TSTP Solution File: SEU257+2 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU257+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 : n017.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 17:43:42 EDT 2023
% Result : Theorem 33.31s 5.29s
% Output : Proof 57.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU257+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n017.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 17:32:38 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 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 7.18/1.76 Prover 4: Preprocessing ...
% 7.70/1.79 Prover 1: Preprocessing ...
% 7.70/1.82 Prover 2: Preprocessing ...
% 7.70/1.82 Prover 5: Preprocessing ...
% 7.70/1.82 Prover 3: Preprocessing ...
% 7.70/1.82 Prover 0: Preprocessing ...
% 7.70/1.82 Prover 6: Preprocessing ...
% 23.36/3.97 Prover 1: Warning: ignoring some quantifiers
% 23.36/4.05 Prover 5: Proving ...
% 24.18/4.08 Prover 1: Constructing countermodel ...
% 24.18/4.09 Prover 3: Warning: ignoring some quantifiers
% 24.18/4.13 Prover 6: Proving ...
% 24.18/4.14 Prover 3: Constructing countermodel ...
% 28.86/4.68 Prover 2: Proving ...
% 32.99/5.21 Prover 4: Warning: ignoring some quantifiers
% 33.31/5.28 Prover 3: proved (4624ms)
% 33.31/5.28
% 33.31/5.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.31/5.29
% 33.31/5.29 Prover 6: stopped
% 33.31/5.29 Prover 5: stopped
% 33.31/5.30 Prover 2: stopped
% 33.89/5.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 33.89/5.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 33.89/5.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 33.89/5.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.89/5.47 Prover 4: Constructing countermodel ...
% 37.54/5.82 Prover 7: Preprocessing ...
% 37.54/5.83 Prover 10: Preprocessing ...
% 38.48/5.97 Prover 11: Preprocessing ...
% 39.26/6.02 Prover 8: Preprocessing ...
% 41.47/6.34 Prover 0: Proving ...
% 41.47/6.34 Prover 0: stopped
% 41.47/6.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 42.23/6.48 Prover 10: Warning: ignoring some quantifiers
% 43.51/6.58 Prover 7: Warning: ignoring some quantifiers
% 43.54/6.58 Prover 10: Constructing countermodel ...
% 43.79/6.68 Prover 13: Preprocessing ...
% 43.79/6.70 Prover 8: Warning: ignoring some quantifiers
% 43.79/6.71 Prover 7: Constructing countermodel ...
% 45.06/6.84 Prover 8: Constructing countermodel ...
% 49.70/7.42 Prover 13: Warning: ignoring some quantifiers
% 50.48/7.58 Prover 13: Constructing countermodel ...
% 55.58/8.16 Prover 1: Found proof (size 140)
% 55.58/8.16 Prover 1: proved (7523ms)
% 55.58/8.17 Prover 4: stopped
% 55.58/8.17 Prover 13: stopped
% 55.58/8.17 Prover 7: stopped
% 55.58/8.17 Prover 8: stopped
% 55.58/8.17 Prover 10: stopped
% 55.92/8.29 Prover 11: Warning: ignoring some quantifiers
% 56.49/8.38 Prover 11: Constructing countermodel ...
% 56.49/8.41 Prover 11: stopped
% 56.49/8.41
% 56.49/8.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.49/8.41
% 56.49/8.44 % SZS output start Proof for theBenchmark
% 56.87/8.46 Assumptions after simplification:
% 56.87/8.46 ---------------------------------
% 56.87/8.46
% 56.87/8.46 (d4_wellord1)
% 57.05/8.49 ! [v0: $i] : ! [v1: any] : ( ~ (well_ordering(v0) = v1) | ~ $i(v0) | ?
% 57.05/8.49 [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : ?
% 57.05/8.49 [v7: any] : (reflexive(v0) = v3 & well_founded_relation(v0) = v7 &
% 57.05/8.49 transitive(v0) = v4 & connected(v0) = v6 & antisymmetric(v0) = v5 &
% 57.05/8.49 relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 =
% 57.05/8.49 0) | ~ (v4 = 0) | ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | (v7 = 0
% 57.05/8.49 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0))))))
% 57.05/8.49
% 57.05/8.49 (dt_k2_wellord1)
% 57.05/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 57.05/8.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2)
% 57.05/8.50 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 57.05/8.50
% 57.05/8.50 (t22_wellord1)
% 57.05/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v1, v0) =
% 57.05/8.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 57.05/8.50 (reflexive(v2) = v5 & reflexive(v1) = v4 & relation(v1) = v3 & ( ~ (v4 = 0)
% 57.05/8.50 | ~ (v3 = 0) | v5 = 0)))
% 57.05/8.50
% 57.05/8.50 (t23_wellord1)
% 57.05/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v1, v0) =
% 57.05/8.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 57.05/8.50 (connected(v2) = v5 & connected(v1) = v4 & relation(v1) = v3 & ( ~ (v4 = 0)
% 57.05/8.50 | ~ (v3 = 0) | v5 = 0)))
% 57.05/8.50
% 57.05/8.50 (t24_wellord1)
% 57.05/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v1, v0) =
% 57.05/8.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 57.05/8.50 (transitive(v2) = v5 & transitive(v1) = v4 & relation(v1) = v3 & ( ~ (v4 =
% 57.05/8.50 0) | ~ (v3 = 0) | v5 = 0)))
% 57.05/8.50
% 57.05/8.50 (t25_wellord1)
% 57.05/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v1, v0) =
% 57.05/8.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 57.05/8.50 (antisymmetric(v2) = v5 & antisymmetric(v1) = v4 & relation(v1) = v3 & ( ~
% 57.05/8.50 (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 57.05/8.50
% 57.05/8.50 (t31_wellord1)
% 57.05/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v1, v0) =
% 57.05/8.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 57.05/8.50 (well_founded_relation(v2) = v5 & well_founded_relation(v1) = v4 &
% 57.05/8.50 relation(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 57.05/8.50
% 57.05/8.50 (t32_wellord1)
% 57.05/8.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 57.05/8.50 relation_restriction(v1, v0) = v2 & well_ordering(v2) = v3 &
% 57.05/8.50 well_ordering(v1) = 0 & relation(v1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 57.05/8.50
% 57.05/8.50 (function-axioms)
% 57.05/8.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 57.05/8.52 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 57.05/8.52 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 57.05/8.52 [v4: $i] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~
% 57.05/8.52 (unordered_triple(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) & ! [v0:
% 57.05/8.52 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & !
% 57.05/8.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & !
