TSTP Solution File: SEU239+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 17:43:35 EDT 2023
% Result : Theorem 9.28s 2.04s
% Output : Proof 14.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Wed Aug 23 19:27:39 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.76/1.08 Prover 4: Preprocessing ...
% 2.76/1.08 Prover 1: Preprocessing ...
% 2.96/1.12 Prover 0: Preprocessing ...
% 2.96/1.12 Prover 2: Preprocessing ...
% 2.96/1.12 Prover 3: Preprocessing ...
% 2.96/1.12 Prover 6: Preprocessing ...
% 2.96/1.12 Prover 5: Preprocessing ...
% 5.67/1.52 Prover 1: Warning: ignoring some quantifiers
% 5.67/1.52 Prover 3: Warning: ignoring some quantifiers
% 5.97/1.53 Prover 4: Warning: ignoring some quantifiers
% 5.97/1.55 Prover 2: Proving ...
% 5.97/1.56 Prover 3: Constructing countermodel ...
% 5.97/1.56 Prover 6: Proving ...
% 5.97/1.56 Prover 5: Proving ...
% 5.97/1.56 Prover 4: Constructing countermodel ...
% 5.97/1.56 Prover 1: Constructing countermodel ...
% 6.50/1.62 Prover 0: Proving ...
% 8.22/1.86 Prover 3: gave up
% 8.22/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.75/1.92 Prover 7: Preprocessing ...
% 8.75/1.96 Prover 1: gave up
% 9.28/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.28/2.01 Prover 8: Preprocessing ...
% 9.28/2.03 Prover 0: proved (1410ms)
% 9.28/2.04
% 9.28/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.28/2.04
% 9.28/2.04 Prover 7: Warning: ignoring some quantifiers
% 9.28/2.04 Prover 5: stopped
% 9.28/2.07 Prover 2: stopped
% 9.28/2.08 Prover 6: stopped
% 9.28/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.28/2.09 Prover 7: Constructing countermodel ...
% 9.28/2.09 Prover 10: Preprocessing ...
% 9.28/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.28/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.28/2.09 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.28/2.11 Prover 11: Preprocessing ...
% 9.28/2.13 Prover 16: Preprocessing ...
% 9.28/2.13 Prover 13: Preprocessing ...
% 9.28/2.15 Prover 8: Warning: ignoring some quantifiers
% 9.28/2.17 Prover 8: Constructing countermodel ...
% 9.28/2.17 Prover 10: Warning: ignoring some quantifiers
% 9.28/2.19 Prover 10: Constructing countermodel ...
% 11.13/2.24 Prover 16: Warning: ignoring some quantifiers
% 11.13/2.25 Prover 16: Constructing countermodel ...
% 11.39/2.27 Prover 13: Warning: ignoring some quantifiers
% 11.39/2.28 Prover 13: Constructing countermodel ...
% 11.39/2.31 Prover 10: gave up
% 11.39/2.33 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.39/2.33 Prover 11: Warning: ignoring some quantifiers
% 11.91/2.34 Prover 11: Constructing countermodel ...
% 11.91/2.36 Prover 19: Preprocessing ...
% 12.20/2.41 Prover 8: gave up
% 12.92/2.50 Prover 19: Warning: ignoring some quantifiers
% 12.92/2.51 Prover 19: Constructing countermodel ...
% 13.66/2.61 Prover 4: Found proof (size 119)
% 13.66/2.61 Prover 4: proved (1977ms)
% 13.66/2.61 Prover 16: stopped
% 13.66/2.61 Prover 7: stopped
% 13.66/2.61 Prover 11: stopped
% 13.66/2.61 Prover 13: stopped
% 13.66/2.61 Prover 19: stopped
% 13.66/2.61
% 13.66/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.66/2.61
% 13.66/2.63 % SZS output start Proof for theBenchmark
% 14.15/2.63 Assumptions after simplification:
% 14.15/2.63 ---------------------------------
% 14.15/2.63
% 14.15/2.63 (cc2_funct_1)
% 14.15/2.66 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.15/2.66 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 14.15/2.66 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 14.15/2.66 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 14.15/2.66 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 14.15/2.66 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 14.15/2.66 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 14.15/2.66 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 14.15/2.66 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 14.15/2.66 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 14.15/2.66 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 14.15/2.66 0)))
% 14.15/2.66
% 14.15/2.66 (commutativity_k2_xboole_0)
% 14.15/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 14.15/2.66 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 14.15/2.66 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 14.15/2.66 | (set_union2(v1, v0) = v2 & $i(v2)))
% 14.15/2.66
% 14.15/2.66 (d1_relat_2)
% 14.15/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.15/2.67 (is_reflexive_in(v0, v1) = 0) | ~ (ordered_pair(v2, v2) = v3) | ~
% 14.15/2.67 (relation(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 14.15/2.67 [v5: any] : (in(v3, v0) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) &
% 14.15/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (is_reflexive_in(v0,
% 14.15/2.67 v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 14.15/2.67 : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ordered_pair(v3, v3) = v4 &
% 14.15/2.67 in(v4, v0) = v5 & in(v3, v1) = 0 & $i(v4) & $i(v3))) & ! [v0: $i] : !
