TSTP Solution File: SEU209+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU209+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 : n015.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 17:43:17 EDT 2023
% Result : Theorem 28.76s 4.69s
% Output : Proof 70.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU209+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 23 14:01:50 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.23/0.65 ________ _____
% 0.23/0.65 ___ __ \_________(_)________________________________
% 0.23/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.23/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.23/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.23/0.65
% 0.23/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.23/0.65 (2023-06-19)
% 0.23/0.65
% 0.23/0.65 (c) Philipp Rümmer, 2009-2023
% 0.23/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.23/0.65 Amanda Stjerna.
% 0.23/0.65 Free software under BSD-3-Clause.
% 0.23/0.65
% 0.23/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.23/0.65
% 0.23/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.23/0.66 Running up to 7 provers in parallel.
% 0.23/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.23/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.23/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.23/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.23/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.23/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.23/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 6.15/1.66 Prover 4: Preprocessing ...
% 6.15/1.69 Prover 1: Preprocessing ...
% 6.75/1.71 Prover 2: Preprocessing ...
% 6.75/1.71 Prover 0: Preprocessing ...
% 6.75/1.71 Prover 5: Preprocessing ...
% 6.75/1.71 Prover 3: Preprocessing ...
% 6.75/1.71 Prover 6: Preprocessing ...
% 18.65/3.33 Prover 1: Warning: ignoring some quantifiers
% 19.33/3.44 Prover 3: Warning: ignoring some quantifiers
% 19.33/3.48 Prover 6: Proving ...
% 19.33/3.49 Prover 5: Proving ...
% 19.33/3.50 Prover 3: Constructing countermodel ...
% 19.33/3.50 Prover 1: Constructing countermodel ...
% 20.16/3.63 Prover 4: Warning: ignoring some quantifiers
% 21.49/3.75 Prover 2: Proving ...
% 22.22/3.82 Prover 4: Constructing countermodel ...
% 22.22/3.89 Prover 0: Proving ...
% 28.76/4.68 Prover 3: proved (4006ms)
% 28.76/4.69
% 28.76/4.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.76/4.69
% 28.76/4.69 Prover 6: stopped
% 28.76/4.69 Prover 0: stopped
% 28.76/4.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 28.76/4.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 28.76/4.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.76/4.69 Prover 5: stopped
% 28.76/4.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.76/4.71 Prover 2: stopped
% 28.76/4.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 30.14/5.00 Prover 10: Preprocessing ...
% 30.14/5.00 Prover 7: Preprocessing ...
% 30.14/5.01 Prover 8: Preprocessing ...
% 31.10/5.11 Prover 11: Preprocessing ...
% 31.10/5.12 Prover 13: Preprocessing ...
% 33.68/5.42 Prover 10: Warning: ignoring some quantifiers
% 34.36/5.45 Prover 7: Warning: ignoring some quantifiers
% 34.36/5.48 Prover 10: Constructing countermodel ...
% 34.75/5.50 Prover 7: Constructing countermodel ...
% 35.34/5.57 Prover 8: Warning: ignoring some quantifiers
% 35.34/5.62 Prover 8: Constructing countermodel ...
% 35.34/5.63 Prover 13: Warning: ignoring some quantifiers
% 35.34/5.70 Prover 13: Constructing countermodel ...
% 38.51/5.99 Prover 11: Warning: ignoring some quantifiers
% 39.25/6.10 Prover 11: Constructing countermodel ...
% 57.53/8.48 Prover 10: gave up
% 57.74/8.51 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 58.57/8.64 Prover 16: Preprocessing ...
% 61.56/9.00 Prover 16: Warning: ignoring some quantifiers
% 61.56/9.03 Prover 16: Constructing countermodel ...