% 57.05/8.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) =
% 57.05/8.52 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 57.05/8.52 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 57.05/8.52 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 57.05/8.52 ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) =
% 57.05/8.52 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 57.05/8.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (well_orders(v3, v2) = v1) | ~
% 57.05/8.52 (well_orders(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 57.05/8.52 [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 57.05/8.52 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 57.05/8.52 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 57.05/8.52 (set_difference(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (is_well_founded_in(v3, v2) = v1) | ~ (is_well_founded_in(v3, v2) = v0)) &
% 57.05/8.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 57.05/8.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 57.05/8.52 $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) &
% 57.05/8.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 57.05/8.52 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 57.05/8.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (fiber(v3,
% 57.05/8.52 v2) = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 57.05/8.52 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(v3, v2) = v0)) & !
% 57.05/8.52 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 57.05/8.52 $i] : (v1 = v0 | ~ (is_transitive_in(v3, v2) = v1) | ~
% 57.05/8.52 (is_transitive_in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) = v0)) & !
% 57.05/8.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.52 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 57.05/8.52 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 57.05/8.53 $i] : ! [v3: $i] : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~
% 57.05/8.53 (is_antisymmetric_in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 57.05/8.53 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) |
% 57.05/8.53 ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 57.05/8.53 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 57.05/8.53 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 57.05/8.53 ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) &
% 57.05/8.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 57.05/8.53 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3,
% 57.05/8.53 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 57.05/8.53 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 57.05/8.53 (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 57.05/8.53 $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) =
% 57.05/8.53 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 57.05/8.53 $i] : ! [v3: $i] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~
% 57.05/8.53 (ordinal_subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 57.05/8.53 ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 57.05/8.53 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 57.05/8.53 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 57.05/8.53 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 57.05/8.53 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 57.05/8.53 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 57.05/8.53 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3,
% 57.05/8.53 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 57.05/8.53 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 57.05/8.53 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 57.05/8.53 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~
% 57.05/8.53 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 57.05/8.53 $i] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) =
% 57.05/8.53 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 57.05/8.53 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0:
% 57.05/8.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 57.05/8.53 ~ (being_limit_ordinal(v2) = v1) | ~ (being_limit_ordinal(v2) = v0)) & !
% 57.05/8.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 57.05/8.53 ~ (relation_rng(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (well_ordering(v2) = v1) |
% 57.05/8.53 ~ (well_ordering(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~
% 57.05/8.53 (reflexive(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 57.05/8.53 ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 57.05/8.53 [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) =
% 57.05/8.53 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 57.05/8.53 $i] : (v1 = v0 | ~ (well_founded_relation(v2) = v1) | ~
% 57.05/8.53 (well_founded_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 57.05/8.53 : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] :
% 57.05/8.53 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~
% 57.05/8.53 (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 57.05/8.53 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1:
% 57.05/8.53 $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & !
% 57.05/8.53 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 57.05/8.53 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0)) & ! [v0:
% 57.05/8.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 57.05/8.53 ~ (connected(v2) = v1) | ~ (connected(v2) = v0)) & ! [v0: $i] : ! [v1:
% 57.05/8.53 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 57.05/8.53 (relation_field(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (antisymmetric(v2) = v1) |
% 57.05/8.53 ~ (antisymmetric(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 57.05/8.53 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 57.05/8.53 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1)
