TSTP Solution File: SEU204+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU204+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 : n023.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 17:43:15 EDT 2023
% Result : Theorem 26.32s 4.24s
% Output : Proof 73.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU204+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 16:40:43 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.65/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.33/1.46 Prover 1: Preprocessing ...
% 5.33/1.48 Prover 4: Preprocessing ...
% 5.81/1.52 Prover 6: Preprocessing ...
% 5.81/1.52 Prover 0: Preprocessing ...
% 5.81/1.52 Prover 2: Preprocessing ...
% 5.81/1.52 Prover 3: Preprocessing ...
% 5.81/1.52 Prover 5: Preprocessing ...
% 17.03/3.02 Prover 1: Warning: ignoring some quantifiers
% 17.90/3.14 Prover 3: Warning: ignoring some quantifiers
% 17.90/3.14 Prover 1: Constructing countermodel ...
% 17.90/3.16 Prover 5: Proving ...
% 17.90/3.16 Prover 3: Constructing countermodel ...
% 18.37/3.19 Prover 6: Proving ...
% 18.87/3.25 Prover 4: Warning: ignoring some quantifiers
% 19.57/3.35 Prover 4: Constructing countermodel ...
% 20.05/3.40 Prover 2: Proving ...
% 20.67/3.48 Prover 0: Proving ...
% 26.32/4.24 Prover 3: proved (3578ms)
% 26.32/4.24
% 26.32/4.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.32/4.24
% 26.32/4.24 Prover 6: stopped
% 26.32/4.24 Prover 5: stopped
% 26.32/4.26 Prover 2: stopped
% 26.32/4.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.32/4.27 Prover 0: stopped
% 26.32/4.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.32/4.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 26.32/4.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.32/4.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 28.75/4.53 Prover 8: Preprocessing ...
% 28.96/4.56 Prover 10: Preprocessing ...
% 28.96/4.58 Prover 13: Preprocessing ...
% 28.96/4.62 Prover 7: Preprocessing ...
% 29.53/4.65 Prover 11: Preprocessing ...
% 32.67/5.07 Prover 10: Warning: ignoring some quantifiers
% 32.67/5.12 Prover 8: Warning: ignoring some quantifiers
% 33.35/5.14 Prover 10: Constructing countermodel ...
% 33.35/5.17 Prover 8: Constructing countermodel ...
% 33.80/5.26 Prover 7: Warning: ignoring some quantifiers
% 34.50/5.29 Prover 7: Constructing countermodel ...
% 34.82/5.32 Prover 13: Warning: ignoring some quantifiers
% 35.01/5.39 Prover 13: Constructing countermodel ...
% 37.99/5.74 Prover 11: Warning: ignoring some quantifiers
% 38.59/5.82 Prover 11: Constructing countermodel ...
% 68.04/9.67 Prover 13: stopped
% 68.04/9.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 69.12/9.80 Prover 16: Preprocessing ...
% 70.94/10.04 Prover 16: Warning: ignoring some quantifiers
% 70.94/10.07 Prover 16: Constructing countermodel ...
