 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 12.88/2.70 | (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3)))
% 12.88/2.71 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.88/2.71 | (sum(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 12.88/2.71 | ! [v4: $i] : ( ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : (
% 12.88/2.71 | ~ (v5 = 0) & member(v4, v1) = v5)))
% 12.88/2.71 |
% 12.88/2.71 | ALPHA: (function-axioms) implies:
% 12.88/2.71 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.88/2.71 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 12.88/2.71 | = v0))
% 12.88/2.71 |
% 12.88/2.71 | DELTA: instantiating (thI40) with fresh symbols all_15_0, all_15_1, all_15_2,
% 12.88/2.71 | all_15_3, all_15_4, all_15_5 gives:
% 12.88/2.71 | (10) ~ (all_15_0 = 0) & sum(all_15_3) = all_15_2 &
% 12.88/2.71 | unordered_pair(all_15_5, all_15_4) = all_15_3 & union(all_15_5,
% 12.88/2.71 | all_15_4) = all_15_1 & equal_set(all_15_2, all_15_1) = all_15_0 &
% 12.88/2.71 | $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) &
% 12.88/2.71 | $i(all_15_5)
% 12.88/2.71 |
% 12.88/2.71 | ALPHA: (10) implies:
% 12.88/2.71 | (11) ~ (all_15_0 = 0)
% 12.88/2.71 | (12) $i(all_15_5)
% 12.88/2.71 | (13) $i(all_15_4)
% 12.88/2.71 | (14) $i(all_15_3)
% 12.88/2.71 | (15) $i(all_15_2)
% 12.88/2.71 | (16) $i(all_15_1)
% 12.88/2.71 | (17) equal_set(all_15_2, all_15_1) = all_15_0
% 12.88/2.71 | (18) union(all_15_5, all_15_4) = all_15_1
% 12.88/2.71 | (19) unordered_pair(all_15_5, all_15_4) = all_15_3
% 12.88/2.71 | (20) sum(all_15_3) = all_15_2
% 12.88/2.71 |
% 12.88/2.71 | GROUND_INST: instantiating (2) with all_15_2, all_15_1, all_15_0, simplifying
% 12.88/2.71 | with (15), (16), (17) gives:
% 12.88/2.71 | (21) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1,
% 12.88/2.71 | all_15_2) = v1 & subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) |
% 12.88/2.71 | ~ (v0 = 0)))
% 12.88/2.72 |
% 12.88/2.72 | BETA: splitting (21) gives:
% 12.88/2.72 |
% 12.88/2.72 | Case 1:
% 12.88/2.72 | |
% 12.88/2.72 | | (22) all_15_0 = 0
% 12.88/2.72 | |
% 12.88/2.72 | | REDUCE: (11), (22) imply:
% 12.88/2.72 | | (23) $false
% 12.88/2.72 | |
% 12.88/2.72 | | CLOSE: (23) is inconsistent.
% 12.88/2.72 | |
% 12.88/2.72 | Case 2:
% 12.88/2.72 | |
% 12.88/2.72 | | (24) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v1 &
% 12.88/2.72 | | subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.88/2.72 | |
% 12.88/2.72 | | DELTA: instantiating (24) with fresh symbols all_24_0, all_24_1 gives:
% 12.88/2.72 | | (25) subset(all_15_1, all_15_2) = all_24_0 & subset(all_15_2, all_15_1) =
% 12.88/2.72 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0))
% 12.88/2.72 | |
% 12.88/2.72 | | ALPHA: (25) implies:
% 12.88/2.72 | | (26) subset(all_15_2, all_15_1) = all_24_1
% 12.88/2.72 | | (27) subset(all_15_1, all_15_2) = all_24_0
% 12.88/2.72 | | (28) ~ (all_24_0 = 0) | ~ (all_24_1 = 0)
% 12.88/2.72 | |
% 12.88/2.72 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_1,
% 12.88/2.72 | | simplifying with (15), (16), (26) gives:
% 12.88/2.72 | | (29) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.88/2.72 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 12.88/2.72 | |
% 12.88/2.72 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_0,
% 12.88/2.72 | | simplifying with (15), (16), (27) gives:
% 12.88/2.72 | | (30) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.88/2.72 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 12.88/2.72 | |
% 12.88/2.72 | | BETA: splitting (28) gives:
% 12.88/2.72 | |
% 12.88/2.72 | | Case 1:
% 12.88/2.72 | | |
% 12.88/2.72 | | | (31) ~ (all_24_0 = 0)
% 12.88/2.72 | | |
% 12.88/2.72 | | | BETA: splitting (30) gives:
% 12.88/2.72 | | |
% 12.88/2.72 | | | Case 1:
% 12.88/2.72 | | | |
% 12.88/2.73 | | | | (32) all_24_0 = 0
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | REDUCE: (31), (32) imply:
% 12.88/2.73 | | | | (33) $false
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | CLOSE: (33) is inconsistent.