% 57.05/8.53 | ~ (identity_relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 57.05/8.53 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 57.05/8.53 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) =
% 57.05/8.53 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 57.05/8.53 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~
% 57.05/8.53 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) =
% 57.05/8.53 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 57.05/8.53 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 57.05/8.53 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 57.05/8.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 57.05/8.53 (empty(v2) = v0))
% 57.05/8.53
% 57.05/8.53 Further assumptions not needed in the proof:
% 57.05/8.53 --------------------------------------------
% 57.05/8.53 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1,
% 57.05/8.53 cc1_relat_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1, commutativity_k2_tarski,
% 57.05/8.53 commutativity_k2_xboole_0, commutativity_k3_xboole_0, connectedness_r1_ordinal1,
% 57.05/8.53 d10_relat_1, d10_xboole_0, d11_relat_1, d12_funct_1, d12_relat_1, d12_relat_2,
% 57.05/8.53 d13_funct_1, d13_relat_1, d14_relat_1, d14_relat_2, d16_relat_2, d1_enumset1,
% 57.05/8.53 d1_ordinal1, d1_relat_1, d1_relat_2, d1_setfam_1, d1_tarski, d1_wellord1,
% 57.05/8.53 d1_xboole_0, d1_zfmisc_1, d2_ordinal1, d2_relat_1, d2_subset_1, d2_tarski,
% 57.05/8.53 d2_wellord1, d2_xboole_0, d2_zfmisc_1, d3_ordinal1, d3_relat_1, d3_tarski,
% 57.05/8.53 d3_wellord1, d3_xboole_0, d4_funct_1, d4_ordinal1, d4_relat_1, d4_relat_2,
% 57.05/8.53 d4_subset_1, d4_tarski, d4_xboole_0, d5_funct_1, d5_relat_1, d5_subset_1,
% 57.05/8.53 d5_tarski, d5_wellord1, d6_ordinal1, d6_relat_1, d6_relat_2, d6_wellord1,
% 57.05/8.53 d7_relat_1, d7_xboole_0, d8_funct_1, d8_relat_1, d8_relat_2, d8_setfam_1,
% 57.05/8.53 d8_xboole_0, d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_enumset1,
% 57.05/8.53 dt_k1_funct_1, dt_k1_ordinal1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski,
% 57.05/8.53 dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_relat_1,
% 57.05/8.53 dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1,
% 57.05/8.53 dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski,
% 57.05/8.53 dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1,
% 57.05/8.53 dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1, dt_k9_relat_1,
% 57.05/8.53 dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1, fc11_relat_1, fc12_relat_1,
% 57.05/8.53 fc13_relat_1, fc1_funct_1, fc1_ordinal1, fc1_relat_1, fc1_subset_1,
% 57.05/8.53 fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_ordinal1, fc2_relat_1,
% 57.05/8.53 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_ordinal1, fc3_relat_1,
% 57.05/8.53 fc3_subset_1, fc3_xboole_0, fc4_funct_1, fc4_ordinal1, fc4_relat_1,
% 57.05/8.53 fc4_subset_1, fc5_funct_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1,
% 57.05/8.53 fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 57.05/8.53 involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 57.05/8.53 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1,
% 57.05/8.53 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l29_wellord1, l2_wellord1,
% 57.05/8.53 l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_wellord1, l3_zfmisc_1, l4_wellord1,
% 57.05/8.53 l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, l82_funct_1, rc1_funct_1,
% 57.05/8.53 rc1_ordinal1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1,
% 57.05/8.53 rc2_ordinal1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 57.05/8.53 rc3_ordinal1, rc3_relat_1, rc4_funct_1, redefinition_k5_setfam_1,
% 57.05/8.53 redefinition_k6_setfam_1, redefinition_k6_subset_1, redefinition_r1_ordinal1,
% 57.05/8.53 reflexivity_r1_ordinal1, reflexivity_r1_tarski, symmetry_r1_xboole_0,
% 57.05/8.53 t106_zfmisc_1, t10_ordinal1, t10_zfmisc_1, t115_relat_1, t116_relat_1,
% 57.05/8.53 t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1,
% 57.05/8.53 t12_xboole_1, t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1,
% 57.05/8.53 t145_funct_1, t145_relat_1, t146_funct_1, t146_relat_1, t147_funct_1,
% 57.05/8.53 t160_relat_1, t166_relat_1, t167_relat_1, t16_wellord1, t174_relat_1,
% 57.05/8.53 t178_relat_1, t17_wellord1, t17_xboole_1, t18_wellord1, t19_wellord1,
% 57.05/8.53 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1,
% 57.05/8.53 t20_wellord1, t21_funct_1, t21_ordinal1, t21_relat_1, t21_wellord1, t22_funct_1,
% 57.05/8.53 t23_funct_1, t23_ordinal1, t24_ordinal1, t25_relat_1, t26_xboole_1,
% 57.05/8.53 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1,
% 57.05/8.53 t31_ordinal1, t32_ordinal1, t33_ordinal1, t33_xboole_1, t33_zfmisc_1,
% 57.05/8.53 t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 57.05/8.53 t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_ordinal1, t3_subset,
% 57.05/8.53 t3_xboole_0, t3_xboole_1, t40_xboole_1, t41_ordinal1, t42_ordinal1,
% 57.05/8.53 t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_relat_1, t46_setfam_1,
% 57.05/8.53 t46_zfmisc_1, t47_relat_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole,
% 57.05/8.53 t4_subset, t4_xboole_0, t50_subset_1, t54_funct_1, t54_subset_1, t55_funct_1,
% 57.05/8.53 t56_relat_1, t57_funct_1, t5_subset, t5_wellord1, t60_relat_1, t60_xboole_1,
% 57.05/8.53 t62_funct_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, t68_funct_1,
% 57.05/8.53 t69_enumset1, t6_boole, t6_zfmisc_1, t70_funct_1, t71_relat_1, t72_funct_1,
% 57.05/8.53 t74_relat_1, t7_boole, t7_tarski, t7_xboole_1, t83_xboole_1, t86_relat_1,
% 57.05/8.53 t88_relat_1, t8_boole, t8_funct_1, t8_wellord1, t8_xboole_1, t8_zfmisc_1,