% 72.78/10.28 Prover 8: Found proof (size 61)
% 72.78/10.28 Prover 8: proved (5979ms)
% 72.78/10.28 Prover 4: stopped
% 72.78/10.28 Prover 11: stopped
% 72.78/10.28 Prover 10: stopped
% 72.78/10.28 Prover 1: stopped
% 72.78/10.29 Prover 16: stopped
% 72.78/10.29 Prover 7: stopped
% 72.78/10.29
% 72.78/10.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 72.78/10.29
% 72.78/10.29 % SZS output start Proof for theBenchmark
% 72.97/10.30 Assumptions after simplification:
% 72.97/10.30 ---------------------------------
% 72.97/10.30
% 72.97/10.30 (d2_subset_1)
% 73.12/10.33 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~
% 73.12/10.33 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & in(v1,
% 73.12/10.33 v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 =
% 73.12/10.33 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) =
% 73.12/10.33 v2) | ~ (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 73.12/10.33 (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 73.12/10.33
% 73.12/10.33 (d3_tarski)
% 73.12/10.34 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 73.12/10.34 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 73.12/10.34 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 73.12/10.34 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 73.12/10.34 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 73.12/10.34
% 73.12/10.34 (d5_relat_1)
% 73.12/10.34 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 73.12/10.34 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 73.12/10.34 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 73.12/10.34 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) =
% 73.12/10.34 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 73.12/10.34 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6)
% 73.12/10.34 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 73.12/10.34 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 73.12/10.34 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 73.12/10.34 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 73.12/10.34 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) &
% 73.12/10.34 $i(v3)))))))
% 73.12/10.34
% 73.12/10.34 (rc2_subset_1)
% 73.12/10.34 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 73.12/10.35 : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2)))
% 73.12/10.35
% 73.12/10.35 (rc2_xboole_0)
% 73.12/10.35 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0))
% 73.12/10.35
% 73.12/10.35 (t143_relat_1)
% 73.12/10.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 73.12/10.35 (relation_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 73.12/10.35 | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : (relation_dom(v2) = v6 &
% 73.12/10.35 relation(v2) = v5 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v4 = 0) | ? [v7: $i] :
% 73.12/10.35 ? [v8: $i] : (ordered_pair(v7, v0) = v8 & in(v8, v2) = 0 & in(v7,
% 73.12/10.35 v6) = 0 & in(v7, v1) = 0 & $i(v8) & $i(v7))) & (v4 = 0 | ! [v7:
% 73.12/10.35 $i] : ( ~ (in(v7, v6) = 0) | ~ $i(v7) | ? [v8: $i] : ? [v9:
% 73.12/10.35 any] : ? [v10: any] : (ordered_pair(v7, v0) = v8 & in(v8, v2) =
% 73.12/10.35 v9 & in(v7, v1) = v10 & $i(v8) & ( ~ (v10 = 0) | ~ (v9 =
% 73.12/10.35 0)))))))))
% 73.12/10.35
% 73.12/10.35 (t144_relat_1)
% 73.12/10.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 73.12/10.35 = 0) & relation_rng(v1) = v3 & relation_image(v1, v0) = v2 & subset(v2,
% 73.12/10.35 v3) = v4 & relation(v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 73.12/10.35
% 73.12/10.35 (t1_zfmisc_1)
% 73.12/10.36 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set)
% 73.12/10.36 = v0 & $i(v0))
% 73.12/10.36
% 73.12/10.36 (t6_boole)
% 73.12/10.36 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 73.12/10.36 $i(v0))
% 73.12/10.36
% 73.12/10.36 (function-axioms)
% 73.12/10.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 73.12/10.39 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 73.12/10.39 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 73.12/10.39 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~
% 73.12/10.39 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 73.12/10.39 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 73.12/10.39 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 73.12/10.39 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 73.12/10.39 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 73.12/10.39 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 73.12/10.39 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 73.12/10.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~
% 73.12/10.39 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 73.12/10.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 73.12/10.39 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 73.12/10.39 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 73.12/10.39 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 73.12/10.39 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 73.12/10.39 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 73.12/10.39 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 73.12/10.39 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 73.12/10.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 73.12/10.39 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 73.12/10.39 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 73.12/10.39 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 73.12/10.39 ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~
% 73.12/10.39 (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 73.12/10.39 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1)
% 73.12/10.39 | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 73.12/10.39 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 73.12/10.39 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 73.12/10.39 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1)
% 73.12/10.39 | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 73.12/10.39 : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 73.12/10.39 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 73.12/10.39 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 73.12/10.39 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 73.12/10.39 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 73.12/10.39 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 73.12/10.39 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3,
% 73.12/10.39 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 73.12/10.39 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 73.12/10.39 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 73.12/10.39 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i]
% 73.12/10.39 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 73.12/10.39 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 73.12/10.39 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i]
% 73.12/10.39 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) =
% 73.12/10.39 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 73.12/10.39 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : !
% 73.12/10.39 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 73.12/10.39 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 73.12/10.39 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : !
