TSTP Solution File: SET811+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 15:26:32 EDT 2023
% Result : Theorem 11.12s 2.23s
% Output : Proof 16.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET811+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 12:22:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.12/1.09 Prover 4: Preprocessing ...
% 3.12/1.09 Prover 1: Preprocessing ...
% 3.12/1.13 Prover 6: Preprocessing ...
% 3.12/1.13 Prover 2: Preprocessing ...
% 3.12/1.13 Prover 0: Preprocessing ...
% 3.12/1.13 Prover 5: Preprocessing ...
% 3.12/1.13 Prover 3: Preprocessing ...
% 6.56/1.60 Prover 5: Proving ...
% 6.95/1.65 Prover 2: Proving ...
% 7.24/1.66 Prover 6: Proving ...
% 7.24/1.68 Prover 3: Constructing countermodel ...
% 7.24/1.68 Prover 1: Constructing countermodel ...
% 8.12/1.79 Prover 0: Proving ...
% 8.12/1.80 Prover 4: Constructing countermodel ...
% 9.22/1.96 Prover 1: gave up
% 9.22/1.96 Prover 3: gave up
% 9.22/1.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.22/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.22/1.99 Prover 8: Preprocessing ...
% 9.22/2.00 Prover 7: Preprocessing ...
% 9.22/2.01 Prover 6: gave up
% 9.22/2.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.80/2.07 Prover 9: Preprocessing ...
% 9.80/2.11 Prover 7: Warning: ignoring some quantifiers
% 9.80/2.13 Prover 7: Constructing countermodel ...
% 11.12/2.19 Prover 8: Warning: ignoring some quantifiers
% 11.12/2.20 Prover 8: Constructing countermodel ...
% 11.12/2.22 Prover 0: proved (1592ms)
% 11.12/2.22
% 11.12/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.12/2.23
% 11.12/2.23 Prover 2: stopped
% 11.12/2.23 Prover 5: stopped
% 11.12/2.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.12/2.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.12/2.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.68/2.26 Prover 11: Preprocessing ...
% 11.68/2.28 Prover 10: Preprocessing ...
% 11.68/2.29 Prover 13: Preprocessing ...
% 12.45/2.36 Prover 10: Warning: ignoring some quantifiers
% 12.45/2.38 Prover 10: Constructing countermodel ...
% 12.45/2.40 Prover 13: Warning: ignoring some quantifiers
% 12.45/2.41 Prover 8: gave up
% 12.45/2.42 Prover 13: Constructing countermodel ...
% 12.45/2.42 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.10/2.45 Prover 16: Preprocessing ...
% 13.10/2.45 Prover 9: Constructing countermodel ...
% 13.10/2.46 Prover 9: stopped
% 13.10/2.47 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.51/2.51 Prover 10: gave up
% 13.51/2.52 Prover 19: Preprocessing ...
% 13.51/2.53 Prover 16: Warning: ignoring some quantifiers
% 13.51/2.54 Prover 16: Constructing countermodel ...
% 13.51/2.54 Prover 11: Constructing countermodel ...
% 13.98/2.70 Prover 19: Warning: ignoring some quantifiers
% 14.71/2.71 Prover 19: Constructing countermodel ...