% 57.05/8.53 t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski,
% 57.05/8.53 t9_zfmisc_1
% 57.05/8.53
% 57.05/8.53 Those formulas are unsatisfiable:
% 57.05/8.53 ---------------------------------
% 57.05/8.53
% 57.05/8.53 Begin of proof
% 57.05/8.53 |
% 57.05/8.53 | ALPHA: (function-axioms) implies:
% 57.05/8.53 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 57.05/8.53 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 57.05/8.53 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 57.05/8.53 | (v1 = v0 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = v0))
% 57.05/8.53 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 57.05/8.53 | (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0))
% 57.05/8.53 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 57.05/8.53 | (v1 = v0 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0))
% 57.05/8.53 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 57.05/8.53 | (v1 = v0 | ~ (well_founded_relation(v2) = v1) | ~
% 57.05/8.53 | (well_founded_relation(v2) = v0))
% 57.05/8.54 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 57.05/8.54 | (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0))
% 57.05/8.54 |
% 57.05/8.54 | DELTA: instantiating (t32_wellord1) with fresh symbols all_306_0, all_306_1,
% 57.05/8.54 | all_306_2, all_306_3 gives:
% 57.05/8.54 | (7) ~ (all_306_0 = 0) & relation_restriction(all_306_2, all_306_3) =
% 57.05/8.54 | all_306_1 & well_ordering(all_306_1) = all_306_0 &
% 57.05/8.54 | well_ordering(all_306_2) = 0 & relation(all_306_2) = 0 & $i(all_306_1)
% 57.05/8.54 | & $i(all_306_2) & $i(all_306_3)
% 57.05/8.54 |
% 57.05/8.54 | ALPHA: (7) implies:
% 57.05/8.54 | (8) ~ (all_306_0 = 0)
% 57.05/8.54 | (9) $i(all_306_3)
% 57.05/8.54 | (10) $i(all_306_2)
% 57.05/8.54 | (11) $i(all_306_1)
% 57.05/8.54 | (12) relation(all_306_2) = 0
% 57.05/8.54 | (13) well_ordering(all_306_2) = 0
% 57.05/8.54 | (14) well_ordering(all_306_1) = all_306_0
% 57.05/8.54 | (15) relation_restriction(all_306_2, all_306_3) = all_306_1
% 57.05/8.54 |
% 57.32/8.54 | GROUND_INST: instantiating (d4_wellord1) with all_306_2, 0, simplifying with
% 57.32/8.54 | (10), (13) gives:
% 57.32/8.54 | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 57.32/8.54 | any] : ? [v5: any] : (reflexive(all_306_2) = v1 &
% 57.32/8.54 | well_founded_relation(all_306_2) = v5 & transitive(all_306_2) = v2 &
% 57.32/8.54 | connected(all_306_2) = v4 & antisymmetric(all_306_2) = v3 &
% 57.32/8.54 | relation(all_306_2) = v0 & ( ~ (v0 = 0) | (v5 = 0 & v4 = 0 & v3 = 0
% 57.32/8.54 | & v2 = 0 & v1 = 0)))
% 57.32/8.54 |
% 57.32/8.54 | GROUND_INST: instantiating (d4_wellord1) with all_306_1, all_306_0,
% 57.32/8.54 | simplifying with (11), (14) gives:
% 57.32/8.54 | (17) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 57.32/8.54 | any] : ? [v5: any] : (reflexive(all_306_1) = v1 &
% 57.32/8.54 | well_founded_relation(all_306_1) = v5 & transitive(all_306_1) = v2 &
% 57.32/8.54 | connected(all_306_1) = v4 & antisymmetric(all_306_1) = v3 &
% 57.32/8.54 | relation(all_306_1) = v0 & ( ~ (v0 = 0) | (( ~ (v5 = 0) | ~ (v4 =
% 57.32/8.54 | 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | all_306_0 =
% 57.32/8.54 | 0) & ( ~ (all_306_0 = 0) | (v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0
% 57.32/8.54 | & v1 = 0)))))
% 57.32/8.54 |
% 57.32/8.54 | GROUND_INST: instantiating (t22_wellord1) with all_306_3, all_306_2,
% 57.32/8.54 | all_306_1, simplifying with (9), (10), (15) gives:
% 57.32/8.54 | (18) ? [v0: any] : ? [v1: any] : ? [v2: any] : (reflexive(all_306_1) =
% 57.32/8.54 | v2 & reflexive(all_306_2) = v1 & relation(all_306_2) = v0 & ( ~ (v1
% 57.32/8.54 | = 0) | ~ (v0 = 0) | v2 = 0))
% 57.32/8.54 |
% 57.32/8.54 | GROUND_INST: instantiating (t31_wellord1) with all_306_3, all_306_2,
% 57.32/8.54 | all_306_1, simplifying with (9), (10), (15) gives:
% 57.32/8.54 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 57.32/8.54 | (well_founded_relation(all_306_1) = v2 &
% 57.32/8.54 | well_founded_relation(all_306_2) = v1 & relation(all_306_2) = v0 & (
% 57.32/8.54 | ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 57.32/8.54 |
% 57.32/8.54 | GROUND_INST: instantiating (t24_wellord1) with all_306_3, all_306_2,
% 57.32/8.55 | all_306_1, simplifying with (9), (10), (15) gives:
% 57.32/8.55 | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] : (transitive(all_306_1) =
% 57.32/8.55 | v2 & transitive(all_306_2) = v1 & relation(all_306_2) = v0 & ( ~ (v1
% 57.32/8.55 | = 0) | ~ (v0 = 0) | v2 = 0))
% 57.32/8.55 |
% 57.32/8.55 | GROUND_INST: instantiating (t23_wellord1) with all_306_3, all_306_2,
% 57.32/8.55 | all_306_1, simplifying with (9), (10), (15) gives:
% 57.32/8.55 | (21) ? [v0: any] : ? [v1: any] : ? [v2: any] : (connected(all_306_1) =
% 57.32/8.55 | v2 & connected(all_306_2) = v1 & relation(all_306_2) = v0 & ( ~ (v1
% 57.32/8.55 | = 0) | ~ (v0 = 0) | v2 = 0))
% 57.32/8.55 |
% 57.32/8.55 | GROUND_INST: instantiating (t25_wellord1) with all_306_3, all_306_2,
% 57.32/8.55 | all_306_1, simplifying with (9), (10), (15) gives:
% 57.32/8.55 | (22) ? [v0: any] : ? [v1: any] : ? [v2: any] : (antisymmetric(all_306_1)
% 57.32/8.55 | = v2 & antisymmetric(all_306_2) = v1 & relation(all_306_2) = v0 & (
% 57.32/8.55 | ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 57.32/8.55 |
% 57.32/8.55 | GROUND_INST: instantiating (dt_k2_wellord1) with all_306_2, all_306_3,
% 57.32/8.55 | all_306_1, simplifying with (9), (10), (15) gives:
% 57.32/8.55 | (23) ? [v0: any] : ? [v1: any] : (relation(all_306_1) = v1 &
% 57.32/8.55 | relation(all_306_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 57.32/8.55 |
% 57.32/8.55 | DELTA: instantiating (23) with fresh symbols all_529_0, all_529_1 gives:
% 57.32/8.55 | (24) relation(all_306_1) = all_529_0 & relation(all_306_2) = all_529_1 & (