% 73.12/10.39 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 73.12/10.39 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 73.12/10.39 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 73.12/10.39 : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~
% 73.12/10.39 (identity_relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 73.12/10.39 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 73.12/10.39 (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 73.12/10.39 : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) &
% 73.12/10.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (subset_difference(v2,
% 73.12/10.39 v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 73.12/10.39 MultipleValueBool] : (are_equipotent(v1, v0) = v2) & ? [v0: $i] : ? [v1:
% 73.12/10.39 $i] : ? [v2: MultipleValueBool] : (disjoint(v1, v0) = v2) & ? [v0: $i] :
% 73.12/10.39 ? [v1: $i] : ? [v2: MultipleValueBool] : (element(v1, v0) = v2) & ? [v0: $i]
% 73.12/10.39 : ? [v1: $i] : ? [v2: MultipleValueBool] : (subset(v1, v0) = v2) & ? [v0:
% 73.12/10.39 $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (proper_subset(v1, v0) =
% 73.12/10.39 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (in(v1, v0) =
% 73.12/10.39 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (meet_of_subsets(v1, v0) =
% 73.12/10.39 v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 73.12/10.39 (union_of_subsets(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 73.12/10.39 $i] : (complements_of_subsets(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1:
% 73.12/10.39 $i] : ? [v2: $i] : (relation_composition(v1, v0) = v2 & $i(v2)) & ? [v0:
% 73.12/10.39 $i] : ? [v1: $i] : ? [v2: $i] : (subset_complement(v1, v0) = v2 & $i(v2))
% 73.12/10.39 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_difference(v1, v0) = v2 &
% 73.12/10.39 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cartesian_product2(v1,
% 73.12/10.39 v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 73.12/10.39 (relation_image(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 73.12/10.39 $i] : (relation_rng_restriction(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 73.12/10.39 [v1: $i] : ? [v2: $i] : (relation_dom_restriction(v1, v0) = v2 & $i(v2)) & ?
% 73.12/10.39 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2 & $i(v2)) &
% 73.12/10.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_intersection2(v1, v0) = v2 &
% 73.12/10.39 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_union2(v1, v0) = v2
% 73.12/10.39 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (unordered_pair(v1,
% 73.12/10.39 v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] : (empty(v0)
% 73.12/10.39 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (relation(v0) = v1) & ?
% 73.12/10.39 [v0: $i] : ? [v1: $i] : (relation_inverse(v0) = v1 & $i(v1)) & ? [v0: $i] :
% 73.12/10.39 ? [v1: $i] : (relation_field(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 73.12/10.39 (relation_rng(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (union(v0) = v1
% 73.12/10.39 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (cast_to_subset(v0) = v1 & $i(v1)) &
% 73.12/10.39 ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1)) & ? [v0: $i] :
% 73.12/10.39 ? [v1: $i] : (powerset(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 73.12/10.39 (singleton(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (set_meet(v0) = v1
% 73.12/10.39 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (identity_relation(v0) = v1 &
% 73.12/10.39 $i(v1))
% 73.12/10.39
% 73.12/10.39 Further assumptions not needed in the proof:
% 73.12/10.39 --------------------------------------------
% 73.12/10.40 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1,
% 73.12/10.40 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0,
% 73.12/10.40 d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, d13_relat_1, d1_relat_1,