% 69.80/10.12 Prover 8: Found proof (size 71)
% 69.80/10.12 Prover 8: proved (5394ms)
% 69.80/10.12 Prover 7: stopped
% 69.80/10.12 Prover 16: stopped
% 69.80/10.12 Prover 13: stopped
% 69.80/10.12 Prover 1: stopped
% 69.80/10.12 Prover 4: stopped
% 69.80/10.12 Prover 11: stopped
% 69.80/10.12
% 69.80/10.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.80/10.12
% 69.80/10.13 % SZS output start Proof for theBenchmark
% 69.80/10.14 Assumptions after simplification:
% 69.80/10.14 ---------------------------------
% 69.80/10.14
% 69.80/10.14 (d2_subset_1)
% 70.43/10.17 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~
% 70.43/10.17 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & in(v1,
% 70.43/10.17 v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 =
% 70.43/10.17 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) =
% 70.43/10.17 v2) | ~ (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 70.43/10.17 (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 70.43/10.17
% 70.43/10.17 (d3_tarski)
% 70.43/10.17 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 70.43/10.17 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 70.43/10.17 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 70.43/10.17 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 70.43/10.17 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 70.43/10.17
% 70.43/10.17 (d4_relat_1)
% 70.43/10.18 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 70.43/10.18 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 70.43/10.18 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 70.43/10.18 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 70.43/10.18 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 70.43/10.18 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 70.43/10.18 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 70.43/10.18 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 70.43/10.18 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 70.43/10.18 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 70.43/10.18 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 70.43/10.18 $i(v3)))))))
% 70.43/10.18
% 70.43/10.18 (fc6_relat_1)
% 70.43/10.18 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 70.43/10.18 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 &
% 70.43/10.18 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 70.43/10.18
% 70.43/10.18 (rc2_relat_1)
% 70.43/10.18 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & relation(v0) = 0
% 70.43/10.18 & $i(v0))
% 70.43/10.18
% 70.43/10.18 (rc2_subset_1)
% 70.43/10.18 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 70.43/10.18 : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2)))
% 70.43/10.18
% 70.43/10.18 (t166_relat_1)
% 70.43/10.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 70.43/10.19 (relation_inverse_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ $i(v2) |
% 70.43/10.19 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : (relation_rng(v2) = v6 &
% 70.43/10.19 relation(v2) = v5 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v4 = 0) | ? [v7: $i] :
% 70.43/10.19 ? [v8: $i] : (ordered_pair(v0, v7) = v8 & in(v8, v2) = 0 & in(v7,
% 70.43/10.19 v6) = 0 & in(v7, v1) = 0 & $i(v8) & $i(v7))) & (v4 = 0 | ! [v7:
% 70.43/10.19 $i] : ( ~ (in(v7, v6) = 0) | ~ $i(v7) | ? [v8: $i] : ? [v9:
% 70.43/10.19 any] : ? [v10: any] : (ordered_pair(v0, v7) = v8 & in(v8, v2) =
% 70.43/10.19 v9 & in(v7, v1) = v10 & $i(v8) & ( ~ (v10 = 0) | ~ (v9 =
% 70.43/10.19 0)))))))))
% 70.43/10.19
% 70.43/10.19 (t167_relat_1)
% 70.43/10.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 70.43/10.19 = 0) & relation_dom(v1) = v3 & relation_inverse_image(v1, v0) = v2 &
% 70.43/10.19 subset(v2, v3) = v4 & relation(v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 70.43/10.19
% 70.43/10.19 (t1_zfmisc_1)
% 70.43/10.19 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set)
% 70.43/10.19 = v0 & $i(v0))
% 70.43/10.19
% 70.43/10.19 (t65_relat_1)
% 70.43/10.19 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 70.43/10.19 $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0)
% 70.43/10.19 = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & (
% 70.43/10.19 ~ (v1 = empty_set) | v3 = empty_set)))))
% 70.43/10.19
% 70.43/10.19 (t6_boole)
% 70.43/10.19 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 70.43/10.19 $i(v0))
% 70.43/10.19
% 70.43/10.19 (function-axioms)
% 70.43/10.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 70.43/10.21 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 70.43/10.21 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 70.43/10.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~
% 70.43/10.21 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 70.43/10.21 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 70.43/10.21 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 70.43/10.21 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 70.43/10.21 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 70.43/10.21 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 70.43/10.21 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 70.43/10.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~
% 70.43/10.21 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 70.43/10.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 70.43/10.21 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 70.43/10.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 70.43/10.21 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 70.43/10.21 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 70.43/10.21 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 70.43/10.21 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 70.43/10.21 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 70.43/10.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 70.43/10.21 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 70.43/10.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) |
% 70.43/10.21 ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 70.43/10.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 70.43/10.21 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 70.43/10.21 ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~
% 70.43/10.21 (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 70.43/10.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1)
% 70.43/10.21 | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 70.43/10.21 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 70.43/10.21 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 70.43/10.21 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1)
% 70.43/10.21 | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 70.43/10.21 : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 70.43/10.21 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 70.43/10.21 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 70.43/10.21 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 70.43/10.21 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 70.43/10.21 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 70.43/10.21 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3,
% 70.43/10.21 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 70.43/10.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 70.43/10.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 70.43/10.21 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i]
% 70.43/10.21 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 70.43/10.21 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 70.43/10.21 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i]
% 70.43/10.21 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) =
% 70.43/10.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 70.43/10.21 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : !
% 70.43/10.21 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 70.43/10.21 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 70.43/10.21 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : !
% 70.43/10.21 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 70.43/10.21 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 70.43/10.21 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 70.43/10.21 : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~
% 70.43/10.21 (identity_relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 70.43/10.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 70.43/10.21 (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 70.43/10.21 : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) &
% 70.43/10.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (subset_difference(v2,
% 70.43/10.21 v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 70.43/10.21 MultipleValueBool] : (are_equipotent(v1, v0) = v2) & ? [v0: $i] : ? [v1:
% 70.43/10.21 $i] : ? [v2: MultipleValueBool] : (disjoint(v1, v0) = v2) & ? [v0: $i] :
% 70.43/10.21 ? [v1: $i] : ? [v2: MultipleValueBool] : (element(v1, v0) = v2) & ? [v0: $i]
% 70.43/10.21 : ? [v1: $i] : ? [v2: MultipleValueBool] : (subset(v1, v0) = v2) & ? [v0:
% 70.43/10.21 $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (proper_subset(v1, v0) =
% 70.43/10.21 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (in(v1, v0) =
% 70.43/10.21 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (meet_of_subsets(v1, v0) =
% 70.43/10.21 v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 70.43/10.21 (union_of_subsets(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 70.43/10.21 $i] : (complements_of_subsets(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1:
% 70.43/10.21 $i] : ? [v2: $i] : (relation_composition(v1, v0) = v2 & $i(v2)) & ? [v0:
% 70.43/10.21 $i] : ? [v1: $i] : ? [v2: $i] : (subset_complement(v1, v0) = v2 & $i(v2))
% 70.43/10.21 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_difference(v1, v0) = v2 &
% 70.43/10.21 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cartesian_product2(v1,
% 70.43/10.21 v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 70.43/10.21 (relation_inverse_image(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] :
% 70.43/10.21 ? [v2: $i] : (relation_image(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1:
% 70.43/10.21 $i] : ? [v2: $i] : (relation_rng_restriction(v1, v0) = v2 & $i(v2)) & ?
% 70.43/10.21 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom_restriction(v1, v0) = v2
% 70.43/10.21 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0)
% 70.43/10.21 = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 70.43/10.21 (set_intersection2(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ?
% 70.43/10.21 [v2: $i] : (set_union2(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ?
% 70.43/10.21 [v2: $i] : (unordered_pair(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1:
% 70.43/10.21 MultipleValueBool] : (empty(v0) = v1) & ? [v0: $i] : ? [v1:
% 70.43/10.21 MultipleValueBool] : (relation(v0) = v1) & ? [v0: $i] : ? [v1: $i] :
% 70.43/10.21 (relation_inverse(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 70.43/10.21 (relation_field(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 70.43/10.21 (relation_rng(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (union(v0) = v1
% 70.43/10.21 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (cast_to_subset(v0) = v1 & $i(v1)) &
% 70.43/10.21 ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1)) & ? [v0: $i] :
% 70.43/10.21 ? [v1: $i] : (powerset(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 70.43/10.21 (singleton(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (set_meet(v0) = v1
% 70.43/10.21 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (identity_relation(v0) = v1 &
% 70.43/10.21 $i(v1))
% 70.43/10.21
% 70.43/10.21 Further assumptions not needed in the proof:
% 70.43/10.21 --------------------------------------------
% 70.43/10.21 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1,
% 70.43/10.21 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0,
% 70.43/10.21 d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, d13_relat_1, d14_relat_1,
% 70.43/10.21 d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_relat_1,
% 70.43/10.21 d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_relat_1, d3_xboole_0, d4_subset_1,
% 70.43/10.21 d4_tarski, d4_xboole_0, d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1,
% 70.43/10.21 d7_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k10_relat_1,