% 15.39/2.81 Prover 4: Found proof (size 93)
% 15.39/2.81 Prover 4: proved (2176ms)
% 15.39/2.81 Prover 13: stopped
% 15.39/2.81 Prover 16: stopped
% 15.39/2.81 Prover 7: stopped
% 15.39/2.81 Prover 11: stopped
% 15.39/2.81 Prover 19: stopped
% 15.39/2.82
% 15.39/2.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.39/2.82
% 15.39/2.83 % SZS output start Proof for theBenchmark
% 15.39/2.83 Assumptions after simplification:
% 15.39/2.83 ---------------------------------
% 15.39/2.83
% 15.39/2.83 (equal_set)
% 16.03/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 16.03/2.86 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 16.03/2.86 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 16.03/2.86 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) |
% 16.03/2.86 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 &
% 16.03/2.86 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] :
% 16.03/2.86 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 16.03/2.86 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) =
% 16.03/2.86 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 16.03/2.86 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 &
% 16.03/2.86 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) =
% 16.03/2.86 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0,
% 16.03/2.86 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i]
% 16.03/2.86 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 16.03/2.86 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~
% 16.03/2.86 (v2 = 0) | v3 = 0)))
% 16.03/2.86
% 16.03/2.86 (initial_segment)
% 16.03/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.03/2.87 int] : (v5 = 0 | ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4)
% 16.03/2.87 = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 16.03/2.87 [v7: any] : (apply(v1, v3, v0) = v7 & member(v3, v2) = v6 & ( ~ (v7 = 0) |
% 16.03/2.87 ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 16.03/2.87 ! [v4: $i] : ( ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0)
% 16.03/2.87 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (apply(v1, v3, v0) = 0 &
% 16.03/2.87 member(v3, v2) = 0))
% 16.03/2.87
% 16.03/2.87 (ordinal_number)
% 16.03/2.87 $i(member_predicate) & $i(on) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2
% 16.03/2.87 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~
% 16.03/2.87 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3)) & ! [v0: $i] :
% 16.03/2.87 ! [v1: int] : (v1 = 0 | ~ (member(v0, on) = v1) | ~ $i(v0) | ? [v2: any] :
% 16.03/2.87 ? [v3: any] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 =
% 16.03/2.87 0 & ~ (v6 = 0) & subset(v4, v0) = v6 & member(v4, v0) = 0) |
% 16.03/2.87 (strict_well_order(member_predicate, v0) = v3 & set(v0) = v2 & ( ~ (v3 =
% 16.03/2.87 0) | ~ (v2 = 0)))))) & ! [v0: $i] : ! [v1: any] : ( ~
% 16.03/2.87 (strict_well_order(member_predicate, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 16.03/2.87 ? [v3: any] : (set(v0) = v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 &
% 16.03/2.87 v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) =
% 16.03/2.87 v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) =
% 16.03/2.87 v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) |
% 16.03/2.87 subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ (set(v0)
% 16.03/2.87 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 16.03/2.87 (strict_well_order(member_predicate, v0) = v3 & member(v0, on) = v2 & ( ~
% 16.03/2.87 (v2 = 0) | (v3 = 0 & v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 16.03/2.87 (subset(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) &
% 16.03/2.87 member(v4, v0) = v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) |
% 16.03/2.87 ~ $i(v4) | subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 16.03/2.87 (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~ $i(v0) |
% 16.03/2.87 subset(v1, v0) = 0) & ! [v0: $i] : ( ~ (strict_well_order(member_predicate,
% 16.03/2.87 v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 16.03/2.87 [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0)
% 16.03/2.87 = v5 & member(v3, v0) = 0) | (set(v0) = v1 & member(v0, on) = v2 & ( ~
% 16.03/2.87 (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (set(v0) = 0) | ~ $i(v0)
% 16.03/2.87 | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 16.03/2.87 ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0) = v5 & member(v3, v0) = 0)
% 16.03/2.87 | (strict_well_order(member_predicate, v0) = v1 & member(v0, on) = v2 &
% 16.03/2.87 ( ~ (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (member(v0, on) = 0) |
% 16.03/2.87 ~ $i(v0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 16.03/2.87
% 16.03/2.87 (rel_member)
% 16.03/2.88 $i(member_predicate) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 16.03/2.88 (apply(member_predicate, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 16.03/2.88 int] : ( ~ (v3 = 0) & member(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] :
% 16.03/2.88 ! [v2: int] : (v2 = 0 | ~ (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.03/2.88 [v3: int] : ( ~ (v3 = 0) & apply(member_predicate, v0, v1) = v3)) & ! [v0:
% 16.03/2.88 $i] : ! [v1: $i] : ( ~ (apply(member_predicate, v0, v1) = 0) | ~ $i(v1) |
% 16.03/2.88 ~ $i(v0) | member(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0,
% 16.03/2.88 v1) = 0) | ~ $i(v1) | ~ $i(v0) | apply(member_predicate, v0, v1) = 0)
% 16.03/2.88
% 16.03/2.88 (subset)
% 16.03/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.03/2.88 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.03/2.88 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 16.03/2.88 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 16.03/2.88 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 16.03/2.88 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.03/2.88 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 16.03/2.88 ~ $i(v0) | member(v2, v1) = 0)
% 16.03/2.88
% 16.03/2.88 (thV5)
% 16.03/2.88 $i(member_predicate) & $i(on) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 16.03/2.88 [v3: int] : ( ~ (v3 = 0) & initial_segment(v1, member_predicate, v0) = v2 &
% 16.03/2.88 equal_set(v1, v2) = v3 & member(v1, v0) = 0 & member(v0, on) = 0 & $i(v2) &
% 16.03/2.88 $i(v1) & $i(v0))
% 16.03/2.88
% 16.03/2.88 (function-axioms)
% 16.03/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 16.03/2.88 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) =
% 16.03/2.88 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.03/2.88 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 16.03/2.88 ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.03/2.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 16.03/2.88 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 16.03/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.03/2.88 : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0))
% 16.03/2.88 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.03/2.88 [v3: $i] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~
% 16.03/2.88 (strict_well_order(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 16.03/2.88 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 16.03/2.88 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.03/2.88 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2)
% 16.03/2.88 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 16.03/2.88 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 16.03/2.88 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1)
% 16.03/2.88 | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.03/2.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.03/2.88 (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0:
% 16.03/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.03/2.88 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 16.03/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.03/2.88 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0:
% 16.03/2.88 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2)
% 16.03/2.88 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.03/2.88 $i] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0)) & ! [v0: $i] : !