% 73.12/10.40 d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_relat_1, d2_tarski,
% 73.12/10.40 d2_xboole_0, d2_zfmisc_1, d3_relat_1, d3_xboole_0, d4_relat_1, d4_subset_1,
% 73.12/10.40 d4_tarski, d4_xboole_0, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1,
% 73.12/10.40 d7_xboole_0, d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k1_relat_1,
% 73.12/10.40 dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1,
% 73.12/10.40 dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1,
% 73.12/10.40 dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski,
% 73.12/10.40 dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1,
% 73.12/10.40 dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, dt_k8_relat_1, dt_k9_relat_1,
% 73.12/10.40 dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1, fc1_relat_1, fc1_subset_1,
% 73.12/10.40 fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1, fc2_xboole_0,
% 73.12/10.40 fc3_subset_1, fc3_xboole_0, fc4_relat_1, fc4_subset_1, fc5_relat_1, fc6_relat_1,
% 73.12/10.40 fc7_relat_1, fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0,
% 73.12/10.40 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 73.12/10.40 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 73.12/10.40 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 73.12/10.40 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 73.12/10.40 rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_relat_1, redefinition_k5_setfam_1,
% 73.12/10.40 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski,
% 73.12/10.40 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1,
% 73.12/10.40 t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1,
% 73.12/10.40 t12_xboole_1, t136_zfmisc_1, t140_relat_1, t17_xboole_1, t19_xboole_1, t1_boole,
% 73.12/10.40 t1_subset, t1_xboole_1, t20_relat_1, t21_relat_1, t25_relat_1, t26_xboole_1,
% 73.12/10.40 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1,
% 73.12/10.40 t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_relat_1, t37_xboole_1,
% 73.12/10.40 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset,
% 73.12/10.40 t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1,
% 73.12/10.40 t45_xboole_1, t46_relat_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1,
% 73.12/10.40 t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0,
% 73.12/10.40 t50_subset_1, t54_subset_1, t56_relat_1, t5_subset, t60_relat_1, t60_xboole_1,
% 73.12/10.40 t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, t69_enumset1, t6_zfmisc_1,
% 73.12/10.40 t71_relat_1, t74_relat_1, t7_boole, t7_xboole_1, t83_xboole_1, t86_relat_1,
% 73.12/10.40 t88_relat_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t90_relat_1, t92_zfmisc_1,
% 73.12/10.40 t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 73.12/10.40
% 73.12/10.40 Those formulas are unsatisfiable:
% 73.12/10.40 ---------------------------------
% 73.12/10.40
% 73.12/10.40 Begin of proof
% 73.12/10.40 |
% 73.12/10.40 | ALPHA: (d2_subset_1) implies:
% 73.12/10.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = v2) | ~
% 73.12/10.40 | (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : (element(v1,
% 73.12/10.40 | v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 73.12/10.40 |
% 73.12/10.40 | ALPHA: (d3_tarski) implies:
% 73.12/10.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 73.12/10.40 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 73.12/10.40 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 73.12/10.40 |
% 73.12/10.40 | ALPHA: (t1_zfmisc_1) implies:
% 73.12/10.40 | (3) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 &
% 73.12/10.40 | $i(v0))
% 73.12/10.40 |
% 73.12/10.40 | ALPHA: (t6_boole) implies:
% 73.12/10.40 | (4) $i(empty_set)
% 73.12/10.40 |
% 73.12/10.40 | ALPHA: (function-axioms) implies:
% 73.12/10.40 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 73.12/10.40 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 73.12/10.40 |