% 70.43/10.21 dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 70.43/10.21 dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1,
% 70.43/10.21 dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1,
% 70.43/10.21 dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1,
% 70.43/10.21 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1,
% 70.43/10.21 dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1, fc1_relat_1,
% 70.43/10.21 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1,
% 70.43/10.21 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, fc4_relat_1, fc4_subset_1,
% 70.43/10.21 fc5_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0,
% 70.43/10.21 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 70.43/10.21 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 70.43/10.21 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 70.43/10.21 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 70.43/10.21 rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_xboole_0, redefinition_k5_setfam_1,
% 70.43/10.21 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski,
% 70.43/10.21 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1,
% 70.43/10.21 t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1,
% 70.43/10.21 t12_xboole_1, t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1,
% 70.43/10.21 t145_relat_1, t146_relat_1, t160_relat_1, t17_xboole_1, t19_xboole_1, t1_boole,
% 70.43/10.21 t1_subset, t1_xboole_1, t20_relat_1, t21_relat_1, t25_relat_1, t26_xboole_1,
% 70.43/10.21 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1,
% 70.43/10.21 t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_relat_1, t37_xboole_1,
% 70.43/10.21 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset,
% 70.43/10.21 t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1,
% 70.43/10.21 t45_xboole_1, t46_relat_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1,
% 70.43/10.21 t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0,
% 70.43/10.21 t50_subset_1, t54_subset_1, t56_relat_1, t5_subset, t60_relat_1, t60_xboole_1,
% 70.43/10.21 t63_xboole_1, t64_relat_1, t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, t71_relat_1,
% 70.43/10.21 t74_relat_1, t7_boole, t7_xboole_1, t83_xboole_1, t86_relat_1, t88_relat_1,
% 70.43/10.21 t8_boole, t8_xboole_1, t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1,
% 70.43/10.21 t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 70.43/10.21
% 70.43/10.21 Those formulas are unsatisfiable:
% 70.43/10.21 ---------------------------------
% 70.43/10.21
% 70.43/10.21 Begin of proof
% 70.43/10.21 |
% 70.43/10.21 | ALPHA: (d2_subset_1) implies:
% 70.43/10.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = v2) | ~
% 70.43/10.21 | (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : (element(v1,
% 70.43/10.21 | v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 70.43/10.21 |
% 70.43/10.21 | ALPHA: (d3_tarski) implies:
% 70.43/10.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 70.43/10.22 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 70.43/10.22 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 70.43/10.22 |
% 70.43/10.22 | ALPHA: (t1_zfmisc_1) implies:
% 70.43/10.22 | (3) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 &
% 70.43/10.22 | $i(v0))
% 70.43/10.22 |
% 70.43/10.22 | ALPHA: (t65_relat_1) implies:
% 70.43/10.22 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 70.43/10.22 | ? [v2: any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) =
% 70.43/10.22 | v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 =
% 70.43/10.22 | empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 70.43/10.22 |
% 70.43/10.22 | ALPHA: (t6_boole) implies:
% 70.43/10.22 | (5) $i(empty_set)
% 70.43/10.22 |
% 70.43/10.22 | ALPHA: (function-axioms) implies:
% 70.43/10.22 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 70.43/10.22 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 70.43/10.22 |
% 70.43/10.22 | DELTA: instantiating (3) with fresh symbol all_245_0 gives:
% 70.43/10.22 | (7) powerset(empty_set) = all_245_0 & singleton(empty_set) = all_245_0 &
% 70.43/10.22 | $i(all_245_0)
% 70.43/10.22 |
% 70.43/10.22 | ALPHA: (7) implies:
% 70.43/10.22 | (8) powerset(empty_set) = all_245_0
% 70.43/10.22 |
% 70.43/10.22 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_256_0, all_256_1
% 70.43/10.22 | gives:
% 70.43/10.22 | (9) ~ (all_256_0 = 0) & empty(all_256_1) = all_256_0 & relation(all_256_1)