% 16.03/2.88 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 16.03/2.88 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 16.03/2.88 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 16.03/2.88 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 16.03/2.88 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 16.03/2.88 (power_set(v2) = v0))
% 16.03/2.88
% 16.03/2.88 Further assumptions not needed in the proof:
% 16.03/2.88 --------------------------------------------
% 16.03/2.88 difference, empty_set, intersection, least, power_set, product, set_member,
% 16.03/2.88 singleton, strict_order, strict_well_order, successor, sum, union,
% 16.03/2.88 unordered_pair
% 16.03/2.88
% 16.03/2.88 Those formulas are unsatisfiable:
% 16.03/2.88 ---------------------------------
% 16.03/2.88
% 16.03/2.88 Begin of proof
% 16.03/2.88 |
% 16.03/2.88 | ALPHA: (subset) implies:
% 16.03/2.89 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 16.03/2.89 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 16.03/2.89 | v1) = 0)
% 16.03/2.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 16.03/2.89 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 16.03/2.89 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 16.03/2.89 |
% 16.03/2.89 | ALPHA: (equal_set) implies:
% 16.03/2.89 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 16.03/2.89 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 &
% 16.03/2.89 | subset(v1, v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 16.03/2.89 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) = 0) | ~ $i(v1) | ~
% 16.03/2.89 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 &
% 16.03/2.89 | subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 16.03/2.89 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) |
% 16.28/2.89 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0,
% 16.28/2.89 | v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 =
% 16.28/2.89 | 0))))
% 16.28/2.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) |
% 16.28/2.89 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0,
% 16.28/2.89 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 =
% 16.28/2.89 | 0))))
% 16.28/2.89 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 16.28/2.89 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.28/2.89 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 16.28/2.89 | 0))))
% 16.28/2.89 |
% 16.28/2.89 | ALPHA: (ordinal_number) implies:
% 16.28/2.89 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (member(v1, v0) = 0) | ~ (member(v0,
% 16.28/2.89 | on) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 16.28/2.89 |
% 16.28/2.89 | ALPHA: (rel_member) implies:
% 16.28/2.89 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~ $i(v1) | ~
% 16.28/2.89 | $i(v0) | apply(member_predicate, v0, v1) = 0)
% 16.28/2.89 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (member(v0,
% 16.28/2.89 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 16.28/2.89 | & apply(member_predicate, v0, v1) = v3))
% 16.28/2.89 |
% 16.28/2.89 | ALPHA: (initial_segment) implies:
% 16.28/2.89 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.28/2.89 | ( ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~
% 16.28/2.89 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (apply(v1, v3, v0) = 0
% 16.28/2.89 | & member(v3, v2) = 0))
% 16.28/2.89 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.28/2.89 | ! [v5: int] : (v5 = 0 | ~ (initial_segment(v0, v1, v2) = v4) | ~
