TSTP Solution File: SEU182+2 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU182+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 17:43:06 EDT 2023
% Result : Theorem 25.88s 4.34s
% Output : Proof 33.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU182+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 17:08:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.34/1.48 Prover 4: Preprocessing ...
% 4.34/1.50 Prover 1: Preprocessing ...
% 4.34/1.52 Prover 6: Preprocessing ...
% 4.34/1.52 Prover 5: Preprocessing ...
% 4.73/1.52 Prover 0: Preprocessing ...
% 4.73/1.52 Prover 2: Preprocessing ...
% 4.73/1.52 Prover 3: Preprocessing ...
% 13.72/2.69 Prover 1: Warning: ignoring some quantifiers
% 15.12/2.85 Prover 1: Constructing countermodel ...
% 15.55/2.92 Prover 3: Warning: ignoring some quantifiers
% 15.55/2.93 Prover 5: Proving ...
% 15.95/2.96 Prover 6: Proving ...
% 15.95/2.99 Prover 3: Constructing countermodel ...
% 15.95/3.08 Prover 4: Warning: ignoring some quantifiers
% 15.95/3.21 Prover 4: Constructing countermodel ...
% 16.95/3.23 Prover 2: Proving ...
% 19.50/3.44 Prover 0: Proving ...
% 25.88/4.32 Prover 3: proved (3676ms)
% 25.88/4.32
% 25.88/4.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.88/4.34
% 25.88/4.35 Prover 2: stopped
% 25.88/4.35 Prover 6: stopped
% 25.88/4.35 Prover 0: stopped
% 25.88/4.37 Prover 5: stopped
% 25.88/4.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.88/4.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.88/4.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.88/4.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.88/4.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 28.03/4.61 Prover 7: Preprocessing ...
% 28.03/4.67 Prover 10: Preprocessing ...
% 28.03/4.68 Prover 8: Preprocessing ...
% 28.03/4.69 Prover 11: Preprocessing ...
% 28.74/4.70 Prover 13: Preprocessing ...
% 29.47/4.94 Prover 10: Warning: ignoring some quantifiers
% 29.47/4.95 Prover 7: Warning: ignoring some quantifiers
% 29.47/5.02 Prover 7: Constructing countermodel ...
% 29.47/5.02 Prover 10: Constructing countermodel ...
% 31.22/5.05 Prover 8: Warning: ignoring some quantifiers
% 31.22/5.05 Prover 13: Warning: ignoring some quantifiers
% 31.22/5.07 Prover 1: Found proof (size 102)
% 31.22/5.07 Prover 1: proved (4427ms)
% 31.22/5.07 Prover 7: stopped
% 31.22/5.07 Prover 4: stopped
% 31.22/5.07 Prover 8: Constructing countermodel ...
% 31.22/5.08 Prover 8: stopped
% 31.22/5.08 Prover 10: stopped
% 31.22/5.08 Prover 13: Constructing countermodel ...
% 31.22/5.10 Prover 13: stopped
% 32.29/5.28 Prover 11: Warning: ignoring some quantifiers
% 32.42/5.31 Prover 11: Constructing countermodel ...
% 32.59/5.33 Prover 11: stopped
% 32.59/5.33
% 32.59/5.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.59/5.33
% 32.59/5.34 % SZS output start Proof for theBenchmark
% 32.59/5.35 Assumptions after simplification:
% 32.59/5.35 ---------------------------------
% 32.59/5.35
% 32.59/5.35 (d3_tarski)
% 32.59/5.39 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 32.59/5.39 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 32.59/5.39 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 32.59/5.39 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 32.59/5.39 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 32.59/5.39
% 32.59/5.39 (d4_relat_1)
% 32.59/5.40 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 32.59/5.40 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 32.59/5.40 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 32.59/5.40 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 32.59/5.40 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 32.59/5.40 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 32.59/5.40 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 32.59/5.40 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 32.59/5.40 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 32.59/5.40 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 32.59/5.40 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 32.59/5.40 $i(v3)))))))
% 32.59/5.40
% 32.59/5.40 (d8_relat_1)
% 32.89/5.41 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] :
% 32.89/5.41 ( ~ (relation_composition(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3
% 32.89/5.41 = 0) & relation(v1) = v3) | ! [v3: $i] : ( ~ (relation(v3) = 0) | ~
% 32.89/5.41 $i(v3) | (( ~ (v3 = v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 32.89/5.41 [v7: int] : (v7 = 0 | ~ (ordered_pair(v4, v5) = v6) | ~ (in(v6,
% 32.89/5.41 v2) = v7) | ~ $i(v5) | ~ $i(v4) | ! [v8: $i] : ! [v9:
% 32.89/5.41 $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~ (in(v9, v0) = 0) |
% 32.89/5.41 ~ $i(v8) | ? [v10: $i] : ? [v11: int] : ( ~ (v11 = 0) &
% 32.89/5.41 ordered_pair(v8, v5) = v10 & in(v10, v1) = v11 & $i(v10))))
% 32.89/5.41 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4,
% 32.89/5.41 v5) = v6) | ~ (in(v6, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ?
% 32.89/5.41 [v7: $i] : ? [v8: $i] : ? [v9: $i] : (ordered_pair(v7, v5) =
% 32.89/5.41 v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) = 0 & in(v8, v0) =
% 32.89/5.41 0 & $i(v9) & $i(v8) & $i(v7))))) & (v3 = v2 | ? [v4: $i] : ?
% 32.89/5.41 [v5: $i] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v4, v5) = v6 &
% 32.89/5.41 in(v6, v3) = v7 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v7 = 0) | !
% 32.89/5.41 [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~
% 32.89/5.41 (in(v9, v0) = 0) | ~ $i(v8) | ? [v10: $i] : ? [v11: int] :
% 32.89/5.41 ( ~ (v11 = 0) & ordered_pair(v8, v5) = v10 & in(v10, v1) = v11
% 32.89/5.41 & $i(v10)))) & (v7 = 0 | ? [v8: $i] : ? [v9: $i] : ?