% 57.32/8.55 | ~ (all_529_1 = 0) | all_529_0 = 0)
% 57.37/8.55 |
% 57.37/8.55 | ALPHA: (24) implies:
% 57.37/8.55 | (25) relation(all_306_2) = all_529_1
% 57.37/8.55 | (26) relation(all_306_1) = all_529_0
% 57.37/8.55 | (27) ~ (all_529_1 = 0) | all_529_0 = 0
% 57.37/8.55 |
% 57.37/8.55 | DELTA: instantiating (22) with fresh symbols all_539_0, all_539_1, all_539_2
% 57.37/8.55 | gives:
% 57.37/8.55 | (28) antisymmetric(all_306_1) = all_539_0 & antisymmetric(all_306_2) =
% 57.37/8.55 | all_539_1 & relation(all_306_2) = all_539_2 & ( ~ (all_539_1 = 0) | ~
% 57.37/8.55 | (all_539_2 = 0) | all_539_0 = 0)
% 57.37/8.55 |
% 57.37/8.55 | ALPHA: (28) implies:
% 57.37/8.55 | (29) relation(all_306_2) = all_539_2
% 57.37/8.55 | (30) antisymmetric(all_306_2) = all_539_1
% 57.37/8.55 | (31) antisymmetric(all_306_1) = all_539_0
% 57.37/8.55 | (32) ~ (all_539_1 = 0) | ~ (all_539_2 = 0) | all_539_0 = 0
% 57.37/8.55 |
% 57.37/8.55 | DELTA: instantiating (20) with fresh symbols all_541_0, all_541_1, all_541_2
% 57.37/8.55 | gives:
% 57.37/8.55 | (33) transitive(all_306_1) = all_541_0 & transitive(all_306_2) = all_541_1
% 57.37/8.55 | & relation(all_306_2) = all_541_2 & ( ~ (all_541_1 = 0) | ~
% 57.37/8.55 | (all_541_2 = 0) | all_541_0 = 0)
% 57.37/8.55 |
% 57.37/8.55 | ALPHA: (33) implies:
% 57.37/8.55 | (34) relation(all_306_2) = all_541_2
% 57.37/8.55 | (35) transitive(all_306_2) = all_541_1
% 57.37/8.55 | (36) transitive(all_306_1) = all_541_0
% 57.37/8.55 | (37) ~ (all_541_1 = 0) | ~ (all_541_2 = 0) | all_541_0 = 0
% 57.37/8.55 |
% 57.37/8.55 | DELTA: instantiating (19) with fresh symbols all_543_0, all_543_1, all_543_2
% 57.37/8.55 | gives:
% 57.37/8.55 | (38) well_founded_relation(all_306_1) = all_543_0 &
% 57.37/8.55 | well_founded_relation(all_306_2) = all_543_1 & relation(all_306_2) =
% 57.37/8.55 | all_543_2 & ( ~ (all_543_1 = 0) | ~ (all_543_2 = 0) | all_543_0 = 0)
% 57.37/8.55 |
% 57.37/8.55 | ALPHA: (38) implies:
% 57.37/8.55 | (39) relation(all_306_2) = all_543_2
% 57.37/8.55 | (40) well_founded_relation(all_306_2) = all_543_1
% 57.37/8.55 | (41) well_founded_relation(all_306_1) = all_543_0
% 57.37/8.55 | (42) ~ (all_543_1 = 0) | ~ (all_543_2 = 0) | all_543_0 = 0
% 57.37/8.55 |
% 57.37/8.55 | DELTA: instantiating (21) with fresh symbols all_545_0, all_545_1, all_545_2
% 57.37/8.55 | gives:
% 57.37/8.55 | (43) connected(all_306_1) = all_545_0 & connected(all_306_2) = all_545_1 &
% 57.37/8.55 | relation(all_306_2) = all_545_2 & ( ~ (all_545_1 = 0) | ~ (all_545_2
% 57.37/8.55 | = 0) | all_545_0 = 0)
% 57.37/8.55 |
% 57.37/8.55 | ALPHA: (43) implies:
% 57.37/8.55 | (44) relation(all_306_2) = all_545_2
% 57.37/8.55 | (45) connected(all_306_2) = all_545_1
% 57.37/8.56 | (46) connected(all_306_1) = all_545_0
% 57.37/8.56 | (47) ~ (all_545_1 = 0) | ~ (all_545_2 = 0) | all_545_0 = 0
% 57.37/8.56 |
% 57.37/8.56 | DELTA: instantiating (18) with fresh symbols all_547_0, all_547_1, all_547_2
% 57.37/8.56 | gives:
% 57.37/8.56 | (48) reflexive(all_306_1) = all_547_0 & reflexive(all_306_2) = all_547_1 &
% 57.37/8.56 | relation(all_306_2) = all_547_2 & ( ~ (all_547_1 = 0) | ~ (all_547_2
% 57.37/8.56 | = 0) | all_547_0 = 0)
% 57.37/8.56 |
% 57.37/8.56 | ALPHA: (48) implies:
% 57.37/8.56 | (49) relation(all_306_2) = all_547_2
% 57.37/8.56 | (50) reflexive(all_306_2) = all_547_1
% 57.37/8.56 | (51) reflexive(all_306_1) = all_547_0
% 57.37/8.56 | (52) ~ (all_547_1 = 0) | ~ (all_547_2 = 0) | all_547_0 = 0
% 57.37/8.56 |
% 57.37/8.56 | DELTA: instantiating (16) with fresh symbols all_549_0, all_549_1, all_549_2,
% 57.37/8.56 | all_549_3, all_549_4, all_549_5 gives:
% 57.37/8.56 | (53) reflexive(all_306_2) = all_549_4 & well_founded_relation(all_306_2) =
% 57.37/8.56 | all_549_0 & transitive(all_306_2) = all_549_3 & connected(all_306_2) =
% 57.37/8.56 | all_549_1 & antisymmetric(all_306_2) = all_549_2 & relation(all_306_2)
% 57.37/8.56 | = all_549_5 & ( ~ (all_549_5 = 0) | (all_549_0 = 0 & all_549_1 = 0 &
% 57.37/8.56 | all_549_2 = 0 & all_549_3 = 0 & all_549_4 = 0))
% 57.37/8.56 |
% 57.37/8.56 | ALPHA: (53) implies:
% 57.37/8.56 | (54) relation(all_306_2) = all_549_5
% 57.37/8.56 | (55) antisymmetric(all_306_2) = all_549_2
% 57.37/8.56 | (56) connected(all_306_2) = all_549_1
% 57.37/8.56 | (57) transitive(all_306_2) = all_549_3
% 57.37/8.56 | (58) well_founded_relation(all_306_2) = all_549_0
% 57.37/8.56 | (59) reflexive(all_306_2) = all_549_4
% 57.37/8.56 | (60) ~ (all_549_5 = 0) | (all_549_0 = 0 & all_549_1 = 0 & all_549_2 = 0 &
% 57.37/8.56 | all_549_3 = 0 & all_549_4 = 0)
% 57.37/8.56 |
% 57.37/8.56 | DELTA: instantiating (17) with fresh symbols all_623_0, all_623_1, all_623_2,
% 57.37/8.56 | all_623_3, all_623_4, all_623_5 gives:
% 57.37/8.56 | (61) reflexive(all_306_1) = all_623_4 & well_founded_relation(all_306_1) =
% 57.37/8.56 | all_623_0 & transitive(all_306_1) = all_623_3 & connected(all_306_1) =
% 57.37/8.56 | all_623_1 & antisymmetric(all_306_1) = all_623_2 & relation(all_306_1)
% 57.37/8.56 | = all_623_5 & ( ~ (all_623_5 = 0) | (( ~ (all_623_0 = 0) | ~
% 57.37/8.56 | (all_623_1 = 0) | ~ (all_623_2 = 0) | ~ (all_623_3 = 0) | ~
% 57.37/8.56 | (all_623_4 = 0) | all_306_0 = 0) & ( ~ (all_306_0 = 0) |
% 57.37/8.56 | (all_623_0 = 0 & all_623_1 = 0 & all_623_2 = 0 & all_623_3 = 0 &
% 57.37/8.56 | all_623_4 = 0))))
% 57.37/8.56 |
% 57.37/8.56 | ALPHA: (61) implies:
% 57.37/8.56 | (62) relation(all_306_1) = all_623_5
% 57.37/8.56 | (63) antisymmetric(all_306_1) = all_623_2
% 57.37/8.56 | (64) connected(all_306_1) = all_623_1
% 57.37/8.56 | (65) transitive(all_306_1) = all_623_3
% 57.37/8.56 | (66) well_founded_relation(all_306_1) = all_623_0
% 57.37/8.56 | (67) reflexive(all_306_1) = all_623_4
% 57.37/8.56 | (68) ~ (all_623_5 = 0) | (( ~ (all_623_0 = 0) | ~ (all_623_1 = 0) | ~