% 16.28/2.89 | (member(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.28/2.89 | $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v1, v3, v0) = v7 &
% 16.28/2.89 | member(v3, v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 16.28/2.89 |
% 16.28/2.89 | ALPHA: (thV5) implies:
% 16.28/2.89 | (13) $i(member_predicate)
% 16.28/2.90 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 16.28/2.90 | & initial_segment(v1, member_predicate, v0) = v2 & equal_set(v1, v2)
% 16.28/2.90 | = v3 & member(v1, v0) = 0 & member(v0, on) = 0 & $i(v2) & $i(v1) &
% 16.28/2.90 | $i(v0))
% 16.28/2.90 |
% 16.28/2.90 | ALPHA: (function-axioms) implies:
% 16.28/2.90 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.28/2.90 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 16.28/2.90 | v2) = v0))
% 16.28/2.90 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.28/2.90 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 16.28/2.90 | v2) = v0))
% 16.28/2.90 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.28/2.90 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 16.28/2.90 | ~ (apply(v4, v3, v2) = v0))
% 16.28/2.90 |
% 16.28/2.90 | DELTA: instantiating (14) with fresh symbols all_23_0, all_23_1, all_23_2,
% 16.28/2.90 | all_23_3 gives:
% 16.28/2.90 | (18) ~ (all_23_0 = 0) & initial_segment(all_23_2, member_predicate,
% 16.28/2.90 | all_23_3) = all_23_1 & equal_set(all_23_2, all_23_1) = all_23_0 &
% 16.28/2.90 | member(all_23_2, all_23_3) = 0 & member(all_23_3, on) = 0 &
% 16.28/2.90 | $i(all_23_1) & $i(all_23_2) & $i(all_23_3)
% 16.28/2.90 |
% 16.28/2.90 | ALPHA: (18) implies:
% 16.28/2.90 | (19) ~ (all_23_0 = 0)
% 16.28/2.90 | (20) $i(all_23_3)
% 16.28/2.90 | (21) $i(all_23_2)
% 16.28/2.90 | (22) $i(all_23_1)
% 16.28/2.90 | (23) member(all_23_3, on) = 0
% 16.28/2.90 | (24) member(all_23_2, all_23_3) = 0
% 16.28/2.90 | (25) equal_set(all_23_2, all_23_1) = all_23_0
% 16.28/2.90 | (26) initial_segment(all_23_2, member_predicate, all_23_3) = all_23_1
% 16.28/2.90 |
% 16.28/2.90 | GROUND_INST: instantiating (8) with all_23_3, all_23_2, simplifying with (20),
% 16.28/2.90 | (21), (23), (24) gives:
% 16.28/2.90 | (27) subset(all_23_2, all_23_3) = 0
% 16.28/2.90 |
% 16.28/2.90 | GROUND_INST: instantiating (7) with all_23_2, all_23_1, all_23_0, simplifying
% 16.28/2.90 | with (21), (22), (25) gives:
% 16.28/2.90 | (28) all_23_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_23_1,
% 16.28/2.90 | all_23_2) = v1 & subset(all_23_2, all_23_1) = v0 & ( ~ (v1 = 0) |
% 16.28/2.90 | ~ (v0 = 0)))
% 16.28/2.90 |
% 16.28/2.90 | BETA: splitting (28) gives:
% 16.28/2.90 |
% 16.28/2.90 | Case 1:
% 16.28/2.90 | |
% 16.28/2.90 | | (29) all_23_0 = 0
% 16.28/2.90 | |
% 16.28/2.90 | | REDUCE: (19), (29) imply:
% 16.28/2.90 | | (30) $false
% 16.28/2.90 | |
% 16.28/2.90 | | CLOSE: (30) is inconsistent.
% 16.28/2.90 | |
% 16.28/2.90 | Case 2:
% 16.28/2.90 | |
% 16.28/2.90 | | (31) ? [v0: any] : ? [v1: any] : (subset(all_23_1, all_23_2) = v1 &
% 16.28/2.90 | | subset(all_23_2, all_23_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 16.28/2.90 | |
% 16.28/2.90 | | DELTA: instantiating (31) with fresh symbols all_35_0, all_35_1 gives:
% 16.28/2.90 | | (32) subset(all_23_1, all_23_2) = all_35_0 & subset(all_23_2, all_23_1) =
% 16.28/2.90 | | all_35_1 & ( ~ (all_35_0 = 0) | ~ (all_35_1 = 0))
% 16.28/2.90 | |
% 16.28/2.90 | | ALPHA: (32) implies:
% 16.28/2.90 | | (33) subset(all_23_2, all_23_1) = all_35_1
% 16.28/2.90 | | (34) subset(all_23_1, all_23_2) = all_35_0