% 70.43/10.22 | = 0 & $i(all_256_1)
% 70.43/10.22 |
% 70.43/10.22 | ALPHA: (9) implies:
% 70.43/10.22 | (10) ~ (all_256_0 = 0)
% 70.43/10.22 | (11) $i(all_256_1)
% 70.43/10.22 | (12) empty(all_256_1) = all_256_0
% 70.43/10.22 |
% 70.43/10.22 | DELTA: instantiating (t167_relat_1) with fresh symbols all_265_0, all_265_1,
% 70.43/10.22 | all_265_2, all_265_3, all_265_4 gives:
% 70.43/10.22 | (13) ~ (all_265_0 = 0) & relation_dom(all_265_3) = all_265_1 &
% 70.43/10.22 | relation_inverse_image(all_265_3, all_265_4) = all_265_2 &
% 70.43/10.22 | subset(all_265_2, all_265_1) = all_265_0 & relation(all_265_3) = 0 &
% 70.43/10.22 | $i(all_265_1) & $i(all_265_2) & $i(all_265_3) & $i(all_265_4)
% 70.43/10.22 |
% 70.43/10.22 | ALPHA: (13) implies:
% 70.43/10.22 | (14) ~ (all_265_0 = 0)
% 70.43/10.22 | (15) $i(all_265_4)
% 70.43/10.22 | (16) $i(all_265_3)
% 70.43/10.22 | (17) $i(all_265_2)
% 70.43/10.22 | (18) $i(all_265_1)
% 70.43/10.22 | (19) relation(all_265_3) = 0
% 70.43/10.22 | (20) subset(all_265_2, all_265_1) = all_265_0
% 70.43/10.22 | (21) relation_inverse_image(all_265_3, all_265_4) = all_265_2
% 70.43/10.22 | (22) relation_dom(all_265_3) = all_265_1
% 70.43/10.22 |
% 70.43/10.22 | GROUND_INST: instantiating (2) with all_265_2, all_265_1, all_265_0,
% 70.43/10.22 | simplifying with (17), (18), (20) gives:
% 70.43/10.22 | (23) all_265_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 70.43/10.22 | all_265_1) = v1 & in(v0, all_265_2) = 0 & $i(v0))
% 70.43/10.22 |
% 70.43/10.23 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_245_0,
% 70.43/10.23 | simplifying with (5), (8) gives:
% 70.43/10.23 | (24) ? [v0: $i] : (element(v0, all_245_0) = 0 & empty(v0) = 0 & $i(v0))
% 70.43/10.23 |
% 70.43/10.23 | GROUND_INST: instantiating (4) with all_265_3, all_265_1, simplifying with
% 70.43/10.23 | (16), (22) gives:
% 70.72/10.23 | (25) ? [v0: any] : ? [v1: $i] : (relation_rng(all_265_3) = v1 &
% 70.72/10.23 | relation(all_265_3) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v1 =
% 70.72/10.23 | empty_set) | all_265_1 = empty_set) & ( ~ (all_265_1 =
% 70.72/10.23 | empty_set) | v1 = empty_set))))
% 70.72/10.23 |
% 70.72/10.23 | GROUND_INST: instantiating (d4_relat_1) with all_265_3, all_265_1, simplifying
% 70.72/10.23 | with (16), (22) gives:
% 70.72/10.23 | (26) ? [v0: int] : ( ~ (v0 = 0) & relation(all_265_3) = v0) | ( ? [v0:
% 70.72/10.23 | any] : (v0 = all_265_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] :
% 70.72/10.23 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4:
% 70.72/10.23 | $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 70.72/10.23 | all_265_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 70.72/10.23 | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_265_3) =
% 70.72/10.23 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_265_1) | ( ! [v0: $i] :
% 70.72/10.23 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_265_1) = v1) | ~ $i(v0)
% 70.72/10.23 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3)
% 70.72/10.23 | | ~ (in(v3, all_265_3) = 0) | ~ $i(v2))) & ! [v0: $i] : (
% 70.72/10.23 | ~ (in(v0, all_265_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 70.72/10.23 | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_265_3) = 0 &
% 70.72/10.23 | $i(v2) & $i(v1))))))
% 70.72/10.23 |
% 70.72/10.23 | DELTA: instantiating (24) with fresh symbol all_331_0 gives:
% 70.72/10.23 | (27) element(all_331_0, all_245_0) = 0 & empty(all_331_0) = 0 &
% 70.72/10.23 | $i(all_331_0)
% 70.72/10.23 |
% 70.72/10.23 | ALPHA: (27) implies:
% 70.72/10.23 | (28) $i(all_331_0)
% 70.72/10.23 | (29) empty(all_331_0) = 0
% 70.72/10.23 |
% 70.72/10.23 | DELTA: instantiating (25) with fresh symbols all_349_0, all_349_1 gives:
% 70.72/10.23 | (30) relation_rng(all_265_3) = all_349_0 & relation(all_265_3) = all_349_1
% 70.72/10.23 | & $i(all_349_0) & ( ~ (all_349_1 = 0) | (( ~ (all_349_0 = empty_set) |
% 70.72/10.23 | all_265_1 = empty_set) & ( ~ (all_265_1 = empty_set) | all_349_0
% 70.72/10.23 | = empty_set)))
% 70.72/10.23 |
% 70.72/10.23 | ALPHA: (30) implies:
% 70.72/10.23 | (31) relation_rng(all_265_3) = all_349_0
% 70.72/10.23 |
% 70.72/10.23 | BETA: splitting (23) gives:
% 70.72/10.23 |
% 70.72/10.23 | Case 1:
% 70.72/10.23 | |
% 70.72/10.23 | | (32) all_265_0 = 0
% 70.72/10.23 | |
% 70.72/10.23 | | REDUCE: (14), (32) imply:
% 70.72/10.23 | | (33) $false
% 70.72/10.23 | |
% 70.72/10.23 | | CLOSE: (33) is inconsistent.