% 57.37/8.56 | (all_623_2 = 0) | ~ (all_623_3 = 0) | ~ (all_623_4 = 0) |
% 57.37/8.56 | all_306_0 = 0) & ( ~ (all_306_0 = 0) | (all_623_0 = 0 & all_623_1
% 57.37/8.56 | = 0 & all_623_2 = 0 & all_623_3 = 0 & all_623_4 = 0)))
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with all_541_2, all_543_2, all_306_2,
% 57.37/8.56 | simplifying with (34), (39) gives:
% 57.37/8.56 | (69) all_543_2 = all_541_2
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with all_541_2, all_545_2, all_306_2,
% 57.37/8.56 | simplifying with (34), (44) gives:
% 57.37/8.56 | (70) all_545_2 = all_541_2
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with all_539_2, all_545_2, all_306_2,
% 57.37/8.56 | simplifying with (29), (44) gives:
% 57.37/8.56 | (71) all_545_2 = all_539_2
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with all_529_1, all_545_2, all_306_2,
% 57.37/8.56 | simplifying with (25), (44) gives:
% 57.37/8.56 | (72) all_545_2 = all_529_1
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with 0, all_549_5, all_306_2, simplifying with
% 57.37/8.56 | (12), (54) gives:
% 57.37/8.56 | (73) all_549_5 = 0
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with all_547_2, all_549_5, all_306_2,
% 57.37/8.56 | simplifying with (49), (54) gives:
% 57.37/8.56 | (74) all_549_5 = all_547_2
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with all_543_2, all_549_5, all_306_2,
% 57.37/8.56 | simplifying with (39), (54) gives:
% 57.37/8.56 | (75) all_549_5 = all_543_2
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (1) with all_529_0, all_623_5, all_306_1,
% 57.37/8.56 | simplifying with (26), (62) gives:
% 57.37/8.56 | (76) all_623_5 = all_529_0
% 57.37/8.56 |
% 57.37/8.56 | GROUND_INST: instantiating (2) with all_539_1, all_549_2, all_306_2,
% 57.37/8.56 | simplifying with (30), (55) gives:
% 57.37/8.56 | (77) all_549_2 = all_539_1
% 57.37/8.56 |
% 57.37/8.57 | GROUND_INST: instantiating (2) with all_539_0, all_623_2, all_306_1,
% 57.37/8.57 | simplifying with (31), (63) gives:
% 57.37/8.57 | (78) all_623_2 = all_539_0
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (3) with all_545_1, all_549_1, all_306_2,
% 57.37/8.57 | simplifying with (45), (56) gives:
% 57.37/8.57 | (79) all_549_1 = all_545_1
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (3) with all_545_0, all_623_1, all_306_1,
% 57.37/8.57 | simplifying with (46), (64) gives:
% 57.37/8.57 | (80) all_623_1 = all_545_0
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (4) with all_541_1, all_549_3, all_306_2,
% 57.37/8.57 | simplifying with (35), (57) gives:
% 57.37/8.57 | (81) all_549_3 = all_541_1
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (4) with all_541_0, all_623_3, all_306_1,
% 57.37/8.57 | simplifying with (36), (65) gives:
% 57.37/8.57 | (82) all_623_3 = all_541_0
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (5) with all_543_1, all_549_0, all_306_2,
% 57.37/8.57 | simplifying with (40), (58) gives:
% 57.37/8.57 | (83) all_549_0 = all_543_1
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (5) with all_543_0, all_623_0, all_306_1,
% 57.37/8.57 | simplifying with (41), (66) gives:
% 57.37/8.57 | (84) all_623_0 = all_543_0
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (6) with all_547_1, all_549_4, all_306_2,
% 57.37/8.57 | simplifying with (50), (59) gives:
% 57.37/8.57 | (85) all_549_4 = all_547_1
% 57.37/8.57 |
% 57.37/8.57 | GROUND_INST: instantiating (6) with all_547_0, all_623_4, all_306_1,
% 57.37/8.57 | simplifying with (51), (67) gives:
% 57.37/8.57 | (86) all_623_4 = all_547_0
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (73), (74) imply:
% 57.37/8.57 | (87) all_547_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (74), (75) imply:
% 57.37/8.57 | (88) all_547_2 = all_543_2
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (87), (88) imply:
% 57.37/8.57 | (89) all_543_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | SIMP: (89) implies:
% 57.37/8.57 | (90) all_543_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (71), (72) imply:
% 57.37/8.57 | (91) all_539_2 = all_529_1
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (70), (71) imply:
% 57.37/8.57 | (92) all_541_2 = all_539_2
% 57.37/8.57 |
% 57.37/8.57 | SIMP: (92) implies:
% 57.37/8.57 | (93) all_541_2 = all_539_2
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (69), (90) imply:
% 57.37/8.57 | (94) all_541_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | SIMP: (94) implies:
% 57.37/8.57 | (95) all_541_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (93), (95) imply:
% 57.37/8.57 | (96) all_539_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | SIMP: (96) implies:
% 57.37/8.57 | (97) all_539_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (91), (97) imply:
% 57.37/8.57 | (98) all_529_1 = 0
% 57.37/8.57 |
% 57.37/8.57 | SIMP: (98) implies:
% 57.37/8.57 | (99) all_529_1 = 0
% 57.37/8.57 |
% 57.37/8.57 | COMBINE_EQS: (71), (97) imply:
% 57.37/8.57 | (100) all_545_2 = 0
% 57.37/8.57 |
% 57.37/8.57 | BETA: splitting (27) gives:
% 57.37/8.57 |
% 57.37/8.57 | Case 1:
% 57.37/8.57 | |
% 57.37/8.57 | | (101) ~ (all_529_1 = 0)
% 57.37/8.57 | |
% 57.37/8.57 | | REDUCE: (99), (101) imply:
% 57.37/8.57 | | (102) $false
% 57.37/8.57 | |
% 57.37/8.57 | | CLOSE: (102) is inconsistent.
% 57.37/8.57 | |
% 57.37/8.57 | Case 2:
% 57.37/8.57 | |
% 57.37/8.57 | | (103) all_529_0 = 0
% 57.37/8.57 | |
% 57.37/8.57 | | COMBINE_EQS: (76), (103) imply:
% 57.37/8.57 | | (104) all_623_5 = 0
% 57.37/8.57 | |
% 57.37/8.57 | | BETA: splitting (60) gives:
% 57.37/8.57 | |
% 57.37/8.57 | | Case 1:
% 57.37/8.57 | | |
% 57.37/8.57 | | | (105) ~ (all_549_5 = 0)
% 57.37/8.57 | | |
% 57.37/8.57 | | | REDUCE: (73), (105) imply:
% 57.37/8.57 | | | (106) $false
% 57.37/8.57 | | |
% 57.37/8.57 | | | CLOSE: (106) is inconsistent.