% 32.89/5.41 [v10: $i] : (ordered_pair(v8, v5) = v10 & ordered_pair(v4, v8) =
% 32.89/5.41 v9 & in(v10, v1) = 0 & in(v9, v0) = 0 & $i(v10) & $i(v9) &
% 32.89/5.41 $i(v8)))))))))
% 32.89/5.41
% 32.89/5.41 (dt_k5_relat_1)
% 32.89/5.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 32.89/5.41 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 32.89/5.41 (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) |
% 32.89/5.41 ~ (v3 = 0) | v5 = 0)))
% 32.89/5.41
% 32.89/5.41 (fc1_subset_1)
% 32.89/5.41 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int]
% 32.89/5.41 : ( ~ (v2 = 0) & empty(v1) = v2))
% 32.89/5.41
% 32.89/5.41 (rc1_subset_1)
% 32.89/5.41 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 32.89/5.41 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~
% 32.89/5.41 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3))))
% 32.89/5.41
% 32.89/5.41 (rc2_xboole_0)
% 32.89/5.41 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0))
% 32.89/5.41
% 32.89/5.41 (t2_subset)
% 32.89/5.41 ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 32.89/5.41 | ? [v2: any] : ? [v3: any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0
% 32.89/5.41 | v2 = 0)))
% 32.89/5.41
% 32.89/5.41 (t44_relat_1)
% 32.89/5.41 ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = v1 & relation(v0) = 0 & $i(v1)
% 32.89/5.41 & $i(v0) & ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5
% 32.89/5.41 = 0) & relation_composition(v0, v2) = v3 & relation_dom(v3) = v4 &
% 32.89/5.41 relation(v2) = 0 & subset(v4, v1) = v5 & $i(v4) & $i(v3) & $i(v2)))
% 32.89/5.41
% 32.89/5.41 (function-axioms)
% 32.89/5.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 32.89/5.42 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 32.89/5.42 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 32.89/5.42 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~
% 32.89/5.42 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 32.89/5.42 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 32.89/5.42 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 32.89/5.42 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 32.89/5.42 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 32.89/5.42 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 32.89/5.42 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 32.89/5.42 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~
% 32.89/5.42 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 32.89/5.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 32.89/5.42 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 32.89/5.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 32.89/5.42 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 32.89/5.42 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 32.89/5.42 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 32.89/5.42 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 32.89/5.42 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 32.89/5.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 32.89/5.42 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 32.89/5.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 32.89/5.42 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 32.89/5.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 32.89/5.42 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 32.89/5.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 32.89/5.42 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 32.89/5.42 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 32.89/5.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 32.89/5.42 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 32.89/5.42 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 32.89/5.42 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3,
% 32.89/5.42 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 32.89/5.42 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 32.89/5.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 32.89/5.42 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i]
% 32.89/5.42 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 32.89/5.42 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 32.89/5.42 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i]
% 32.89/5.42 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) =
% 32.89/5.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 32.89/5.42 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : !
% 32.89/5.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 32.89/5.42 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 32.89/5.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 32.89/5.42 (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 32.89/5.42 (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 32.89/5.42 ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) &
% 32.89/5.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) |
% 32.89/5.42 ~ (set_meet(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 32.89/5.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 32.89/5.42 (relation(v2) = v0))
% 32.89/5.42
% 32.89/5.42 Further assumptions not needed in the proof:
% 32.89/5.42 --------------------------------------------
% 32.89/5.43 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski,
% 32.89/5.43 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_relat_1,
% 32.89/5.43 d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_subset_1, d2_tarski,
% 32.89/5.43 d2_xboole_0, d2_zfmisc_1, d3_xboole_0, d4_subset_1, d4_tarski, d4_xboole_0,
% 32.89/5.43 d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0,
% 32.89/5.43 d8_setfam_1, d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski,
% 32.89/5.43 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski,
% 32.89/5.43 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski,
% 32.89/5.43 dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_setfam_1,
% 32.89/5.43 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, dt_m1_subset_1,
% 32.89/5.43 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1,
% 32.89/5.43 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, fc4_subset_1, idempotence_k2_xboole_0,
% 32.89/5.43 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 32.89/5.43 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 32.89/5.43 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 32.89/5.43 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 32.89/5.43 rc1_relat_1, rc1_xboole_0, rc2_subset_1, redefinition_k5_setfam_1,
% 32.89/5.43 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski,
% 32.89/5.43 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1,
% 32.89/5.43 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset,
% 32.89/5.43 t1_xboole_1, t1_zfmisc_1, t20_relat_1, t21_relat_1, t25_relat_1, t26_xboole_1,
% 32.89/5.43 t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1,
% 32.89/5.43 t33_zfmisc_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 32.89/5.43 t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0,
% 32.89/5.43 t3_xboole_1, t40_xboole_1, t43_subset_1, t45_xboole_1, t46_setfam_1,
% 32.89/5.43 t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset,
% 32.89/5.43 t4_xboole_0, t50_subset_1, t54_subset_1, t5_subset, t60_xboole_1, t63_xboole_1,
% 32.89/5.43 t65_zfmisc_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1,
% 32.89/5.43 t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1,
% 32.89/5.43 t9_tarski, t9_zfmisc_1
% 32.89/5.43
% 32.89/5.43 Those formulas are unsatisfiable:
% 32.89/5.43 ---------------------------------
% 32.89/5.43
% 32.89/5.43 Begin of proof
% 32.89/5.43 |
% 32.89/5.43 | ALPHA: (d3_tarski) implies:
% 32.89/5.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 32.89/5.43 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 32.89/5.43 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 32.89/5.43 |
% 32.89/5.43 | ALPHA: (function-axioms) implies:
% 32.89/5.43 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 32.89/5.43 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 32.89/5.43 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 32.89/5.43 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 32.89/5.43 |
% 32.89/5.43 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_135_0, all_135_1
% 32.89/5.43 | gives:
% 32.89/5.43 | (4) ~ (all_135_0 = 0) & empty(all_135_1) = all_135_0 & $i(all_135_1)
% 32.89/5.43 |
% 32.89/5.43 | ALPHA: (4) implies:
% 32.89/5.43 | (5) ~ (all_135_0 = 0)
% 32.89/5.43 | (6) $i(all_135_1)
% 32.89/5.43 | (7) empty(all_135_1) = all_135_0
% 32.89/5.43 |
% 32.89/5.43 | DELTA: instantiating (t44_relat_1) with fresh symbols all_156_0, all_156_1
% 32.89/5.43 | gives:
% 32.89/5.43 | (8) relation_dom(all_156_1) = all_156_0 & relation(all_156_1) = 0 &
% 32.89/5.43 | $i(all_156_0) & $i(all_156_1) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 32.89/5.43 | : ? [v3: int] : ( ~ (v3 = 0) & relation_composition(all_156_1, v0) =
% 32.89/5.43 | v1 & relation_dom(v1) = v2 & relation(v0) = 0 & subset(v2, all_156_0)
% 32.89/5.43 | = v3 & $i(v2) & $i(v1) & $i(v0))
% 32.89/5.43 |
% 32.89/5.43 | ALPHA: (8) implies:
% 32.89/5.43 | (9) $i(all_156_1)
% 32.89/5.43 | (10) $i(all_156_0)
% 32.89/5.43 | (11) relation(all_156_1) = 0
% 32.89/5.43 | (12) relation_dom(all_156_1) = all_156_0
% 32.89/5.43 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 32.89/5.43 | & relation_composition(all_156_1, v0) = v1 & relation_dom(v1) = v2 &
% 32.89/5.43 | relation(v0) = 0 & subset(v2, all_156_0) = v3 & $i(v2) & $i(v1) &
% 32.89/5.43 | $i(v0))
% 32.89/5.43 |
% 32.89/5.43 | DELTA: instantiating (13) with fresh symbols all_174_0, all_174_1, all_174_2,
% 32.89/5.43 | all_174_3 gives:
% 32.89/5.44 | (14) ~ (all_174_0 = 0) & relation_composition(all_156_1, all_174_3) =
% 32.89/5.44 | all_174_2 & relation_dom(all_174_2) = all_174_1 & relation(all_174_3)
% 32.89/5.44 | = 0 & subset(all_174_1, all_156_0) = all_174_0 & $i(all_174_1) &
% 32.89/5.44 | $i(all_174_2) & $i(all_174_3)
% 32.89/5.44 |
% 32.89/5.44 | ALPHA: (14) implies:
% 32.89/5.44 | (15) ~ (all_174_0 = 0)
% 32.89/5.44 | (16) $i(all_174_3)
% 32.89/5.44 | (17) $i(all_174_2)
% 32.89/5.44 | (18) $i(all_174_1)
% 32.89/5.44 | (19) subset(all_174_1, all_156_0) = all_174_0
% 32.89/5.44 | (20) relation(all_174_3) = 0
% 32.89/5.44 | (21) relation_dom(all_174_2) = all_174_1
% 32.89/5.44 | (22) relation_composition(all_156_1, all_174_3) = all_174_2
% 32.89/5.44 |
% 32.89/5.44 | GROUND_INST: instantiating (1) with all_174_1, all_156_0, all_174_0,
% 32.89/5.44 | simplifying with (10), (18), (19) gives:
% 32.89/5.44 | (23) all_174_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 32.89/5.44 | all_174_1) = 0 & in(v0, all_156_0) = v1 & $i(v0))
% 32.89/5.44 |
% 32.89/5.44 | GROUND_INST: instantiating (d8_relat_1) with all_156_1, simplifying with (9),
% 32.89/5.44 | (11) gives:
% 32.89/5.44 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_156_1, v0) =
% 32.89/5.44 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & relation(v0) = v2)
% 32.89/5.44 | | ! [v2: $i] : ( ~ (relation(v2) = 0) | ~ $i(v2) | (( ~ (v2 = v1)
% 32.89/5.44 | | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] :
% 32.89/5.44 | (v6 = 0 | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) =
% 32.89/5.44 | v6) | ~ $i(v4) | ~ $i(v3) | ! [v7: $i] : ! [v8: $i]
% 32.89/5.44 | : ( ~ (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_156_1)
% 32.89/5.44 | = 0) | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~
% 32.89/5.44 | (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) =
% 32.89/5.44 | v10 & $i(v9)))) & ! [v3: $i] : ! [v4: $i] : ! [v5:
% 32.89/5.44 | $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) =
% 32.89/5.44 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] :
% 32.89/5.44 | ? [v8: $i] : (ordered_pair(v6, v4) = v8 &
% 32.89/5.44 | ordered_pair(v3, v6) = v7 & in(v8, v0) = 0 & in(v7,
% 32.89/5.44 | all_156_1) = 0 & $i(v8) & $i(v7) & $i(v6))))) & (v2 =
% 32.89/5.44 | v1 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] :
% 32.89/5.44 | (ordered_pair(v3, v4) = v5 & in(v5, v2) = v6 & $i(v5) & $i(v4)
% 32.89/5.44 | & $i(v3) & ( ~ (v6 = 0) | ! [v7: $i] : ! [v8: $i] : ( ~
% 32.89/5.44 | (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_156_1) = 0)
% 32.89/5.44 | | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~ (v10 =
% 32.89/5.44 | 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) = v10 &
% 32.89/5.44 | $i(v9)))) & (v6 = 0 | ? [v7: $i] : ? [v8: $i] : ?
% 32.89/5.44 | [v9: $i] : (ordered_pair(v7, v4) = v9 & ordered_pair(v3,
% 32.89/5.44 | v7) = v8 & in(v9, v0) = 0 & in(v8, all_156_1) = 0 &
% 32.89/5.44 | $i(v9) & $i(v8) & $i(v7))))))))
% 32.89/5.44 |
% 32.89/5.44 | GROUND_INST: instantiating (rc1_subset_1) with all_135_1, all_135_0,
% 32.89/5.44 | simplifying with (6), (7) gives:
% 32.89/5.44 | (25) all_135_0 = 0 | ? [v0: $i] : (powerset(all_135_1) = v0 & $i(v0) & ?
% 32.89/5.44 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 &
% 32.89/5.44 | empty(v1) = v2 & $i(v1)))
% 32.89/5.44 |
% 32.89/5.45 | GROUND_INST: instantiating (d4_relat_1) with all_156_1, all_156_0, simplifying
% 32.89/5.45 | with (9), (12) gives:
% 32.89/5.45 | (26) ? [v0: int] : ( ~ (v0 = 0) & relation(all_156_1) = v0) | ( ? [v0:
% 32.89/5.45 | any] : (v0 = all_156_0 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] :
% 32.89/5.45 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4:
% 32.89/5.45 | $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 32.89/5.45 | all_156_1) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 32.89/5.45 | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_156_1) =
% 32.89/5.45 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_156_0) | ( ! [v0: $i] :
% 32.89/5.45 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_156_0) = v1) | ~ $i(v0)
% 32.89/5.45 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3)
% 32.89/5.45 | | ~ (in(v3, all_156_1) = 0) | ~ $i(v2))) & ! [v0: $i] : (
% 32.89/5.45 | ~ (in(v0, all_156_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 32.89/5.45 | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_156_1) = 0 &
% 32.89/5.45 | $i(v2) & $i(v1))))))
% 32.89/5.45 |
% 32.89/5.45 | GROUND_INST: instantiating (d4_relat_1) with all_174_2, all_174_1, simplifying
% 32.89/5.45 | with (17), (21) gives:
% 32.89/5.45 | (27) ? [v0: int] : ( ~ (v0 = 0) & relation(all_174_2) = v0) | ( ? [v0:
% 32.89/5.45 | any] : (v0 = all_174_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] :
% 32.89/5.45 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4:
% 32.89/5.45 | $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 32.89/5.45 | all_174_2) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 32.89/5.45 | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_174_2) =
% 32.89/5.45 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_174_1) | ( ! [v0: $i] :
% 32.89/5.45 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_174_1) = v1) | ~ $i(v0)
% 32.89/5.45 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3)
% 32.89/5.45 | | ~ (in(v3, all_174_2) = 0) | ~ $i(v2))) & ! [v0: $i] : (
% 32.89/5.45 | ~ (in(v0, all_174_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 32.89/5.45 | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_174_2) = 0 &
% 32.89/5.45 | $i(v2) & $i(v1))))))
% 32.89/5.45 |
% 32.89/5.45 | GROUND_INST: instantiating (dt_k5_relat_1) with all_156_1, all_174_3,
% 32.89/5.45 | all_174_2, simplifying with (9), (16), (22) gives:
% 32.89/5.45 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_174_2) = v2
% 32.89/5.45 | & relation(all_174_3) = v1 & relation(all_156_1) = v0 & ( ~ (v1 = 0)
% 32.89/5.45 | | ~ (v0 = 0) | v2 = 0))
% 32.89/5.45 |
% 32.89/5.45 | GROUND_INST: instantiating (24) with all_174_3, all_174_2, simplifying with
% 32.89/5.45 | (16), (22) gives:
% 32.89/5.46 | (29) ? [v0: int] : ( ~ (v0 = 0) & relation(all_174_3) = v0) | ! [v0: $i]
% 32.89/5.46 | : ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 = all_174_2) | ( !