% 70.72/10.23 | |
% 70.72/10.23 | Case 2:
% 70.72/10.23 | |
% 70.72/10.23 | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_265_1) = v1 &
% 70.72/10.23 | | in(v0, all_265_2) = 0 & $i(v0))
% 70.72/10.23 | |
% 70.72/10.23 | | DELTA: instantiating (34) with fresh symbols all_390_0, all_390_1 gives:
% 70.72/10.23 | | (35) ~ (all_390_0 = 0) & in(all_390_1, all_265_1) = all_390_0 &
% 70.72/10.23 | | in(all_390_1, all_265_2) = 0 & $i(all_390_1)
% 70.72/10.23 | |
% 70.72/10.23 | | ALPHA: (35) implies:
% 70.72/10.23 | | (36) ~ (all_390_0 = 0)
% 70.72/10.24 | | (37) $i(all_390_1)
% 70.72/10.24 | | (38) in(all_390_1, all_265_2) = 0
% 70.72/10.24 | | (39) in(all_390_1, all_265_1) = all_390_0
% 70.72/10.24 | |
% 70.72/10.24 | | BETA: splitting (26) gives:
% 70.72/10.24 | |
% 70.72/10.24 | | Case 1:
% 70.72/10.24 | | |
% 70.72/10.24 | | | (40) ? [v0: int] : ( ~ (v0 = 0) & relation(all_265_3) = v0)
% 70.72/10.24 | | |
% 70.72/10.24 | | | DELTA: instantiating (40) with fresh symbol all_462_0 gives:
% 70.72/10.24 | | | (41) ~ (all_462_0 = 0) & relation(all_265_3) = all_462_0
% 70.72/10.24 | | |
% 70.72/10.24 | | | ALPHA: (41) implies:
% 70.72/10.24 | | | (42) ~ (all_462_0 = 0)
% 70.72/10.24 | | | (43) relation(all_265_3) = all_462_0
% 70.72/10.24 | | |
% 70.72/10.24 | | | GROUND_INST: instantiating (6) with 0, all_462_0, all_265_3, simplifying
% 70.72/10.24 | | | with (19), (43) gives:
% 70.72/10.24 | | | (44) all_462_0 = 0
% 70.72/10.24 | | |
% 70.72/10.24 | | | REDUCE: (42), (44) imply:
% 70.72/10.24 | | | (45) $false
% 70.72/10.24 | | |
% 70.72/10.24 | | | CLOSE: (45) is inconsistent.
% 70.72/10.24 | | |
% 70.72/10.24 | | Case 2:
% 70.72/10.24 | | |
% 70.72/10.24 | | | (46) ? [v0: any] : (v0 = all_265_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 70.72/10.24 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 70.72/10.24 | | | : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 70.72/10.24 | | | all_265_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i]
% 70.72/10.24 | | | : ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4,
% 70.72/10.24 | | | all_265_3) = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_265_1)
% 70.72/10.24 | | | | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_265_1)
% 70.72/10.24 | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 70.72/10.24 | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_265_3) = 0) |
% 70.72/10.24 | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_265_1) = 0) |
% 70.72/10.24 | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1)
% 70.72/10.24 | | | = v2 & in(v2, all_265_3) = 0 & $i(v2) & $i(v1)))))
% 70.72/10.24 | | |
% 70.72/10.24 | | | ALPHA: (46) implies:
% 70.72/10.24 | | | (47) ~ $i(all_265_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 70.72/10.24 | | | (in(v0, all_265_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3:
% 70.72/10.24 | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 70.72/10.24 | | | all_265_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 70.72/10.24 | | | (in(v0, all_265_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 70.72/10.24 | | | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_265_3) = 0 &
% 70.72/10.24 | | | $i(v2) & $i(v1))))
% 70.72/10.24 | | |
% 70.72/10.24 | | | BETA: splitting (47) gives:
% 70.72/10.24 | | |
% 70.72/10.24 | | | Case 1:
% 70.72/10.24 | | | |
% 70.72/10.24 | | | | (48) ~ $i(all_265_1)
% 70.72/10.24 | | | |
% 70.72/10.24 | | | | PRED_UNIFY: (18), (48) imply:
% 70.72/10.24 | | | | (49) $false
% 70.72/10.24 | | | |
% 70.72/10.24 | | | | CLOSE: (49) is inconsistent.