% 73.12/10.40 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_237_0, all_237_1
% 73.12/10.40 | gives:
% 73.12/10.40 | (6) ~ (all_237_0 = 0) & empty(all_237_1) = all_237_0 & $i(all_237_1)
% 73.12/10.40 |
% 73.12/10.40 | ALPHA: (6) implies:
% 73.12/10.40 | (7) ~ (all_237_0 = 0)
% 73.12/10.40 | (8) $i(all_237_1)
% 73.12/10.41 | (9) empty(all_237_1) = all_237_0
% 73.12/10.41 |
% 73.12/10.41 | DELTA: instantiating (3) with fresh symbol all_244_0 gives:
% 73.12/10.41 | (10) powerset(empty_set) = all_244_0 & singleton(empty_set) = all_244_0 &
% 73.12/10.41 | $i(all_244_0)
% 73.12/10.41 |
% 73.12/10.41 | ALPHA: (10) implies:
% 73.12/10.41 | (11) powerset(empty_set) = all_244_0
% 73.12/10.41 |
% 73.12/10.41 | DELTA: instantiating (t144_relat_1) with fresh symbols all_257_0, all_257_1,
% 73.12/10.41 | all_257_2, all_257_3, all_257_4 gives:
% 73.12/10.41 | (12) ~ (all_257_0 = 0) & relation_rng(all_257_3) = all_257_1 &
% 73.12/10.41 | relation_image(all_257_3, all_257_4) = all_257_2 & subset(all_257_2,
% 73.12/10.41 | all_257_1) = all_257_0 & relation(all_257_3) = 0 & $i(all_257_1) &
% 73.12/10.41 | $i(all_257_2) & $i(all_257_3) & $i(all_257_4)
% 73.12/10.41 |
% 73.12/10.41 | ALPHA: (12) implies:
% 73.12/10.41 | (13) ~ (all_257_0 = 0)
% 73.12/10.41 | (14) $i(all_257_4)
% 73.12/10.41 | (15) $i(all_257_3)
% 73.12/10.41 | (16) $i(all_257_2)
% 73.12/10.41 | (17) $i(all_257_1)
% 73.12/10.41 | (18) relation(all_257_3) = 0
% 73.12/10.41 | (19) subset(all_257_2, all_257_1) = all_257_0
% 73.12/10.41 | (20) relation_image(all_257_3, all_257_4) = all_257_2
% 73.12/10.41 | (21) relation_rng(all_257_3) = all_257_1
% 73.12/10.41 |
% 73.12/10.41 | GROUND_INST: instantiating (2) with all_257_2, all_257_1, all_257_0,
% 73.12/10.41 | simplifying with (16), (17), (19) gives:
% 73.12/10.41 | (22) all_257_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 73.12/10.41 | all_257_1) = v1 & in(v0, all_257_2) = 0 & $i(v0))
% 73.12/10.41 |
% 73.12/10.41 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_244_0,
% 73.12/10.41 | simplifying with (4), (11) gives:
% 73.12/10.41 | (23) ? [v0: $i] : (element(v0, all_244_0) = 0 & empty(v0) = 0 & $i(v0))
% 73.12/10.41 |
% 73.12/10.41 | GROUND_INST: instantiating (d5_relat_1) with all_257_3, all_257_1, simplifying
% 73.12/10.41 | with (15), (21) gives:
% 73.12/10.41 | (24) ? [v0: int] : ( ~ (v0 = 0) & relation(all_257_3) = v0) | ( ? [v0:
% 73.12/10.41 | any] : (v0 = all_257_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] :
% 73.12/10.41 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4:
% 73.12/10.41 | $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4,
% 73.12/10.41 | all_257_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 73.12/10.41 | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_257_3) =
% 73.12/10.41 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_257_1) | ( ! [v0: $i] :
% 73.12/10.41 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_257_1) = v1) | ~ $i(v0)
% 73.12/10.41 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3)
% 73.12/10.41 | | ~ (in(v3, all_257_3) = 0) | ~ $i(v2))) & ! [v0: $i] : (
% 73.12/10.41 | ~ (in(v0, all_257_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 73.12/10.41 | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_257_3) = 0 &
% 73.12/10.41 | $i(v2) & $i(v1))))))
% 73.12/10.41 |
% 73.12/10.41 | DELTA: instantiating (23) with fresh symbol all_319_0 gives:
% 73.12/10.42 | (25) element(all_319_0, all_244_0) = 0 & empty(all_319_0) = 0 &
% 73.12/10.42 | $i(all_319_0)
% 73.12/10.42 |
% 73.12/10.42 | ALPHA: (25) implies:
% 73.12/10.42 | (26) $i(all_319_0)
% 73.12/10.42 | (27) empty(all_319_0) = 0
% 73.12/10.42 |
% 73.12/10.42 | BETA: splitting (22) gives:
% 73.12/10.42 |
% 73.12/10.42 | Case 1:
% 73.12/10.42 | |
% 73.12/10.42 | | (28) all_257_0 = 0
% 73.12/10.42 | |
% 73.12/10.42 | | REDUCE: (13), (28) imply:
% 73.12/10.42 | | (29) $false
% 73.12/10.42 | |
% 73.12/10.42 | | CLOSE: (29) is inconsistent.