% 57.37/8.57 | | |
% 57.37/8.57 | | Case 2:
% 57.37/8.57 | | |
% 57.37/8.57 | | | (107) all_549_0 = 0 & all_549_1 = 0 & all_549_2 = 0 & all_549_3 = 0 &
% 57.37/8.57 | | | all_549_4 = 0
% 57.37/8.57 | | |
% 57.37/8.57 | | | ALPHA: (107) implies:
% 57.37/8.57 | | | (108) all_549_4 = 0
% 57.37/8.57 | | | (109) all_549_3 = 0
% 57.37/8.57 | | | (110) all_549_2 = 0
% 57.37/8.57 | | | (111) all_549_1 = 0
% 57.37/8.57 | | | (112) all_549_0 = 0
% 57.37/8.57 | | |
% 57.37/8.57 | | | COMBINE_EQS: (83), (112) imply:
% 57.37/8.57 | | | (113) all_543_1 = 0
% 57.37/8.57 | | |
% 57.37/8.57 | | | COMBINE_EQS: (79), (111) imply:
% 57.37/8.57 | | | (114) all_545_1 = 0
% 57.37/8.57 | | |
% 57.37/8.57 | | | SIMP: (114) implies:
% 57.37/8.57 | | | (115) all_545_1 = 0
% 57.37/8.57 | | |
% 57.37/8.58 | | | COMBINE_EQS: (77), (110) imply:
% 57.37/8.58 | | | (116) all_539_1 = 0
% 57.37/8.58 | | |
% 57.37/8.58 | | | SIMP: (116) implies:
% 57.37/8.58 | | | (117) all_539_1 = 0
% 57.37/8.58 | | |
% 57.37/8.58 | | | COMBINE_EQS: (81), (109) imply:
% 57.37/8.58 | | | (118) all_541_1 = 0
% 57.37/8.58 | | |
% 57.37/8.58 | | | COMBINE_EQS: (85), (108) imply:
% 57.37/8.58 | | | (119) all_547_1 = 0
% 57.37/8.58 | | |
% 57.37/8.58 | | | SIMP: (119) implies:
% 57.37/8.58 | | | (120) all_547_1 = 0
% 57.37/8.58 | | |
% 57.37/8.58 | | | BETA: splitting (47) gives:
% 57.37/8.58 | | |
% 57.37/8.58 | | | Case 1:
% 57.37/8.58 | | | |
% 57.37/8.58 | | | | (121) ~ (all_545_1 = 0)
% 57.37/8.58 | | | |
% 57.37/8.58 | | | | REDUCE: (115), (121) imply:
% 57.37/8.58 | | | | (122) $false
% 57.37/8.58 | | | |
% 57.37/8.58 | | | | CLOSE: (122) is inconsistent.
% 57.37/8.58 | | | |
% 57.37/8.58 | | | Case 2:
% 57.37/8.58 | | | |
% 57.37/8.58 | | | | (123) ~ (all_545_2 = 0) | all_545_0 = 0
% 57.37/8.58 | | | |
% 57.37/8.58 | | | | BETA: splitting (123) gives:
% 57.37/8.58 | | | |
% 57.37/8.58 | | | | Case 1:
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | | (124) ~ (all_545_2 = 0)
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | | REDUCE: (100), (124) imply:
% 57.37/8.58 | | | | | (125) $false
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | | CLOSE: (125) is inconsistent.
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | Case 2:
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | | (126) all_545_0 = 0
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | | COMBINE_EQS: (80), (126) imply:
% 57.37/8.58 | | | | | (127) all_623_1 = 0
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | | BETA: splitting (32) gives:
% 57.37/8.58 | | | | |
% 57.37/8.58 | | | | | Case 1:
% 57.37/8.58 | | | | | |
% 57.37/8.58 | | | | | | (128) ~ (all_539_1 = 0)
% 57.37/8.58 | | | | | |
% 57.37/8.58 | | | | | | REDUCE: (117), (128) imply:
% 57.37/8.58 | | | | | | (129) $false
% 57.37/8.58 | | | | | |
% 57.37/8.58 | | | | | | CLOSE: (129) is inconsistent.
% 57.37/8.58 | | | | | |
% 57.37/8.58 | | | | | Case 2:
% 57.37/8.58 | | | | | |
% 57.37/8.58 | | | | | | (130) ~ (all_539_2 = 0) | all_539_0 = 0
% 57.37/8.58 | | | | | |
% 57.37/8.58 | | | | | | BETA: splitting (130) gives:
% 57.37/8.58 | | | | | |
% 57.37/8.58 | | | | | | Case 1:
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | | (131) ~ (all_539_2 = 0)
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | | REDUCE: (97), (131) imply:
% 57.37/8.58 | | | | | | | (132) $false
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | | CLOSE: (132) is inconsistent.
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | Case 2:
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | | (133) all_539_0 = 0
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | | COMBINE_EQS: (78), (133) imply:
% 57.37/8.58 | | | | | | | (134) all_623_2 = 0
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | | BETA: splitting (42) gives:
% 57.37/8.58 | | | | | | |
% 57.37/8.58 | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | |
% 57.37/8.58 | | | | | | | | (135) ~ (all_543_1 = 0)
% 57.37/8.58 | | | | | | | |
% 57.37/8.58 | | | | | | | | REDUCE: (113), (135) imply:
% 57.37/8.58 | | | | | | | | (136) $false
% 57.37/8.58 | | | | | | | |
% 57.37/8.58 | | | | | | | | CLOSE: (136) is inconsistent.
% 57.37/8.58 | | | | | | | |
% 57.37/8.58 | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | |
% 57.37/8.58 | | | | | | | | (137) ~ (all_543_2 = 0) | all_543_0 = 0
% 57.37/8.58 | | | | | | | |
% 57.37/8.58 | | | | | | | | BETA: splitting (52) gives:
% 57.37/8.58 | | | | | | | |
% 57.37/8.58 | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | |
% 57.37/8.58 | | | | | | | | | (138) ~ (all_547_1 = 0)
% 57.37/8.58 | | | | | | | | |
% 57.37/8.58 | | | | | | | | | REDUCE: (120), (138) imply:
% 57.37/8.58 | | | | | | | | | (139) $false
% 57.37/8.58 | | | | | | | | |
% 57.37/8.58 | | | | | | | | | CLOSE: (139) is inconsistent.
% 57.37/8.58 | | | | | | | | |
% 57.37/8.58 | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | |
% 57.37/8.58 | | | | | | | | | (140) ~ (all_547_2 = 0) | all_547_0 = 0
% 57.37/8.58 | | | | | | | | |
% 57.37/8.58 | | | | | | | | | BETA: splitting (140) gives:
% 57.37/8.58 | | | | | | | | |
% 57.37/8.58 | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | (141) ~ (all_547_2 = 0)
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | REDUCE: (87), (141) imply:
% 57.37/8.58 | | | | | | | | | | (142) $false
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | CLOSE: (142) is inconsistent.