% 16.28/2.90 | | (35) ~ (all_35_0 = 0) | ~ (all_35_1 = 0)
% 16.28/2.90 | |
% 16.28/2.90 | | GROUND_INST: instantiating (4) with all_23_3, all_23_2, simplifying with
% 16.28/2.90 | | (20), (21), (27) gives:
% 16.28/2.91 | | (36) ? [v0: any] : ? [v1: any] : (equal_set(all_23_3, all_23_2) = v1 &
% 16.28/2.91 | | subset(all_23_3, all_23_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (3) with all_23_2, all_23_3, simplifying with
% 16.28/2.91 | | (20), (21), (27) gives:
% 16.28/2.91 | | (37) ? [v0: any] : ? [v1: any] : (equal_set(all_23_2, all_23_3) = v1 &
% 16.28/2.91 | | subset(all_23_3, all_23_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (6) with all_23_3, all_23_2, 0, simplifying with
% 16.28/2.91 | | (20), (21), (27) gives:
% 16.28/2.91 | | (38) ? [v0: any] : ? [v1: any] : (equal_set(all_23_3, all_23_2) = v0 &
% 16.28/2.91 | | subset(all_23_3, all_23_2) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (5) with all_23_2, all_23_3, 0, simplifying with
% 16.28/2.91 | | (20), (21), (27) gives:
% 16.28/2.91 | | (39) ? [v0: any] : ? [v1: any] : (equal_set(all_23_2, all_23_3) = v0 &
% 16.28/2.91 | | subset(all_23_3, all_23_2) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (2) with all_23_2, all_23_1, all_35_1,
% 16.28/2.91 | | simplifying with (21), (22), (33) gives:
% 16.28/2.91 | | (40) all_35_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 16.28/2.91 | | member(v0, all_23_1) = v1 & member(v0, all_23_2) = 0 & $i(v0))
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (2) with all_23_1, all_23_2, all_35_0,
% 16.28/2.91 | | simplifying with (21), (22), (34) gives:
% 16.28/2.91 | | (41) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 16.28/2.91 | | member(v0, all_23_1) = 0 & member(v0, all_23_2) = v1 & $i(v0))
% 16.28/2.91 | |
% 16.28/2.91 | | DELTA: instantiating (36) with fresh symbols all_45_0, all_45_1 gives:
% 16.28/2.91 | | (42) equal_set(all_23_3, all_23_2) = all_45_0 & subset(all_23_3,
% 16.28/2.91 | | all_23_2) = all_45_1 & ( ~ (all_45_1 = 0) | all_45_0 = 0)
% 16.28/2.91 | |
% 16.28/2.91 | | ALPHA: (42) implies:
% 16.28/2.91 | | (43) subset(all_23_3, all_23_2) = all_45_1
% 16.28/2.91 | |
% 16.28/2.91 | | DELTA: instantiating (39) with fresh symbols all_47_0, all_47_1 gives:
% 16.28/2.91 | | (44) equal_set(all_23_2, all_23_3) = all_47_1 & subset(all_23_3,
% 16.28/2.91 | | all_23_2) = all_47_0 & ( ~ (all_47_1 = 0) | all_47_0 = 0)
% 16.28/2.91 | |
% 16.28/2.91 | | ALPHA: (44) implies:
% 16.28/2.91 | | (45) subset(all_23_3, all_23_2) = all_47_0
% 16.28/2.91 | |
% 16.28/2.91 | | DELTA: instantiating (38) with fresh symbols all_49_0, all_49_1 gives:
% 16.28/2.91 | | (46) equal_set(all_23_3, all_23_2) = all_49_1 & subset(all_23_3,
% 16.28/2.91 | | all_23_2) = all_49_0 & ( ~ (all_49_1 = 0) | all_49_0 = 0)
% 16.28/2.91 | |
% 16.28/2.91 | | ALPHA: (46) implies:
% 16.28/2.91 | | (47) subset(all_23_3, all_23_2) = all_49_0
% 16.28/2.91 | |
% 16.28/2.91 | | DELTA: instantiating (37) with fresh symbols all_51_0, all_51_1 gives:
% 16.28/2.91 | | (48) equal_set(all_23_2, all_23_3) = all_51_0 & subset(all_23_3,
% 16.28/2.91 | | all_23_2) = all_51_1 & ( ~ (all_51_1 = 0) | all_51_0 = 0)
% 16.28/2.91 | |
% 16.28/2.91 | | ALPHA: (48) implies:
% 16.28/2.91 | | (49) subset(all_23_3, all_23_2) = all_51_1
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (16) with all_45_1, all_49_0, all_23_2, all_23_3,
% 16.28/2.91 | | simplifying with (43), (47) gives:
% 16.28/2.91 | | (50) all_49_0 = all_45_1