% 73.12/10.42 | |
% 73.12/10.42 | Case 2:
% 73.12/10.42 | |
% 73.12/10.42 | | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_257_1) = v1 &
% 73.12/10.42 | | in(v0, all_257_2) = 0 & $i(v0))
% 73.12/10.42 | |
% 73.12/10.42 | | DELTA: instantiating (30) with fresh symbols all_444_0, all_444_1 gives:
% 73.12/10.42 | | (31) ~ (all_444_0 = 0) & in(all_444_1, all_257_1) = all_444_0 &
% 73.12/10.42 | | in(all_444_1, all_257_2) = 0 & $i(all_444_1)
% 73.12/10.42 | |
% 73.12/10.42 | | ALPHA: (31) implies:
% 73.12/10.42 | | (32) ~ (all_444_0 = 0)
% 73.12/10.42 | | (33) $i(all_444_1)
% 73.12/10.42 | | (34) in(all_444_1, all_257_2) = 0
% 73.12/10.42 | | (35) in(all_444_1, all_257_1) = all_444_0
% 73.12/10.42 | |
% 73.12/10.42 | | BETA: splitting (24) gives:
% 73.12/10.42 | |
% 73.12/10.42 | | Case 1:
% 73.12/10.42 | | |
% 73.12/10.42 | | | (36) ? [v0: int] : ( ~ (v0 = 0) & relation(all_257_3) = v0)
% 73.12/10.42 | | |
% 73.12/10.42 | | | DELTA: instantiating (36) with fresh symbol all_474_0 gives:
% 73.12/10.42 | | | (37) ~ (all_474_0 = 0) & relation(all_257_3) = all_474_0
% 73.12/10.42 | | |
% 73.12/10.42 | | | ALPHA: (37) implies:
% 73.12/10.42 | | | (38) ~ (all_474_0 = 0)
% 73.12/10.42 | | | (39) relation(all_257_3) = all_474_0
% 73.12/10.42 | | |
% 73.12/10.42 | | | GROUND_INST: instantiating (5) with 0, all_474_0, all_257_3, simplifying
% 73.12/10.42 | | | with (18), (39) gives:
% 73.12/10.42 | | | (40) all_474_0 = 0
% 73.12/10.42 | | |
% 73.12/10.42 | | | REDUCE: (38), (40) imply:
% 73.12/10.42 | | | (41) $false
% 73.12/10.42 | | |
% 73.12/10.42 | | | CLOSE: (41) is inconsistent.
% 73.12/10.42 | | |
% 73.12/10.42 | | Case 2:
% 73.12/10.42 | | |
% 73.59/10.42 | | | (42) ? [v0: any] : (v0 = all_257_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 73.59/10.42 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 73.59/10.42 | | | : ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4,
% 73.59/10.42 | | | all_257_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i]
% 73.59/10.42 | | | : ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4,
% 73.59/10.42 | | | all_257_3) = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_257_1)
% 73.59/10.42 | | | | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_257_1)
% 73.59/10.42 | | | = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 73.59/10.42 | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_257_3) = 0) |
% 73.59/10.42 | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_257_1) = 0) |
% 73.59/10.42 | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0)
% 73.59/10.42 | | | = v2 & in(v2, all_257_3) = 0 & $i(v2) & $i(v1)))))
% 73.59/10.42 | | |
% 73.59/10.42 | | | ALPHA: (42) implies:
% 73.59/10.43 | | | (43) ~ $i(all_257_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 73.59/10.43 | | | (in(v0, all_257_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3:
% 73.59/10.43 | | | $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3,
% 73.59/10.43 | | | all_257_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 73.59/10.43 | | | (in(v0, all_257_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 73.59/10.43 | | | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_257_3) = 0 &
% 73.59/10.43 | | | $i(v2) & $i(v1))))
% 73.59/10.43 | | |
% 73.59/10.43 | | | BETA: splitting (43) gives:
% 73.59/10.43 | | |
% 73.59/10.43 | | | Case 1:
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | (44) ~ $i(all_257_1)
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | PRED_UNIFY: (17), (44) imply:
% 73.59/10.43 | | | | (45) $false
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | CLOSE: (45) is inconsistent.