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | (143) all_547_0 = 0
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | COMBINE_EQS: (86), (143) imply:
% 57.37/8.58 | | | | | | | | | | (144) all_623_4 = 0
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | BETA: splitting (37) gives:
% 57.37/8.58 | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | (145) ~ (all_541_1 = 0)
% 57.37/8.58 | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | REDUCE: (118), (145) imply:
% 57.37/8.58 | | | | | | | | | | | (146) $false
% 57.37/8.58 | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 57.37/8.58 | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | (147) ~ (all_541_2 = 0) | all_541_0 = 0
% 57.37/8.58 | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | BETA: splitting (147) gives:
% 57.37/8.58 | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | (148) ~ (all_541_2 = 0)
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | REDUCE: (95), (148) imply:
% 57.37/8.58 | | | | | | | | | | | | (149) $false
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | (150) all_541_0 = 0
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | COMBINE_EQS: (82), (150) imply:
% 57.37/8.58 | | | | | | | | | | | | (151) all_623_3 = 0
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | BETA: splitting (68) gives:
% 57.37/8.58 | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | (152) ~ (all_623_5 = 0)
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | REDUCE: (104), (152) imply:
% 57.37/8.58 | | | | | | | | | | | | | (153) $false
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | (154) ( ~ (all_623_0 = 0) | ~ (all_623_1 = 0) | ~
% 57.37/8.58 | | | | | | | | | | | | | (all_623_2 = 0) | ~ (all_623_3 = 0) | ~
% 57.37/8.58 | | | | | | | | | | | | | (all_623_4 = 0) | all_306_0 = 0) & ( ~
% 57.37/8.58 | | | | | | | | | | | | | (all_306_0 = 0) | (all_623_0 = 0 & all_623_1 = 0
% 57.37/8.58 | | | | | | | | | | | | | & all_623_2 = 0 & all_623_3 = 0 & all_623_4 =
% 57.37/8.58 | | | | | | | | | | | | | 0))
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | ALPHA: (154) implies:
% 57.37/8.58 | | | | | | | | | | | | | (155) ~ (all_623_0 = 0) | ~ (all_623_1 = 0) | ~
% 57.37/8.58 | | | | | | | | | | | | | (all_623_2 = 0) | ~ (all_623_3 = 0) | ~
% 57.37/8.58 | | | | | | | | | | | | | (all_623_4 = 0) | all_306_0 = 0
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | BETA: splitting (155) gives:
% 57.37/8.58 | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | (156) ~ (all_623_0 = 0)
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | REDUCE: (84), (156) imply:
% 57.37/8.58 | | | | | | | | | | | | | | (157) ~ (all_543_0 = 0)
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | (158) ~ (all_543_2 = 0)
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | REDUCE: (90), (158) imply:
% 57.37/8.58 | | | | | | | | | | | | | | | (159) $false
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | (160) all_543_0 = 0
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | REDUCE: (157), (160) imply:
% 57.37/8.58 | | | | | | | | | | | | | | | (161) $false
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | End of split
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | (162) ~ (all_623_1 = 0) | ~ (all_623_2 = 0) | ~
% 57.37/8.58 | | | | | | | | | | | | | | (all_623_3 = 0) | ~ (all_623_4 = 0) | all_306_0 =
% 57.37/8.58 | | | | | | | | | | | | | | 0
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 57.37/8.58 | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | (163) ~ (all_623_1 = 0)
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | REDUCE: (127), (163) imply:
% 57.37/8.58 | | | | | | | | | | | | | | | (164) $false
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | (165) ~ (all_623_2 = 0) | ~ (all_623_3 = 0) | ~
% 57.37/8.58 | | | | | | | | | | | | | | | (all_623_4 = 0) | all_306_0 = 0
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 57.37/8.58 | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | (166) ~ (all_623_2 = 0)
% 57.37/8.58 | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | REDUCE: (134), (166) imply:
% 57.37/8.58 | | | | | | | | | | | | | | | | (167) $false
% 57.37/8.58 | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 57.37/8.58 | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | (168) ~ (all_623_3 = 0) | ~ (all_623_4 = 0) |
% 57.37/8.58 | | | | | | | | | | | | | | | | all_306_0 = 0
% 57.37/8.58 | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 57.37/8.58 | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | | (169) ~ (all_623_3 = 0)
% 57.37/8.58 | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | | REDUCE: (151), (169) imply:
% 57.37/8.58 | | | | | | | | | | | | | | | | | (170) $false
% 57.37/8.58 | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 57.37/8.58 | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | Case 2:
% 57.37/8.58 | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | | (171) ~ (all_623_4 = 0) | all_306_0 = 0
% 57.37/8.58 | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 57.37/8.58 | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | | Case 1:
% 57.37/8.58 | | | | | | | | | | | | | | | | | |
% 57.37/8.58 | | | | | | | | | | | | | | | | | | (172) ~ (all_623_4 = 0)
% 57.37/8.58 | | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | | | REDUCE: (144), (172) imply:
% 57.37/8.59 | | | | | | | | | | | | | | | | | | (173) $false
% 57.37/8.59 | | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 57.37/8.59 | | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | | Case 2:
% 57.37/8.59 | | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | | | (174) all_306_0 = 0
% 57.37/8.59 | | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | | | REDUCE: (8), (174) imply:
% 57.37/8.59 | | | | | | | | | | | | | | | | | | (175) $false
% 57.37/8.59 | | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 57.37/8.59 | | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | | |
% 57.37/8.59 | | | | | | | | | End of split
% 57.37/8.59 | | | | | | | | |
% 57.37/8.59 | | | | | | | | End of split
% 57.37/8.59 | | | | | | | |
% 57.37/8.59 | | | | | | | End of split
% 57.37/8.59 | | | | | | |
% 57.37/8.59 | | | | | | End of split
% 57.37/8.59 | | | | | |
% 57.37/8.59 | | | | | End of split
% 57.37/8.59 | | | | |
% 57.37/8.59 | | | | End of split
% 57.37/8.59 | | | |
% 57.37/8.59 | | | End of split
% 57.37/8.59 | | |
% 57.37/8.59 | | End of split
% 57.37/8.59 | |
% 57.37/8.59 | End of split
% 57.37/8.59 |
% 57.37/8.59 End of proof
% 57.37/8.59 % SZS output end Proof for theBenchmark
% 57.37/8.59
% 57.37/8.59 7966ms
%------------------------------------------------------------------------------