% 32.89/5.46 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 32.89/5.46 | | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_174_2) =
% 32.89/5.46 | v4) | ~ $i(v2) | ~ $i(v1) | ! [v5: $i] : ! [v6: $i] :
% 32.89/5.46 | ( ~ (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_156_1) = 0)
% 32.89/5.46 | | ~ $i(v5) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 32.89/5.46 | ordered_pair(v5, v2) = v7 & in(v7, all_174_3) = v8 &
% 32.89/5.46 | $i(v7)))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 32.89/5.46 | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_174_2) = 0) |
% 32.89/5.46 | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 32.89/5.46 | $i] : (ordered_pair(v4, v2) = v6 & ordered_pair(v1, v4) =
% 32.89/5.46 | v5 & in(v6, all_174_3) = 0 & in(v5, all_156_1) = 0 &
% 32.89/5.46 | $i(v6) & $i(v5) & $i(v4))))) & (v0 = all_174_2 | ? [v1:
% 32.89/5.46 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 32.89/5.46 | (ordered_pair(v1, v2) = v3 & in(v3, v0) = v4 & $i(v3) & $i(v2) &
% 32.89/5.46 | $i(v1) & ( ~ (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~
% 32.89/5.46 | (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_156_1) = 0) |
% 32.89/5.46 | ~ $i(v5) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 32.89/5.46 | ordered_pair(v5, v2) = v7 & in(v7, all_174_3) = v8 &
% 32.89/5.46 | $i(v7)))) & (v4 = 0 | ? [v5: $i] : ? [v6: $i] : ?
% 32.89/5.46 | [v7: $i] : (ordered_pair(v5, v2) = v7 & ordered_pair(v1, v5)
% 32.89/5.46 | = v6 & in(v7, all_174_3) = 0 & in(v6, all_156_1) = 0 &
% 32.89/5.46 | $i(v7) & $i(v6) & $i(v5)))))))
% 32.89/5.46 |
% 32.89/5.46 | DELTA: instantiating (28) with fresh symbols all_200_0, all_200_1, all_200_2
% 32.89/5.46 | gives:
% 32.89/5.46 | (30) relation(all_174_2) = all_200_0 & relation(all_174_3) = all_200_1 &
% 32.89/5.46 | relation(all_156_1) = all_200_2 & ( ~ (all_200_1 = 0) | ~ (all_200_2
% 32.89/5.46 | = 0) | all_200_0 = 0)
% 32.89/5.46 |
% 32.89/5.46 | ALPHA: (30) implies:
% 32.89/5.46 | (31) relation(all_156_1) = all_200_2
% 32.89/5.46 | (32) relation(all_174_3) = all_200_1
% 32.89/5.46 | (33) relation(all_174_2) = all_200_0
% 32.89/5.46 | (34) ~ (all_200_1 = 0) | ~ (all_200_2 = 0) | all_200_0 = 0
% 32.89/5.46 |
% 32.89/5.46 | BETA: splitting (25) gives:
% 32.89/5.46 |
% 32.89/5.46 | Case 1:
% 32.89/5.46 | |
% 32.89/5.46 | | (35) all_135_0 = 0
% 32.89/5.46 | |
% 32.89/5.46 | | REDUCE: (5), (35) imply:
% 32.89/5.46 | | (36) $false
% 32.89/5.46 | |
% 32.89/5.46 | | CLOSE: (36) is inconsistent.
% 32.89/5.46 | |
% 32.89/5.46 | Case 2:
% 32.89/5.46 | |
% 32.89/5.46 | | (37) ? [v0: $i] : (powerset(all_135_1) = v0 & $i(v0) & ? [v1: $i] : ?
% 32.89/5.46 | | [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & empty(v1) = v2 &
% 32.89/5.46 | | $i(v1)))
% 32.89/5.46 | |
% 32.89/5.46 | | DELTA: instantiating (37) with fresh symbol all_209_0 gives:
% 32.89/5.46 | | (38) powerset(all_135_1) = all_209_0 & $i(all_209_0) & ? [v0: $i] : ?
% 32.89/5.46 | | [v1: int] : ( ~ (v1 = 0) & element(v0, all_209_0) = 0 & empty(v0) =
% 32.89/5.46 | | v1 & $i(v0))
% 32.89/5.46 | |
% 32.89/5.46 | | ALPHA: (38) implies:
% 32.89/5.46 | | (39) $i(all_209_0)
% 32.89/5.46 | | (40) powerset(all_135_1) = all_209_0
% 32.89/5.46 | | (41) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_209_0) =
% 32.89/5.46 | | 0 & empty(v0) = v1 & $i(v0))
% 32.89/5.46 | |
% 32.89/5.46 | | DELTA: instantiating (41) with fresh symbols all_211_0, all_211_1 gives:
% 33.20/5.46 | | (42) ~ (all_211_0 = 0) & element(all_211_1, all_209_0) = 0 &
% 33.20/5.46 | | empty(all_211_1) = all_211_0 & $i(all_211_1)
% 33.20/5.46 | |
% 33.20/5.46 | | ALPHA: (42) implies:
% 33.20/5.46 | | (43) $i(all_211_1)
% 33.20/5.46 | | (44) element(all_211_1, all_209_0) = 0
% 33.20/5.46 | |
% 33.20/5.46 | | BETA: splitting (23) gives:
% 33.20/5.46 | |
% 33.20/5.46 | | Case 1:
% 33.20/5.46 | | |
% 33.20/5.47 | | | (45) all_174_0 = 0
% 33.20/5.47 | | |
% 33.20/5.47 | | | REDUCE: (15), (45) imply:
% 33.20/5.47 | | | (46) $false
% 33.20/5.47 | | |
% 33.20/5.47 | | | CLOSE: (46) is inconsistent.