% 73.59/10.43 | | | |
% 73.59/10.43 | | | Case 2:
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | (46) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_257_1) =
% 73.59/10.43 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 73.59/10.43 | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_257_3) = 0) |
% 73.59/10.43 | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_257_1) = 0) | ~
% 73.59/10.43 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) =
% 73.59/10.43 | | | | v2 & in(v2, all_257_3) = 0 & $i(v2) & $i(v1)))
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | ALPHA: (46) implies:
% 73.59/10.43 | | | | (47) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_257_1) =
% 73.59/10.43 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 73.59/10.43 | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_257_3) = 0) |
% 73.59/10.43 | | | | ~ $i(v2)))
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | GROUND_INST: instantiating (t143_relat_1) with all_444_1, all_257_4,
% 73.59/10.43 | | | | all_257_3, all_257_2, 0, simplifying with (14), (15), (20),
% 73.59/10.43 | | | | (33), (34) gives:
% 73.59/10.43 | | | | (48) ? [v0: any] : ? [v1: $i] : (relation_dom(all_257_3) = v1 &
% 73.59/10.43 | | | | relation(all_257_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ? [v2: $i]
% 73.59/10.43 | | | | : ? [v3: $i] : (ordered_pair(v2, all_444_1) = v3 & in(v3,
% 73.59/10.43 | | | | all_257_3) = 0 & in(v2, v1) = 0 & in(v2, all_257_4) = 0
% 73.59/10.43 | | | | & $i(v3) & $i(v2))))
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | GROUND_INST: instantiating (47) with all_444_1, all_444_0, simplifying
% 73.59/10.43 | | | | with (33), (35) gives:
% 73.59/10.43 | | | | (49) all_444_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 73.59/10.43 | | | | (ordered_pair(v0, all_444_1) = v1) | ~ (in(v1, all_257_3) =
% 73.59/10.43 | | | | 0) | ~ $i(v0))
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | GROUND_INST: instantiating (1) with all_319_0, all_237_1, all_237_0,
% 73.59/10.43 | | | | simplifying with (8), (9), (26), (27) gives:
% 73.59/10.43 | | | | (50) ? [v0: any] : (element(all_237_1, all_319_0) = v0 & ( ~ (v0 =
% 73.59/10.43 | | | | 0) | all_237_0 = 0) & ( ~ (all_237_0 = 0) | v0 = 0))
% 73.59/10.43 | | | |
% 73.59/10.43 | | | | DELTA: instantiating (50) with fresh symbol all_548_0 gives:
% 73.59/10.44 | | | | (51) element(all_237_1, all_319_0) = all_548_0 & ( ~ (all_548_0 = 0)
% 73.59/10.44 | | | | | all_237_0 = 0) & ( ~ (all_237_0 = 0) | all_548_0 = 0)
% 73.59/10.44 | | | |
% 73.59/10.44 | | | | ALPHA: (51) implies:
% 73.59/10.44 | | | | (52) ~ (all_548_0 = 0) | all_237_0 = 0
% 73.59/10.44 | | | |
% 73.59/10.44 | | | | DELTA: instantiating (48) with fresh symbols all_562_0, all_562_1 gives:
% 73.59/10.44 | | | | (53) relation_dom(all_257_3) = all_562_0 & relation(all_257_3) =
% 73.59/10.44 | | | | all_562_1 & $i(all_562_0) & ( ~ (all_562_1 = 0) | ? [v0: $i] :
% 73.59/10.44 | | | | ? [v1: $i] : (ordered_pair(v0, all_444_1) = v1 & in(v1,
% 73.59/10.44 | | | | all_257_3) = 0 & in(v0, all_562_0) = 0 & in(v0, all_257_4)
% 73.59/10.44 | | | | = 0 & $i(v1) & $i(v0)))
% 73.59/10.44 | | | |
% 73.59/10.44 | | | | ALPHA: (53) implies:
% 73.59/10.44 | | | | (54) relation(all_257_3) = all_562_1
% 73.59/10.44 | | | | (55) ~ (all_562_1 = 0) | ? [v0: $i] : ? [v1: $i] :
% 73.59/10.44 | | | | (ordered_pair(v0, all_444_1) = v1 & in(v1, all_257_3) = 0 &
% 73.59/10.44 | | | | in(v0, all_562_0) = 0 & in(v0, all_257_4) = 0 & $i(v1) &
% 73.59/10.44 | | | | $i(v0))
% 73.59/10.44 | | | |
% 73.59/10.44 | | | | BETA: splitting (49) gives:
% 73.59/10.44 | | | |
% 73.59/10.44 | | | | Case 1:
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | | (56) all_444_0 = 0
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | | REDUCE: (32), (56) imply:
% 73.59/10.44 | | | | | (57) $false
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | | CLOSE: (57) is inconsistent.