% 12.88/2.73 | | | |
% 12.88/2.73 | | | Case 2:
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 12.88/2.73 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | DELTA: instantiating (34) with fresh symbols all_37_0, all_37_1 gives:
% 12.88/2.73 | | | | (35) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 &
% 12.88/2.73 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1)
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | ALPHA: (35) implies:
% 12.88/2.73 | | | | (36) ~ (all_37_0 = 0)
% 12.88/2.73 | | | | (37) $i(all_37_1)
% 12.88/2.73 | | | | (38) member(all_37_1, all_15_2) = all_37_0
% 12.88/2.73 | | | | (39) member(all_37_1, all_15_1) = 0
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | GROUND_INST: instantiating (8) with all_37_1, all_15_3, all_15_2,
% 12.88/2.73 | | | | all_37_0, simplifying with (14), (20), (37), (38) gives:
% 12.88/2.73 | | | | (40) all_37_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~
% 12.88/2.73 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_3) =
% 12.88/2.73 | | | | v1))
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_5, all_15_4,
% 12.88/2.73 | | | | all_15_1, simplifying with (12), (13), (18), (37), (39)
% 12.88/2.73 | | | | gives:
% 12.88/2.73 | | | | (41) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_4) = v1 &
% 12.88/2.73 | | | | member(all_37_1, all_15_5) = v0 & (v1 = 0 | v0 = 0))
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | DELTA: instantiating (41) with fresh symbols all_44_0, all_44_1 gives:
% 12.88/2.73 | | | | (42) member(all_37_1, all_15_4) = all_44_0 & member(all_37_1,
% 12.88/2.73 | | | | all_15_5) = all_44_1 & (all_44_0 = 0 | all_44_1 = 0)
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | ALPHA: (42) implies:
% 12.88/2.73 | | | | (43) member(all_37_1, all_15_5) = all_44_1
% 12.88/2.73 | | | | (44) member(all_37_1, all_15_4) = all_44_0
% 12.88/2.73 | | | | (45) all_44_0 = 0 | all_44_1 = 0
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | BETA: splitting (40) gives:
% 12.88/2.73 | | | |
% 12.88/2.73 | | | | Case 1:
% 12.88/2.73 | | | | |
% 12.88/2.73 | | | | | (46) all_37_0 = 0
% 12.88/2.73 | | | | |
% 12.88/2.73 | | | | | REDUCE: (36), (46) imply:
% 12.88/2.73 | | | | | (47) $false
% 12.88/2.73 | | | | |
% 12.88/2.73 | | | | | CLOSE: (47) is inconsistent.
% 12.88/2.73 | | | | |
% 12.88/2.74 | | | | Case 2:
% 12.88/2.74 | | | | |
% 12.88/2.74 | | | | | (48) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) | ?
% 12.88/2.74 | | | | | [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_3) = v1))
% 12.88/2.74 | | | | |
% 12.88/2.74 | | | | | BETA: splitting (45) gives:
% 12.88/2.74 | | | | |
% 12.88/2.74 | | | | | Case 1:
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | (49) all_44_0 = 0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | REDUCE: (44), (49) imply:
% 12.88/2.74 | | | | | | (50) member(all_37_1, all_15_4) = 0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | GROUND_INST: instantiating (48) with all_15_4, simplifying with
% 12.88/2.74 | | | | | | (13), (50) gives:
% 12.88/2.74 | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_4, all_15_3) =
% 12.88/2.74 | | | | | | v0)
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | DELTA: instantiating (51) with fresh symbol all_91_0 gives:
% 12.88/2.74 | | | | | | (52) ~ (all_91_0 = 0) & member(all_15_4, all_15_3) = all_91_0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | ALPHA: (52) implies:
% 12.88/2.74 | | | | | | (53) ~ (all_91_0 = 0)
% 12.88/2.74 | | | | | | (54) member(all_15_4, all_15_3) = all_91_0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | GROUND_INST: instantiating (6) with all_15_4, all_15_5, all_15_4,
% 12.88/2.74 | | | | | | all_15_3, all_91_0, simplifying with (12), (13), (19),
% 12.88/2.74 | | | | | | (54) gives:
% 12.88/2.74 | | | | | | (55) all_91_0 = 0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | REDUCE: (53), (55) imply:
% 12.88/2.74 | | | | | | (56) $false
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | CLOSE: (56) is inconsistent.