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (16) with all_49_0, all_51_1, all_23_2, all_23_3,
% 16.28/2.91 | | simplifying with (47), (49) gives:
% 16.28/2.91 | | (51) all_51_1 = all_49_0
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (16) with all_47_0, all_51_1, all_23_2, all_23_3,
% 16.28/2.91 | | simplifying with (45), (49) gives:
% 16.28/2.91 | | (52) all_51_1 = all_47_0
% 16.28/2.91 | |
% 16.28/2.91 | | COMBINE_EQS: (51), (52) imply:
% 16.28/2.91 | | (53) all_49_0 = all_47_0
% 16.28/2.91 | |
% 16.28/2.91 | | SIMP: (53) implies:
% 16.28/2.91 | | (54) all_49_0 = all_47_0
% 16.28/2.91 | |
% 16.28/2.91 | | COMBINE_EQS: (50), (54) imply:
% 16.28/2.91 | | (55) all_47_0 = all_45_1
% 16.28/2.91 | |
% 16.28/2.91 | | SIMP: (55) implies:
% 16.28/2.91 | | (56) all_47_0 = all_45_1
% 16.28/2.91 | |
% 16.28/2.91 | | GROUND_INST: instantiating (6) with all_23_2, all_23_3, all_45_1,
% 16.28/2.91 | | simplifying with (20), (21), (43) gives:
% 16.28/2.92 | | (57) ? [v0: any] : ? [v1: any] : (equal_set(all_23_2, all_23_3) = v0 &
% 16.28/2.92 | | subset(all_23_2, all_23_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 &
% 16.28/2.92 | | all_45_1 = 0)))
% 16.28/2.92 | |
% 16.28/2.92 | | GROUND_INST: instantiating (5) with all_23_3, all_23_2, all_45_1,
% 16.28/2.92 | | simplifying with (20), (21), (43) gives:
% 16.28/2.92 | | (58) ? [v0: any] : ? [v1: any] : (equal_set(all_23_3, all_23_2) = v0 &
% 16.28/2.92 | | subset(all_23_2, all_23_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 &
% 16.28/2.92 | | all_45_1 = 0)))
% 16.28/2.92 | |
% 16.28/2.92 | | DELTA: instantiating (57) with fresh symbols all_84_0, all_84_1 gives:
% 16.28/2.92 | | (59) equal_set(all_23_2, all_23_3) = all_84_1 & subset(all_23_2,
% 16.28/2.92 | | all_23_3) = all_84_0 & ( ~ (all_84_1 = 0) | (all_84_0 = 0 &
% 16.28/2.92 | | all_45_1 = 0))
% 16.28/2.92 | |
% 16.28/2.92 | | ALPHA: (59) implies:
% 16.28/2.92 | | (60) subset(all_23_2, all_23_3) = all_84_0
% 16.28/2.92 | |
% 16.28/2.92 | | DELTA: instantiating (58) with fresh symbols all_86_0, all_86_1 gives:
% 16.28/2.92 | | (61) equal_set(all_23_3, all_23_2) = all_86_1 & subset(all_23_2,
% 16.28/2.92 | | all_23_3) = all_86_0 & ( ~ (all_86_1 = 0) | (all_86_0 = 0 &
% 16.28/2.92 | | all_45_1 = 0))
% 16.28/2.92 | |
% 16.28/2.92 | | ALPHA: (61) implies:
% 16.28/2.92 | | (62) subset(all_23_2, all_23_3) = all_86_0
% 16.28/2.92 | |
% 16.28/2.92 | | GROUND_INST: instantiating (16) with 0, all_86_0, all_23_3, all_23_2,
% 16.28/2.92 | | simplifying with (27), (62) gives:
% 16.28/2.92 | | (63) all_86_0 = 0
% 16.28/2.92 | |
% 16.28/2.92 | | GROUND_INST: instantiating (16) with all_84_0, all_86_0, all_23_3, all_23_2,
% 16.28/2.92 | | simplifying with (60), (62) gives:
% 16.28/2.92 | | (64) all_86_0 = all_84_0
% 16.28/2.92 | |
% 16.28/2.92 | | COMBINE_EQS: (63), (64) imply:
% 16.28/2.92 | | (65) all_84_0 = 0
% 16.28/2.92 | |
% 16.28/2.92 | | SIMP: (65) implies:
% 16.28/2.92 | | (66) all_84_0 = 0
% 16.28/2.92 | |
% 16.28/2.92 | | BETA: splitting (35) gives:
% 16.28/2.92 | |
% 16.28/2.92 | | Case 1:
% 16.28/2.92 | | |
% 16.28/2.92 | | | (67) ~ (all_35_0 = 0)
% 16.28/2.92 | | |
% 16.28/2.92 | | | BETA: splitting (41) gives:
% 16.28/2.92 | | |
% 16.28/2.92 | | | Case 1:
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | (68) all_35_0 = 0
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | REDUCE: (67), (68) imply:
% 16.28/2.92 | | | | (69) $false
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | CLOSE: (69) is inconsistent.