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | Case 2:
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | | (58) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, all_444_1) =
% 73.59/10.44 | | | | | v1) | ~ (in(v1, all_257_3) = 0) | ~ $i(v0))
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | | BETA: splitting (52) gives:
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | | Case 1:
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | | GROUND_INST: instantiating (5) with 0, all_562_1, all_257_3,
% 73.59/10.44 | | | | | | simplifying with (18), (54) gives:
% 73.59/10.44 | | | | | | (59) all_562_1 = 0
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | | BETA: splitting (55) gives:
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | | Case 1:
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | (60) ~ (all_562_1 = 0)
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | REDUCE: (59), (60) imply:
% 73.59/10.44 | | | | | | | (61) $false
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | CLOSE: (61) is inconsistent.
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | Case 2:
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | (62) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_444_1) =
% 73.59/10.44 | | | | | | | v1 & in(v1, all_257_3) = 0 & in(v0, all_562_0) = 0 &
% 73.59/10.44 | | | | | | | in(v0, all_257_4) = 0 & $i(v1) & $i(v0))
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | DELTA: instantiating (62) with fresh symbols all_664_0, all_664_1
% 73.59/10.44 | | | | | | | gives:
% 73.59/10.44 | | | | | | | (63) ordered_pair(all_664_1, all_444_1) = all_664_0 &
% 73.59/10.44 | | | | | | | in(all_664_0, all_257_3) = 0 & in(all_664_1, all_562_0) =
% 73.59/10.44 | | | | | | | 0 & in(all_664_1, all_257_4) = 0 & $i(all_664_0) &
% 73.59/10.44 | | | | | | | $i(all_664_1)
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | ALPHA: (63) implies:
% 73.59/10.44 | | | | | | | (64) $i(all_664_1)
% 73.59/10.44 | | | | | | | (65) in(all_664_0, all_257_3) = 0
% 73.59/10.44 | | | | | | | (66) ordered_pair(all_664_1, all_444_1) = all_664_0
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | GROUND_INST: instantiating (58) with all_664_1, all_664_0,
% 73.59/10.44 | | | | | | | simplifying with (64), (65), (66) gives:
% 73.59/10.44 | | | | | | | (67) $false
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | | CLOSE: (67) is inconsistent.
% 73.59/10.44 | | | | | | |
% 73.59/10.44 | | | | | | End of split
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | Case 2:
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | | (68) all_237_0 = 0
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | | REDUCE: (7), (68) imply:
% 73.59/10.44 | | | | | | (69) $false
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | | CLOSE: (69) is inconsistent.
% 73.59/10.44 | | | | | |
% 73.59/10.44 | | | | | End of split
% 73.59/10.44 | | | | |
% 73.59/10.44 | | | | End of split
% 73.59/10.44 | | | |
% 73.59/10.44 | | | End of split
% 73.59/10.44 | | |
% 73.59/10.44 | | End of split
% 73.59/10.44 | |
% 73.59/10.44 | End of split
% 73.59/10.44 |
% 73.59/10.44 End of proof
% 73.59/10.44 % SZS output end Proof for theBenchmark
% 73.59/10.44
% 73.59/10.44 9808ms
%------------------------------------------------------------------------------