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | Case 2:
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | (57) all_44_1 = 0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | REDUCE: (43), (57) imply:
% 12.88/2.74 | | | | | | (58) member(all_37_1, all_15_5) = 0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | GROUND_INST: instantiating (48) with all_15_5, simplifying with
% 12.88/2.74 | | | | | | (12), (58) gives:
% 12.88/2.74 | | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_5, all_15_3) =
% 12.88/2.74 | | | | | | v0)
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | DELTA: instantiating (59) with fresh symbol all_91_0 gives:
% 12.88/2.74 | | | | | | (60) ~ (all_91_0 = 0) & member(all_15_5, all_15_3) = all_91_0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | ALPHA: (60) implies:
% 12.88/2.74 | | | | | | (61) ~ (all_91_0 = 0)
% 12.88/2.74 | | | | | | (62) member(all_15_5, all_15_3) = all_91_0
% 12.88/2.74 | | | | | |
% 12.88/2.74 | | | | | | GROUND_INST: instantiating (6) with all_15_5, all_15_5, all_15_4,
% 12.88/2.74 | | | | | | all_15_3, all_91_0, simplifying with (12), (13), (19),
% 12.88/2.74 | | | | | | (62) gives:
% 12.88/2.74 | | | | | | (63) all_91_0 = 0
% 12.88/2.74 | | | | | |
% 12.88/2.75 | | | | | | REDUCE: (61), (63) imply:
% 12.88/2.75 | | | | | | (64) $false
% 12.88/2.75 | | | | | |
% 12.88/2.75 | | | | | | CLOSE: (64) is inconsistent.
% 12.88/2.75 | | | | | |
% 12.88/2.75 | | | | | End of split
% 12.88/2.75 | | | | |
% 12.88/2.75 | | | | End of split
% 12.88/2.75 | | | |
% 12.88/2.75 | | | End of split
% 12.88/2.75 | | |
% 12.88/2.75 | | Case 2:
% 12.88/2.75 | | |
% 12.88/2.75 | | | (65) ~ (all_24_1 = 0)
% 12.88/2.75 | | |
% 12.88/2.75 | | | BETA: splitting (29) gives:
% 12.88/2.75 | | |
% 12.88/2.75 | | | Case 1:
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | (66) all_24_1 = 0
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | REDUCE: (65), (66) imply:
% 12.88/2.75 | | | | (67) $false
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | CLOSE: (67) is inconsistent.
% 12.88/2.75 | | | |
% 12.88/2.75 | | | Case 2:
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | (68) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 12.88/2.75 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | DELTA: instantiating (68) with fresh symbols all_37_0, all_37_1 gives:
% 12.88/2.75 | | | | (69) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 &
% 12.88/2.75 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1)
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | ALPHA: (69) implies:
% 12.88/2.75 | | | | (70) ~ (all_37_0 = 0)
% 12.88/2.75 | | | | (71) $i(all_37_1)
% 12.88/2.75 | | | | (72) member(all_37_1, all_15_2) = 0
% 12.88/2.75 | | | | (73) member(all_37_1, all_15_1) = all_37_0
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | GROUND_INST: instantiating (7) with all_37_1, all_15_3, all_15_2,
% 12.88/2.75 | | | | simplifying with (14), (20), (71), (72) gives:
% 12.88/2.75 | | | | (74) ? [v0: $i] : (member(v0, all_15_3) = 0 & member(all_37_1, v0) =
% 12.88/2.75 | | | | 0 & $i(v0))
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_5, all_15_4,
% 12.88/2.75 | | | | all_15_1, all_37_0, simplifying with (12), (13), (18),
% 12.88/2.75 | | | | (71), (73) gives:
% 12.88/2.75 | | | | (75) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 12.88/2.75 | | | | (v0 = 0) & member(all_37_1, all_15_4) = v1 & member(all_37_1,
% 12.88/2.75 | | | | all_15_5) = v0)
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | DELTA: instantiating (74) with fresh symbol all_45_0 gives:
% 12.88/2.75 | | | | (76) member(all_45_0, all_15_3) = 0 & member(all_37_1, all_45_0) = 0
% 12.88/2.75 | | | | & $i(all_45_0)
% 12.88/2.75 | | | |
% 12.88/2.75 | | | | ALPHA: (76) implies:
% 12.88/2.77 | | | | (77) $i(all_45_0)
% 12.88/2.77 | | | | (78) member(all_37_1, all_45_0) = 0
% 12.88/2.77 | | | | (79) member(all_45_0, all_15_3) = 0
% 12.88/2.77 | | | |
% 12.88/2.77 | | | | BETA: splitting (75) gives:
% 12.88/2.77 | | | |
% 12.88/2.77 | | | | Case 1:
% 12.88/2.77 | | | | |
% 12.88/2.77 | | | | | (80) all_37_0 = 0
% 12.88/2.77 | | | | |
% 12.88/2.77 | | | | | REDUCE: (70), (80) imply:
% 12.88/2.77 | | | | | (81) $false
% 12.88/2.77 | | | | |
% 12.88/2.77 | | | | | CLOSE: (81) is inconsistent.