% 16.28/2.92 | | | |
% 16.28/2.92 | | | Case 2:
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | (70) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_23_1)
% 16.28/2.92 | | | | = 0 & member(v0, all_23_2) = v1 & $i(v0))
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | DELTA: instantiating (70) with fresh symbols all_156_0, all_156_1 gives:
% 16.28/2.92 | | | | (71) ~ (all_156_0 = 0) & member(all_156_1, all_23_1) = 0 &
% 16.28/2.92 | | | | member(all_156_1, all_23_2) = all_156_0 & $i(all_156_1)
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | ALPHA: (71) implies:
% 16.28/2.92 | | | | (72) ~ (all_156_0 = 0)
% 16.28/2.92 | | | | (73) $i(all_156_1)
% 16.28/2.92 | | | | (74) member(all_156_1, all_23_2) = all_156_0
% 16.28/2.92 | | | | (75) member(all_156_1, all_23_1) = 0
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | GROUND_INST: instantiating (10) with all_156_1, all_23_2, all_156_0,
% 16.28/2.92 | | | | simplifying with (21), (73), (74) gives:
% 16.28/2.92 | | | | (76) all_156_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 16.28/2.92 | | | | apply(member_predicate, all_156_1, all_23_2) = v0)
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | GROUND_INST: instantiating (11) with all_23_2, member_predicate,
% 16.28/2.92 | | | | all_23_3, all_156_1, all_23_1, simplifying with (13), (20),
% 16.28/2.92 | | | | (21), (26), (73), (75) gives:
% 16.28/2.92 | | | | (77) apply(member_predicate, all_156_1, all_23_2) = 0 &
% 16.28/2.92 | | | | member(all_156_1, all_23_3) = 0
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | ALPHA: (77) implies:
% 16.28/2.92 | | | | (78) apply(member_predicate, all_156_1, all_23_2) = 0
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | BETA: splitting (76) gives:
% 16.28/2.92 | | | |
% 16.28/2.92 | | | | Case 1:
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | (79) all_156_0 = 0
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | REDUCE: (72), (79) imply:
% 16.28/2.92 | | | | | (80) $false
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | CLOSE: (80) is inconsistent.
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | Case 2:
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | (81) ? [v0: int] : ( ~ (v0 = 0) & apply(member_predicate,
% 16.28/2.92 | | | | | all_156_1, all_23_2) = v0)
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | DELTA: instantiating (81) with fresh symbol all_176_0 gives:
% 16.28/2.92 | | | | | (82) ~ (all_176_0 = 0) & apply(member_predicate, all_156_1,
% 16.28/2.92 | | | | | all_23_2) = all_176_0
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | ALPHA: (82) implies:
% 16.28/2.92 | | | | | (83) ~ (all_176_0 = 0)
% 16.28/2.92 | | | | | (84) apply(member_predicate, all_156_1, all_23_2) = all_176_0
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | GROUND_INST: instantiating (17) with 0, all_176_0, all_23_2,
% 16.28/2.92 | | | | | all_156_1, member_predicate, simplifying with (78), (84)
% 16.28/2.92 | | | | | gives:
% 16.28/2.92 | | | | | (85) all_176_0 = 0
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | REDUCE: (83), (85) imply:
% 16.28/2.92 | | | | | (86) $false
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | | CLOSE: (86) is inconsistent.
% 16.28/2.92 | | | | |
% 16.28/2.92 | | | | End of split
% 16.28/2.92 | | | |
% 16.28/2.92 | | | End of split
% 16.28/2.92 | | |
% 16.28/2.92 | | Case 2:
% 16.28/2.92 | | |
% 16.28/2.93 | | | (87) ~ (all_35_1 = 0)
% 16.28/2.93 | | |
% 16.28/2.93 | | | BETA: splitting (40) gives:
% 16.28/2.93 | | |
% 16.28/2.93 | | | Case 1:
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | (88) all_35_1 = 0
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | REDUCE: (87), (88) imply:
% 16.28/2.93 | | | | (89) $false
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | CLOSE: (89) is inconsistent.