% 70.72/10.24 | | | |
% 70.72/10.24 | | | Case 2:
% 70.72/10.24 | | | |
% 70.72/10.25 | | | | (50) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_265_1) =
% 70.72/10.25 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 70.72/10.25 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_265_3) = 0) |
% 70.72/10.25 | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_265_1) = 0) | ~
% 70.72/10.25 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 70.72/10.25 | | | | v2 & in(v2, all_265_3) = 0 & $i(v2) & $i(v1)))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | ALPHA: (50) implies:
% 70.72/10.25 | | | | (51) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_265_1) =
% 70.72/10.25 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 70.72/10.25 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_265_3) = 0) |
% 70.72/10.25 | | | | ~ $i(v2)))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | GROUND_INST: instantiating (t166_relat_1) with all_390_1, all_265_4,
% 70.72/10.25 | | | | all_265_3, all_265_2, 0, simplifying with (15), (16), (21),
% 70.72/10.25 | | | | (37), (38) gives:
% 70.72/10.25 | | | | (52) ? [v0: any] : ? [v1: $i] : (relation_rng(all_265_3) = v1 &
% 70.72/10.25 | | | | relation(all_265_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ? [v2: $i]
% 70.72/10.25 | | | | : ? [v3: $i] : (ordered_pair(all_390_1, v2) = v3 & in(v3,
% 70.72/10.25 | | | | all_265_3) = 0 & in(v2, v1) = 0 & in(v2, all_265_4) = 0
% 70.72/10.25 | | | | & $i(v3) & $i(v2))))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | GROUND_INST: instantiating (51) with all_390_1, all_390_0, simplifying
% 70.72/10.25 | | | | with (37), (39) gives:
% 70.72/10.25 | | | | (53) all_390_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 70.72/10.25 | | | | (ordered_pair(all_390_1, v0) = v1) | ~ (in(v1, all_265_3) =
% 70.72/10.25 | | | | 0) | ~ $i(v0))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | GROUND_INST: instantiating (1) with all_331_0, all_256_1, all_256_0,
% 70.72/10.25 | | | | simplifying with (11), (12), (28), (29) gives:
% 70.72/10.25 | | | | (54) ? [v0: any] : (element(all_256_1, all_331_0) = v0 & ( ~ (v0 =
% 70.72/10.25 | | | | 0) | all_256_0 = 0) & ( ~ (all_256_0 = 0) | v0 = 0))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | GROUND_INST: instantiating (fc6_relat_1) with all_265_3, all_349_0,
% 70.72/10.25 | | | | simplifying with (16), (31) gives:
% 70.72/10.25 | | | | (55) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_349_0) =
% 70.72/10.25 | | | | v2 & empty(all_265_3) = v0 & relation(all_265_3) = v1 & ( ~
% 70.72/10.25 | | | | (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | DELTA: instantiating (54) with fresh symbol all_531_0 gives:
% 70.72/10.25 | | | | (56) element(all_256_1, all_331_0) = all_531_0 & ( ~ (all_531_0 = 0)
% 70.72/10.25 | | | | | all_256_0 = 0) & ( ~ (all_256_0 = 0) | all_531_0 = 0)
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | ALPHA: (56) implies:
% 70.72/10.25 | | | | (57) ~ (all_531_0 = 0) | all_256_0 = 0
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | DELTA: instantiating (55) with fresh symbols all_545_0, all_545_1,
% 70.72/10.25 | | | | all_545_2 gives:
% 70.72/10.25 | | | | (58) empty(all_349_0) = all_545_0 & empty(all_265_3) = all_545_2 &
% 70.72/10.25 | | | | relation(all_265_3) = all_545_1 & ( ~ (all_545_0 = 0) | ~
% 70.72/10.25 | | | | (all_545_1 = 0) | all_545_2 = 0)
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | ALPHA: (58) implies:
% 70.72/10.25 | | | | (59) relation(all_265_3) = all_545_1
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | DELTA: instantiating (52) with fresh symbols all_551_0, all_551_1 gives:
% 70.72/10.25 | | | | (60) relation_rng(all_265_3) = all_551_0 & relation(all_265_3) =
% 70.72/10.25 | | | | all_551_1 & $i(all_551_0) & ( ~ (all_551_1 = 0) | ? [v0: $i] :
% 70.72/10.25 | | | | ? [v1: $i] : (ordered_pair(all_390_1, v0) = v1 & in(v1,
% 70.72/10.25 | | | | all_265_3) = 0 & in(v0, all_551_0) = 0 & in(v0, all_265_4)
% 70.72/10.25 | | | | = 0 & $i(v1) & $i(v0)))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | ALPHA: (60) implies:
% 70.72/10.25 | | | | (61) relation(all_265_3) = all_551_1
% 70.72/10.25 | | | | (62) ~ (all_551_1 = 0) | ? [v0: $i] : ? [v1: $i] :
% 70.72/10.25 | | | | (ordered_pair(all_390_1, v0) = v1 & in(v1, all_265_3) = 0 &
% 70.72/10.25 | | | | in(v0, all_551_0) = 0 & in(v0, all_265_4) = 0 & $i(v1) &
% 70.72/10.25 | | | | $i(v0))
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | BETA: splitting (53) gives:
% 70.72/10.25 | | | |
% 70.72/10.25 | | | | Case 1:
% 70.72/10.25 | | | | |
% 70.72/10.25 | | | | | (63) all_390_0 = 0
% 70.72/10.25 | | | | |
% 70.72/10.25 | | | | | REDUCE: (36), (63) imply:
% 70.72/10.25 | | | | | (64) $false
% 70.72/10.25 | | | | |
% 70.72/10.25 | | | | | CLOSE: (64) is inconsistent.