% 33.20/5.47 | | |
% 33.20/5.47 | | Case 2:
% 33.20/5.47 | | |
% 33.20/5.47 | | | (47) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_174_1) = 0
% 33.20/5.47 | | | & in(v0, all_156_0) = v1 & $i(v0))
% 33.20/5.47 | | |
% 33.20/5.47 | | | DELTA: instantiating (47) with fresh symbols all_224_0, all_224_1 gives:
% 33.20/5.47 | | | (48) ~ (all_224_0 = 0) & in(all_224_1, all_174_1) = 0 & in(all_224_1,
% 33.20/5.47 | | | all_156_0) = all_224_0 & $i(all_224_1)
% 33.20/5.47 | | |
% 33.20/5.47 | | | ALPHA: (48) implies:
% 33.20/5.47 | | | (49) ~ (all_224_0 = 0)
% 33.20/5.47 | | | (50) $i(all_224_1)
% 33.20/5.47 | | | (51) in(all_224_1, all_156_0) = all_224_0
% 33.20/5.47 | | | (52) in(all_224_1, all_174_1) = 0
% 33.20/5.47 | | |
% 33.20/5.47 | | | GROUND_INST: instantiating (2) with 0, all_200_2, all_156_1, simplifying
% 33.20/5.47 | | | with (11), (31) gives:
% 33.20/5.47 | | | (53) all_200_2 = 0
% 33.20/5.47 | | |
% 33.20/5.47 | | | GROUND_INST: instantiating (2) with 0, all_200_1, all_174_3, simplifying
% 33.20/5.47 | | | with (20), (32) gives:
% 33.20/5.47 | | | (54) all_200_1 = 0
% 33.20/5.47 | | |
% 33.20/5.47 | | | BETA: splitting (34) gives:
% 33.20/5.47 | | |
% 33.20/5.47 | | | Case 1:
% 33.20/5.47 | | | |
% 33.20/5.47 | | | | (55) ~ (all_200_1 = 0)
% 33.20/5.47 | | | |
% 33.20/5.47 | | | | REDUCE: (54), (55) imply:
% 33.20/5.47 | | | | (56) $false
% 33.20/5.47 | | | |
% 33.20/5.47 | | | | CLOSE: (56) is inconsistent.
% 33.20/5.47 | | | |
% 33.20/5.47 | | | Case 2:
% 33.20/5.47 | | | |
% 33.20/5.47 | | | | (57) ~ (all_200_2 = 0) | all_200_0 = 0
% 33.20/5.47 | | | |
% 33.20/5.47 | | | | BETA: splitting (26) gives:
% 33.20/5.47 | | | |
% 33.20/5.47 | | | | Case 1:
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & relation(all_156_1) = v0)
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | DELTA: instantiating (58) with fresh symbol all_238_0 gives:
% 33.20/5.47 | | | | | (59) ~ (all_238_0 = 0) & relation(all_156_1) = all_238_0
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | ALPHA: (59) implies:
% 33.20/5.47 | | | | | (60) ~ (all_238_0 = 0)
% 33.20/5.47 | | | | | (61) relation(all_156_1) = all_238_0
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | GROUND_INST: instantiating (2) with 0, all_238_0, all_156_1,
% 33.20/5.47 | | | | | simplifying with (11), (61) gives:
% 33.20/5.47 | | | | | (62) all_238_0 = 0
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | REDUCE: (60), (62) imply:
% 33.20/5.47 | | | | | (63) $false
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | CLOSE: (63) is inconsistent.
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | Case 2:
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | (64) ? [v0: any] : (v0 = all_156_0 | ~ $i(v0) | ? [v1: $i] : ?
% 33.20/5.47 | | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | !
% 33.20/5.47 | | | | | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4)
% 33.20/5.47 | | | | | | ~ (in(v4, all_156_1) = 0) | ~ $i(v3))) & (v2 = 0 |
% 33.20/5.47 | | | | | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v1, v3) = v4 &
% 33.20/5.47 | | | | | in(v4, all_156_1) = 0 & $i(v4) & $i(v3))))) & ( ~
% 33.20/5.47 | | | | | $i(all_156_0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 33.20/5.47 | | | | | (in(v0, all_156_0) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 33.20/5.47 | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 33.20/5.47 | | | | | all_156_1) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 33.20/5.47 | | | | | (in(v0, all_156_0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 33.20/5.47 | | | | | [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 33.20/5.47 | | | | | all_156_1) = 0 & $i(v2) & $i(v1)))))
% 33.20/5.47 | | | | |
% 33.20/5.47 | | | | | ALPHA: (64) implies:
% 33.20/5.48 | | | | | (65) ~ $i(all_156_0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 33.20/5.48 | | | | | (in(v0, all_156_0) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 33.20/5.48 | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 33.20/5.48 | | | | | all_156_1) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 33.20/5.48 | | | | | (in(v0, all_156_0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 33.20/5.48 | | | | | [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_156_1)
% 33.20/5.48 | | | | | = 0 & $i(v2) & $i(v1))))
% 33.20/5.48 | | | | |
% 33.20/5.48 | | | | | BETA: splitting (29) gives:
% 33.20/5.48 | | | | |
% 33.20/5.48 | | | | | Case 1:
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & relation(all_174_3) = v0)
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | DELTA: instantiating (66) with fresh symbol all_237_0 gives:
% 33.20/5.48 | | | | | | (67) ~ (all_237_0 = 0) & relation(all_174_3) = all_237_0
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | ALPHA: (67) implies:
% 33.20/5.48 | | | | | | (68) ~ (all_237_0 = 0)
% 33.20/5.48 | | | | | | (69) relation(all_174_3) = all_237_0
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | GROUND_INST: instantiating (2) with 0, all_237_0, all_174_3,
% 33.20/5.48 | | | | | | simplifying with (20), (69) gives:
% 33.20/5.48 | | | | | | (70) all_237_0 = 0
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | REDUCE: (68), (70) imply:
% 33.20/5.48 | | | | | | (71) $false
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | CLOSE: (71) is inconsistent.
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | Case 2:
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | (72) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0
% 33.20/5.48 | | | | | | = all_174_2) | ( ! [v1: $i] : ! [v2: $i] : ! [v3:
% 33.20/5.48 | | | | | | $i] : ! [v4: int] : (v4 = 0 | ~
% 33.20/5.48 | | | | | | (ordered_pair(v1, v2) = v3) | ~ (in(v3,
% 33.20/5.48 | | | | | | all_174_2) = v4) | ~ $i(v2) | ~ $i(v1) | !