% 16.28/2.93 | | | |
% 16.28/2.93 | | | Case 2:
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | (90) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_23_1)
% 16.28/2.93 | | | | = v1 & member(v0, all_23_2) = 0 & $i(v0))
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | DELTA: instantiating (90) with fresh symbols all_156_0, all_156_1 gives:
% 16.28/2.93 | | | | (91) ~ (all_156_0 = 0) & member(all_156_1, all_23_1) = all_156_0 &
% 16.28/2.93 | | | | member(all_156_1, all_23_2) = 0 & $i(all_156_1)
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | ALPHA: (91) implies:
% 16.28/2.93 | | | | (92) ~ (all_156_0 = 0)
% 16.28/2.93 | | | | (93) $i(all_156_1)
% 16.28/2.93 | | | | (94) member(all_156_1, all_23_2) = 0
% 16.28/2.93 | | | | (95) member(all_156_1, all_23_1) = all_156_0
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | GROUND_INST: instantiating (1) with all_23_2, all_23_3, all_156_1,
% 16.28/2.93 | | | | simplifying with (20), (21), (27), (93), (94) gives:
% 16.28/2.93 | | | | (96) member(all_156_1, all_23_3) = 0
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | GROUND_INST: instantiating (9) with all_156_1, all_23_2, simplifying
% 16.28/2.93 | | | | with (21), (93), (94) gives:
% 16.28/2.93 | | | | (97) apply(member_predicate, all_156_1, all_23_2) = 0
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | GROUND_INST: instantiating (12) with all_23_2, member_predicate,
% 16.28/2.93 | | | | all_23_3, all_156_1, all_23_1, all_156_0, simplifying with
% 16.28/2.93 | | | | (13), (20), (21), (26), (93), (95) gives:
% 16.28/2.93 | | | | (98) all_156_0 = 0 | ? [v0: any] : ? [v1: any] :
% 16.28/2.93 | | | | (apply(member_predicate, all_156_1, all_23_2) = v1 &
% 16.28/2.93 | | | | member(all_156_1, all_23_3) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 16.28/2.93 | | | | 0)))
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | BETA: splitting (98) gives:
% 16.28/2.93 | | | |
% 16.28/2.93 | | | | Case 1:
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | (99) all_156_0 = 0
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | REDUCE: (92), (99) imply:
% 16.28/2.93 | | | | | (100) $false
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | CLOSE: (100) is inconsistent.
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | Case 2:
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | (101) ? [v0: any] : ? [v1: any] : (apply(member_predicate,
% 16.28/2.93 | | | | | all_156_1, all_23_2) = v1 & member(all_156_1, all_23_3) =
% 16.28/2.93 | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | DELTA: instantiating (101) with fresh symbols all_178_0, all_178_1
% 16.28/2.93 | | | | | gives:
% 16.28/2.93 | | | | | (102) apply(member_predicate, all_156_1, all_23_2) = all_178_0 &
% 16.28/2.93 | | | | | member(all_156_1, all_23_3) = all_178_1 & ( ~ (all_178_0 = 0)
% 16.28/2.93 | | | | | | ~ (all_178_1 = 0))
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | ALPHA: (102) implies:
% 16.28/2.93 | | | | | (103) member(all_156_1, all_23_3) = all_178_1
% 16.28/2.93 | | | | | (104) apply(member_predicate, all_156_1, all_23_2) = all_178_0
% 16.28/2.93 | | | | | (105) ~ (all_178_0 = 0) | ~ (all_178_1 = 0)
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | GROUND_INST: instantiating (15) with 0, all_178_1, all_23_3,
% 16.28/2.93 | | | | | all_156_1, simplifying with (96), (103) gives:
% 16.28/2.93 | | | | | (106) all_178_1 = 0
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | GROUND_INST: instantiating (17) with 0, all_178_0, all_23_2,
% 16.28/2.93 | | | | | all_156_1, member_predicate, simplifying with (97), (104)
% 16.28/2.93 | | | | | gives:
% 16.28/2.93 | | | | | (107) all_178_0 = 0
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | BETA: splitting (105) gives:
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | | Case 1:
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | | (108) ~ (all_178_0 = 0)
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | | REDUCE: (107), (108) imply:
% 16.28/2.93 | | | | | | (109) $false
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | | CLOSE: (109) is inconsistent.
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | Case 2:
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | | (110) ~ (all_178_1 = 0)
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | | REDUCE: (106), (110) imply:
% 16.28/2.93 | | | | | | (111) $false
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | | CLOSE: (111) is inconsistent.
% 16.28/2.93 | | | | | |
% 16.28/2.93 | | | | | End of split
% 16.28/2.93 | | | | |
% 16.28/2.93 | | | | End of split
% 16.28/2.93 | | | |
% 16.28/2.93 | | | End of split
% 16.28/2.93 | | |
% 16.28/2.93 | | End of split
% 16.28/2.93 | |
% 16.28/2.93 | End of split
% 16.28/2.93 |
% 16.28/2.93 End of proof
% 16.28/2.93 % SZS output end Proof for theBenchmark
% 16.28/2.93
% 16.28/2.93 2319ms
%------------------------------------------------------------------------------