% 70.72/10.25 | | | | |
% 70.72/10.25 | | | | Case 2:
% 70.72/10.25 | | | | |
% 70.72/10.25 | | | | | (65) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_390_1, v0) =
% 70.72/10.25 | | | | | v1) | ~ (in(v1, all_265_3) = 0) | ~ $i(v0))
% 70.72/10.25 | | | | |
% 70.72/10.25 | | | | | BETA: splitting (57) gives:
% 70.72/10.25 | | | | |
% 70.72/10.25 | | | | | Case 1:
% 70.72/10.25 | | | | | |
% 70.72/10.25 | | | | | |
% 70.72/10.25 | | | | | | GROUND_INST: instantiating (6) with 0, all_551_1, all_265_3,
% 70.72/10.25 | | | | | | simplifying with (19), (61) gives:
% 70.72/10.26 | | | | | | (66) all_551_1 = 0
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | | GROUND_INST: instantiating (6) with all_545_1, all_551_1, all_265_3,
% 70.72/10.26 | | | | | | simplifying with (59), (61) gives:
% 70.72/10.26 | | | | | | (67) all_551_1 = all_545_1
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | | COMBINE_EQS: (66), (67) imply:
% 70.72/10.26 | | | | | | (68) all_545_1 = 0
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | | BETA: splitting (62) gives:
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | | Case 1:
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | (69) ~ (all_551_1 = 0)
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | REDUCE: (66), (69) imply:
% 70.72/10.26 | | | | | | | (70) $false
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | CLOSE: (70) is inconsistent.
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | Case 2:
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | (71) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_390_1, v0) =
% 70.72/10.26 | | | | | | | v1 & in(v1, all_265_3) = 0 & in(v0, all_551_0) = 0 &
% 70.72/10.26 | | | | | | | in(v0, all_265_4) = 0 & $i(v1) & $i(v0))
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | DELTA: instantiating (71) with fresh symbols all_633_0, all_633_1
% 70.72/10.26 | | | | | | | gives:
% 70.72/10.26 | | | | | | | (72) ordered_pair(all_390_1, all_633_1) = all_633_0 &
% 70.72/10.26 | | | | | | | in(all_633_0, all_265_3) = 0 & in(all_633_1, all_551_0) =
% 70.72/10.26 | | | | | | | 0 & in(all_633_1, all_265_4) = 0 & $i(all_633_0) &
% 70.72/10.26 | | | | | | | $i(all_633_1)
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | ALPHA: (72) implies:
% 70.72/10.26 | | | | | | | (73) $i(all_633_1)
% 70.72/10.26 | | | | | | | (74) in(all_633_0, all_265_3) = 0
% 70.72/10.26 | | | | | | | (75) ordered_pair(all_390_1, all_633_1) = all_633_0
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | GROUND_INST: instantiating (65) with all_633_1, all_633_0,
% 70.72/10.26 | | | | | | | simplifying with (73), (74), (75) gives:
% 70.72/10.26 | | | | | | | (76) $false
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | | CLOSE: (76) is inconsistent.
% 70.72/10.26 | | | | | | |
% 70.72/10.26 | | | | | | End of split
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | Case 2:
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | | (77) all_256_0 = 0
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | | REDUCE: (10), (77) imply:
% 70.72/10.26 | | | | | | (78) $false
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | | CLOSE: (78) is inconsistent.
% 70.72/10.26 | | | | | |
% 70.72/10.26 | | | | | End of split
% 70.72/10.26 | | | | |
% 70.72/10.26 | | | | End of split
% 70.72/10.26 | | | |
% 70.72/10.26 | | | End of split
% 70.72/10.26 | | |
% 70.72/10.26 | | End of split
% 70.72/10.26 | |
% 70.72/10.26 | End of split
% 70.72/10.26 |
% 70.72/10.26 End of proof
% 70.72/10.26 % SZS output end Proof for theBenchmark
% 70.72/10.26
% 70.72/10.26 9608ms
%------------------------------------------------------------------------------