% 33.20/5.48 | | | | | | [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v1, v5)
% 33.20/5.48 | | | | | | = v6) | ~ (in(v6, all_156_1) = 0) | ~ $i(v5)
% 33.20/5.48 | | | | | | | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 33.20/5.48 | | | | | | ordered_pair(v5, v2) = v7 & in(v7, all_174_3)
% 33.20/5.48 | | | | | | = v8 & $i(v7)))) & ! [v1: $i] : ! [v2: $i] :
% 33.20/5.48 | | | | | | ! [v3: $i] : ( ~ (ordered_pair(v1, v2) = v3) | ~
% 33.20/5.48 | | | | | | (in(v3, all_174_2) = 0) | ~ $i(v2) | ~ $i(v1) |
% 33.20/5.48 | | | | | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 33.20/5.48 | | | | | | (ordered_pair(v4, v2) = v6 & ordered_pair(v1, v4)
% 33.20/5.48 | | | | | | = v5 & in(v6, all_174_3) = 0 & in(v5, all_156_1)
% 33.20/5.48 | | | | | | = 0 & $i(v6) & $i(v5) & $i(v4))))) & (v0 =
% 33.20/5.48 | | | | | | all_174_2 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 33.20/5.48 | | | | | | ? [v4: any] : (ordered_pair(v1, v2) = v3 & in(v3, v0)
% 33.20/5.48 | | | | | | = v4 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v4 = 0) | !
% 33.20/5.48 | | | | | | [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v1, v5)
% 33.20/5.48 | | | | | | = v6) | ~ (in(v6, all_156_1) = 0) | ~ $i(v5)
% 33.20/5.48 | | | | | | | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 33.20/5.48 | | | | | | ordered_pair(v5, v2) = v7 & in(v7, all_174_3)
% 33.20/5.48 | | | | | | = v8 & $i(v7)))) & (v4 = 0 | ? [v5: $i] : ?
% 33.20/5.48 | | | | | | [v6: $i] : ? [v7: $i] : (ordered_pair(v5, v2) =
% 33.20/5.48 | | | | | | v7 & ordered_pair(v1, v5) = v6 & in(v7,
% 33.20/5.48 | | | | | | all_174_3) = 0 & in(v6, all_156_1) = 0 &
% 33.20/5.48 | | | | | | $i(v7) & $i(v6) & $i(v5)))))))
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | BETA: splitting (57) gives:
% 33.20/5.48 | | | | | |
% 33.20/5.48 | | | | | | Case 1:
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | | (73) ~ (all_200_2 = 0)
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | | REDUCE: (53), (73) imply:
% 33.20/5.48 | | | | | | | (74) $false
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | | CLOSE: (74) is inconsistent.
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | Case 2:
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | | (75) all_200_0 = 0
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | | REDUCE: (33), (75) imply:
% 33.20/5.48 | | | | | | | (76) relation(all_174_2) = 0
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | | BETA: splitting (65) gives:
% 33.20/5.48 | | | | | | |
% 33.20/5.48 | | | | | | | Case 1:
% 33.20/5.48 | | | | | | | |
% 33.20/5.48 | | | | | | | | (77) ~ $i(all_156_0)
% 33.20/5.48 | | | | | | | |
% 33.20/5.48 | | | | | | | | PRED_UNIFY: (10), (77) imply:
% 33.20/5.48 | | | | | | | | (78) $false
% 33.20/5.48 | | | | | | | |
% 33.20/5.48 | | | | | | | | CLOSE: (78) is inconsistent.
% 33.20/5.48 | | | | | | | |
% 33.20/5.48 | | | | | | | Case 2:
% 33.20/5.48 | | | | | | | |
% 33.20/5.48 | | | | | | | | (79) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 33.20/5.48 | | | | | | | | all_156_0) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 33.20/5.48 | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 33.20/5.48 | | | | | | | | (in(v3, all_156_1) = 0) | ~ $i(v2))) & ! [v0: $i]
% 33.20/5.48 | | | | | | | | : ( ~ (in(v0, all_156_0) = 0) | ~ $i(v0) | ? [v1: $i]
% 33.20/5.48 | | | | | | | | : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 33.20/5.48 | | | | | | | | all_156_1) = 0 & $i(v2) & $i(v1)))
% 33.20/5.48 | | | | | | | |
% 33.20/5.48 | | | | | | | | ALPHA: (79) implies:
% 33.20/5.48 | | | | | | | | (80) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 33.20/5.49 | | | | | | | | all_156_0) = v1) | ~ $i(v0) | ! [v2: $i] : !
% 33.20/5.49 | | | | | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 33.20/5.49 | | | | | | | | (in(v3, all_156_1) = 0) | ~ $i(v2)))
% 33.20/5.49 | | | | | | | |
% 33.20/5.49 | | | | | | | | BETA: splitting (27) gives:
% 33.20/5.49 | | | | | | | |
% 33.20/5.49 | | | | | | | | Case 1:
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | (81) ? [v0: int] : ( ~ (v0 = 0) & relation(all_174_2) =
% 33.20/5.49 | | | | | | | | | v0)
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | DELTA: instantiating (81) with fresh symbol all_249_0 gives:
% 33.20/5.49 | | | | | | | | | (82) ~ (all_249_0 = 0) & relation(all_174_2) = all_249_0
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | ALPHA: (82) implies:
% 33.20/5.49 | | | | | | | | | (83) ~ (all_249_0 = 0)
% 33.20/5.49 | | | | | | | | | (84) relation(all_174_2) = all_249_0
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | GROUND_INST: instantiating (2) with 0, all_249_0, all_174_2,
% 33.20/5.49 | | | | | | | | | simplifying with (76), (84) gives:
% 33.20/5.49 | | | | | | | | | (85) all_249_0 = 0
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | REDUCE: (83), (85) imply:
% 33.20/5.49 | | | | | | | | | (86) $false
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | CLOSE: (86) is inconsistent.