% 12.88/2.77 | | | | |
% 12.88/2.77 | | | | Case 2:
% 12.88/2.77 | | | | |
% 12.88/2.77 | | | | | (82) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 12.88/2.77 | | | | | member(all_37_1, all_15_4) = v1 & member(all_37_1, all_15_5)
% 12.88/2.77 | | | | | = v0)
% 12.88/2.77 | | | | |
% 12.88/2.77 | | | | | DELTA: instantiating (82) with fresh symbols all_51_0, all_51_1 gives:
% 12.88/2.78 | | | | | (83) ~ (all_51_0 = 0) & ~ (all_51_1 = 0) & member(all_37_1,
% 12.88/2.78 | | | | | all_15_4) = all_51_0 & member(all_37_1, all_15_5) = all_51_1
% 12.88/2.78 | | | | |
% 12.88/2.78 | | | | | ALPHA: (83) implies:
% 12.88/2.78 | | | | | (84) ~ (all_51_1 = 0)
% 12.88/2.78 | | | | | (85) ~ (all_51_0 = 0)
% 12.88/2.78 | | | | | (86) member(all_37_1, all_15_5) = all_51_1
% 12.88/2.78 | | | | | (87) member(all_37_1, all_15_4) = all_51_0
% 12.88/2.78 | | | | |
% 12.88/2.78 | | | | | GROUND_INST: instantiating (5) with all_45_0, all_15_5, all_15_4,
% 12.88/2.78 | | | | | all_15_3, simplifying with (12), (13), (19), (77), (79)
% 12.88/2.78 | | | | | gives:
% 12.88/2.78 | | | | | (88) all_45_0 = all_15_4 | all_45_0 = all_15_5
% 12.88/2.78 | | | | |
% 12.88/2.78 | | | | | BETA: splitting (88) gives:
% 12.88/2.78 | | | | |
% 12.88/2.78 | | | | | Case 1:
% 12.88/2.78 | | | | | |
% 12.88/2.78 | | | | | | (89) all_45_0 = all_15_4
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | | REDUCE: (78), (89) imply:
% 13.28/2.78 | | | | | | (90) member(all_37_1, all_15_4) = 0
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | | GROUND_INST: instantiating (9) with all_51_0, 0, all_15_4, all_37_1,
% 13.28/2.78 | | | | | | simplifying with (87), (90) gives:
% 13.28/2.78 | | | | | | (91) all_51_0 = 0
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | | REDUCE: (85), (91) imply:
% 13.28/2.78 | | | | | | (92) $false
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | | CLOSE: (92) is inconsistent.
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | Case 2:
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | | (93) all_45_0 = all_15_5
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | | REDUCE: (78), (93) imply:
% 13.28/2.78 | | | | | | (94) member(all_37_1, all_15_5) = 0
% 13.28/2.78 | | | | | |
% 13.28/2.78 | | | | | | GROUND_INST: instantiating (9) with all_51_1, 0, all_15_5, all_37_1,
% 13.28/2.78 | | | | | | simplifying with (86), (94) gives:
% 13.28/2.78 | | | | | | (95) all_51_1 = 0
% 13.28/2.78 | | | | | |
% 13.30/2.78 | | | | | | REDUCE: (84), (95) imply:
% 13.30/2.78 | | | | | | (96) $false
% 13.30/2.78 | | | | | |
% 13.30/2.78 | | | | | | CLOSE: (96) is inconsistent.
% 13.30/2.78 | | | | | |
% 13.30/2.78 | | | | | End of split
% 13.30/2.78 | | | | |
% 13.30/2.78 | | | | End of split
% 13.30/2.78 | | | |
% 13.30/2.78 | | | End of split
% 13.30/2.78 | | |
% 13.30/2.78 | | End of split
% 13.30/2.78 | |
% 13.30/2.78 | End of split
% 13.30/2.78 |
% 13.30/2.78 End of proof
% 13.30/2.78 % SZS output end Proof for theBenchmark
% 13.30/2.78
% 13.30/2.78 2163ms
%------------------------------------------------------------------------------