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | Case 2:
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | (87) ? [v0: any] : (v0 = all_174_1 | ~ $i(v0) | ? [v1:
% 33.20/5.49 | | | | | | | | | $i] : ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & (
% 33.20/5.49 | | | | | | | | | ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : ( ~
% 33.20/5.49 | | | | | | | | | (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 33.20/5.49 | | | | | | | | | all_174_2) = 0) | ~ $i(v3))) & (v2 = 0 |
% 33.20/5.49 | | | | | | | | | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v1, v3)
% 33.20/5.49 | | | | | | | | | = v4 & in(v4, all_174_2) = 0 & $i(v4) &
% 33.20/5.49 | | | | | | | | | $i(v3))))) & ( ~ $i(all_174_1) | ( ! [v0: $i]
% 33.20/5.49 | | | | | | | | | : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_174_1) =
% 33.20/5.49 | | | | | | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] :
% 33.20/5.49 | | | | | | | | | ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 33.20/5.49 | | | | | | | | | all_174_2) = 0) | ~ $i(v2))) & ! [v0:
% 33.20/5.49 | | | | | | | | | $i] : ( ~ (in(v0, all_174_1) = 0) | ~ $i(v0) |
% 33.20/5.49 | | | | | | | | | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1)
% 33.20/5.49 | | | | | | | | | = v2 & in(v2, all_174_2) = 0 & $i(v2) &
% 33.20/5.49 | | | | | | | | | $i(v1)))))
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | ALPHA: (87) implies:
% 33.20/5.49 | | | | | | | | | (88) ~ $i(all_174_1) | ( ! [v0: $i] : ! [v1: int] : (v1 =
% 33.20/5.49 | | | | | | | | | 0 | ~ (in(v0, all_174_1) = v1) | ~ $i(v0) | !
% 33.20/5.49 | | | | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2)
% 33.20/5.49 | | | | | | | | | = v3) | ~ (in(v3, all_174_2) = 0) | ~
% 33.20/5.49 | | | | | | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_174_1)
% 33.20/5.49 | | | | | | | | | = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 33.20/5.49 | | | | | | | | | (ordered_pair(v0, v1) = v2 & in(v2, all_174_2) = 0
% 33.20/5.49 | | | | | | | | | & $i(v2) & $i(v1))))
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | BETA: splitting (88) gives:
% 33.20/5.49 | | | | | | | | |
% 33.20/5.49 | | | | | | | | | Case 1:
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | (89) ~ $i(all_174_1)
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | PRED_UNIFY: (18), (89) imply:
% 33.20/5.49 | | | | | | | | | | (90) $false
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | CLOSE: (90) is inconsistent.
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | Case 2:
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | (91) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 33.20/5.49 | | | | | | | | | | all_174_1) = v1) | ~ $i(v0) | ! [v2: $i] :
% 33.20/5.49 | | | | | | | | | | ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~
% 33.20/5.49 | | | | | | | | | | (in(v3, all_174_2) = 0) | ~ $i(v2))) & ! [v0:
% 33.20/5.49 | | | | | | | | | | $i] : ( ~ (in(v0, all_174_1) = 0) | ~ $i(v0) | ?
% 33.20/5.49 | | | | | | | | | | [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 33.20/5.49 | | | | | | | | | | v2 & in(v2, all_174_2) = 0 & $i(v2) & $i(v1)))
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | ALPHA: (91) implies:
% 33.20/5.49 | | | | | | | | | | (92) ! [v0: $i] : ( ~ (in(v0, all_174_1) = 0) | ~
% 33.20/5.49 | | | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 33.20/5.49 | | | | | | | | | | (ordered_pair(v0, v1) = v2 & in(v2, all_174_2) = 0
% 33.20/5.49 | | | | | | | | | | & $i(v2) & $i(v1)))
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | GROUND_INST: instantiating (80) with all_224_1, all_224_0,
% 33.20/5.49 | | | | | | | | | | simplifying with (50), (51) gives:
% 33.20/5.49 | | | | | | | | | | (93) all_224_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 33.20/5.49 | | | | | | | | | | (ordered_pair(all_224_1, v0) = v1) | ~ (in(v1,
% 33.20/5.49 | | | | | | | | | | all_156_1) = 0) | ~ $i(v0))
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | GROUND_INST: instantiating (92) with all_224_1, simplifying
% 33.20/5.49 | | | | | | | | | | with (50), (52) gives:
% 33.20/5.49 | | | | | | | | | | (94) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_224_1,
% 33.20/5.49 | | | | | | | | | | v0) = v1 & in(v1, all_174_2) = 0 & $i(v1) &
% 33.20/5.49 | | | | | | | | | | $i(v0))
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | GROUND_INST: instantiating (72) with all_174_2, simplifying
% 33.20/5.49 | | | | | | | | | | with (17), (76) gives:
% 33.20/5.49 | | | | | | | | | | (95) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 33.20/5.49 | | | | | | | | | | int] : (v3 = 0 | ~ (ordered_pair(v0, v1) = v2) |
% 33.20/5.49 | | | | | | | | | | ~ (in(v2, all_174_2) = v3) | ~ $i(v1) | ~ $i(v0)
% 33.20/5.49 | | | | | | | | | | | ! [v4: $i] : ! [v5: $i] : ( ~
% 33.20/5.49 | | | | | | | | | | (ordered_pair(v0, v4) = v5) | ~ (in(v5,
% 33.20/5.49 | | | | | | | | | | all_156_1) = 0) | ~ $i(v4) | ? [v6: $i] :
% 33.20/5.49 | | | | | | | | | | ? [v7: int] : ( ~ (v7 = 0) & ordered_pair(v4,
% 33.20/5.49 | | | | | | | | | | v1) = v6 & in(v6, all_174_3) = v7 &
% 33.20/5.49 | | | | | | | | | | $i(v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 33.20/5.49 | | | | | | | | | | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 33.20/5.49 | | | | | | | | | | (in(v2, all_174_2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 33.20/5.49 | | | | | | | | | | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 33.20/5.49 | | | | | | | | | | (ordered_pair(v3, v1) = v5 & ordered_pair(v0, v3)
% 33.20/5.49 | | | | | | | | | | = v4 & in(v5, all_174_3) = 0 & in(v4, all_156_1)
% 33.20/5.49 | | | | | | | | | | = 0 & $i(v5) & $i(v4) & $i(v3)))
% 33.20/5.49 | | | | | | | | | |
% 33.20/5.49 | | | | | | | | | | ALPHA: (95) implies:
% 33.20/5.50 | | | | | | | | | | (96) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 33.20/5.50 | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2,
% 33.20/5.50 | | | | | | | | | | all_174_2) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 33.20/5.50 | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 33.20/5.50 | | | | | | | | | | (ordered_pair(v3, v1) = v5 & ordered_pair(v0, v3)
% 33.20/5.50 | | | | | | | | | | = v4 & in(v5, all_174_3) = 0 & in(v4, all_156_1)
% 33.20/5.50 | | | | | | | | | | = 0 & $i(v5) & $i(v4) & $i(v3)))
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_135_1,
% 33.20/5.50 | | | | | | | | | | all_209_0, simplifying with (6), (40) gives:
% 33.20/5.50 | | | | | | | | | | (97) ? [v0: int] : ( ~ (v0 = 0) & empty(all_209_0) = v0)
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | GROUND_INST: instantiating (t2_subset) with all_211_1,
% 33.20/5.50 | | | | | | | | | | all_209_0, simplifying with (39), (43), (44)
% 33.20/5.50 | | | | | | | | | | gives:
% 33.20/5.50 | | | | | | | | | | (98) ? [v0: any] : ? [v1: any] : (empty(all_209_0) = v0
% 33.20/5.50 | | | | | | | | | | & in(all_211_1, all_209_0) = v1 & (v1 = 0 | v0 =
% 33.20/5.50 | | | | | | | | | | 0))
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | DELTA: instantiating (97) with fresh symbol all_269_0 gives:
% 33.20/5.50 | | | | | | | | | | (99) ~ (all_269_0 = 0) & empty(all_209_0) = all_269_0
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | ALPHA: (99) implies:
% 33.20/5.50 | | | | | | | | | | (100) ~ (all_269_0 = 0)
% 33.20/5.50 | | | | | | | | | | (101) empty(all_209_0) = all_269_0
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | DELTA: instantiating (94) with fresh symbols all_289_0,
% 33.20/5.50 | | | | | | | | | | all_289_1 gives:
% 33.20/5.50 | | | | | | | | | | (102) ordered_pair(all_224_1, all_289_1) = all_289_0 &
% 33.20/5.50 | | | | | | | | | | in(all_289_0, all_174_2) = 0 & $i(all_289_0) &
% 33.20/5.50 | | | | | | | | | | $i(all_289_1)
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | ALPHA: (102) implies:
% 33.20/5.50 | | | | | | | | | | (103) $i(all_289_1)
% 33.20/5.50 | | | | | | | | | | (104) in(all_289_0, all_174_2) = 0
% 33.20/5.50 | | | | | | | | | | (105) ordered_pair(all_224_1, all_289_1) = all_289_0
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_291_0,
% 33.20/5.50 | | | | | | | | | | all_291_1 gives:
% 33.20/5.50 | | | | | | | | | | (106) empty(all_209_0) = all_291_1 & in(all_211_1,
% 33.20/5.50 | | | | | | | | | | all_209_0) = all_291_0 & (all_291_0 = 0 |
% 33.20/5.50 | | | | | | | | | | all_291_1 = 0)
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | ALPHA: (106) implies:
% 33.20/5.50 | | | | | | | | | | (107) empty(all_209_0) = all_291_1
% 33.20/5.50 | | | | | | | | | | (108) all_291_0 = 0 | all_291_1 = 0
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | BETA: splitting (93) gives:
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | Case 1:
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | (109) all_224_0 = 0
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | REDUCE: (49), (109) imply:
% 33.20/5.50 | | | | | | | | | | | (110) $false
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | Case 2:
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | (111) ! [v0: $i] : ! [v1: $i] : ( ~
% 33.20/5.50 | | | | | | | | | | | (ordered_pair(all_224_1, v0) = v1) | ~ (in(v1,
% 33.20/5.50 | | | | | | | | | | | all_156_1) = 0) | ~ $i(v0))
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_269_0, all_291_1,
% 33.20/5.50 | | | | | | | | | | | all_209_0, simplifying with (101), (107) gives:
% 33.20/5.50 | | | | | | | | | | | (112) all_291_1 = all_269_0
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | BETA: splitting (108) gives:
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | Case 1:
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | GROUND_INST: instantiating (96) with all_224_1, all_289_1,
% 33.20/5.50 | | | | | | | | | | | | all_289_0, simplifying with (50), (103), (104),
% 33.20/5.50 | | | | | | | | | | | | (105) gives:
% 33.20/5.50 | | | | | | | | | | | | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 33.20/5.50 | | | | | | | | | | | | (ordered_pair(v0, all_289_1) = v2 &
% 33.20/5.50 | | | | | | | | | | | | ordered_pair(all_224_1, v0) = v1 & in(v2,
% 33.20/5.50 | | | | | | | | | | | | all_174_3) = 0 & in(v1, all_156_1) = 0 &
% 33.20/5.50 | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0))
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | DELTA: instantiating (113) with fresh symbols all_470_0,
% 33.20/5.50 | | | | | | | | | | | | all_470_1, all_470_2 gives:
% 33.20/5.50 | | | | | | | | | | | | (114) ordered_pair(all_470_2, all_289_1) = all_470_0 &
% 33.20/5.50 | | | | | | | | | | | | ordered_pair(all_224_1, all_470_2) = all_470_1 &
% 33.20/5.50 | | | | | | | | | | | | in(all_470_0, all_174_3) = 0 & in(all_470_1,
% 33.20/5.50 | | | | | | | | | | | | all_156_1) = 0 & $i(all_470_0) & $i(all_470_1) &
% 33.20/5.50 | | | | | | | | | | | | $i(all_470_2)
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | ALPHA: (114) implies:
% 33.20/5.50 | | | | | | | | | | | | (115) $i(all_470_2)
% 33.20/5.50 | | | | | | | | | | | | (116) in(all_470_1, all_156_1) = 0
% 33.20/5.50 | | | | | | | | | | | | (117) ordered_pair(all_224_1, all_470_2) = all_470_1
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_470_2, all_470_1,
% 33.20/5.50 | | | | | | | | | | | | simplifying with (115), (116), (117) gives:
% 33.20/5.50 | | | | | | | | | | | | (118) $false
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | CLOSE: (118) is inconsistent.
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | Case 2:
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | (119) all_291_1 = 0
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | COMBINE_EQS: (112), (119) imply:
% 33.20/5.50 | | | | | | | | | | | | (120) all_269_0 = 0
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | SIMP: (120) implies:
% 33.20/5.50 | | | | | | | | | | | | (121) all_269_0 = 0
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | REDUCE: (100), (121) imply:
% 33.20/5.50 | | | | | | | | | | | | (122) $false
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 33.20/5.50 | | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | | End of split
% 33.20/5.50 | | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | | End of split
% 33.20/5.50 | | | | | | | | | |
% 33.20/5.50 | | | | | | | | | End of split
% 33.20/5.50 | | | | | | | | |
% 33.20/5.50 | | | | | | | | End of split
% 33.20/5.50 | | | | | | | |
% 33.20/5.50 | | | | | | | End of split
% 33.20/5.50 | | | | | | |
% 33.20/5.50 | | | | | | End of split
% 33.20/5.50 | | | | | |
% 33.20/5.50 | | | | | End of split
% 33.20/5.50 | | | | |
% 33.20/5.50 | | | | End of split
% 33.20/5.50 | | | |
% 33.20/5.50 | | | End of split
% 33.20/5.50 | | |
% 33.20/5.50 | | End of split
% 33.20/5.50 | |
% 33.20/5.50 | End of split
% 33.20/5.50 |
% 33.20/5.50 End of proof
% 33.20/5.50 % SZS output end Proof for theBenchmark
% 33.20/5.50
% 33.20/5.50 4880ms
%------------------------------------------------------------------------------