% 14.15/2.67 [v1: $i] : ! [v2: $i] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (relation(v0)
% 14.15/2.67 = 0) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 14.15/2.67 $i] : (ordered_pair(v2, v2) = v3 & in(v3, v0) = 0 & $i(v3)))
% 14.15/2.67
% 14.15/2.67 (d6_relat_1)
% 14.34/2.67 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.34/2.67 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_field(v0) = v3
% 14.34/2.67 & relation_rng(v0) = v4 & set_union2(v1, v4) = v5 & relation(v0) = v2 &
% 14.34/2.67 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : !
% 14.34/2.67 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 14.34/2.67 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v3 &
% 14.34/2.67 relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 &
% 14.34/2.67 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : !
% 14.34/2.67 [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 14.34/2.67 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 14.34/2.67 relation_field(v0) = v3 & set_union2(v4, v1) = v5 & relation(v0) = v2 &
% 14.34/2.67 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : ( ~
% 14.34/2.67 (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 14.34/2.67 (relation_dom(v0) = v2 & relation_field(v0) = v1 & relation_rng(v0) = v3 &
% 14.34/2.67 set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 14.34/2.67
% 14.34/2.67 (d9_relat_2)
% 14.34/2.68 ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.34/2.68 any] : ? [v3: $i] : ? [v4: any] : (relation_field(v0) = v3 &
% 14.34/2.68 is_reflexive_in(v0, v3) = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) |
% 14.34/2.68 (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) & ! [v0: $i] : !
% 14.34/2.68 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 14.34/2.68 any] : ? [v4: any] : (reflexive(v0) = v3 & is_reflexive_in(v0, v1) = v4 &
% 14.34/2.68 relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0)
% 14.34/2.68 | v4 = 0))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) |
% 14.34/2.68 ? [v1: any] : ? [v2: $i] : ? [v3: any] : (reflexive(v0) = v1 &
% 14.34/2.68 relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3 & $i(v2) & ( ~ (v3
% 14.34/2.68 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 14.34/2.68
% 14.34/2.68 (l1_wellord1)
% 14.34/2.68 ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ?
% 14.34/2.68 [v5: $i] : ? [v6: int] : (reflexive(v0) = v1 & relation_field(v0) = v2 &
% 14.34/2.68 relation(v0) = 0 & $i(v3) & $i(v2) & $i(v0) & ((v4 = 0 & v1 = 0 & ~ (v6 =
% 14.34/2.68 0) & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v2) = 0 &
% 14.34/2.68 $i(v5)) | ( ~ (v1 = 0) & ! [v7: $i] : ! [v8: $i] : ( ~
% 14.34/2.68 (ordered_pair(v7, v7) = v8) | ~ $i(v7) | ? [v9: any] : ? [v10: any]
% 14.34/2.68 : (in(v8, v0) = v10 & in(v7, v2) = v9 & ( ~ (v9 = 0) | v10 = 0))) & !
% 14.34/2.68 [v7: $i] : ( ~ (in(v7, v2) = 0) | ~ $i(v7) | ? [v8: $i] :
% 14.34/2.68 (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0 & $i(v8))))))
% 14.34/2.68
% 14.34/2.68 (t2_subset)
% 14.34/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 14.34/2.68 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 14.34/2.68 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 14.34/2.68 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 14.34/2.68 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 14.34/2.68
% 14.34/2.68 (function-axioms)
% 14.34/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.34/2.69 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 14.34/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.34/2.69 [v3: $i] : (v1 = v0 | ~ (is_reflexive_in(v3, v2) = v1) | ~
% 14.34/2.69 (is_reflexive_in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.34/2.69 ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3,
% 14.34/2.69 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 14.34/2.69 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & !
% 14.34/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.34/2.69 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 14.34/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.34/2.69 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 14.34/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.34/2.69 ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 14.34/2.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 14.34/2.69 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 14.34/2.69 v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0:
% 14.34/2.69 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 14.34/2.69 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 14.34/2.69 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0:
% 14.34/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.34/2.69 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 14.34/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.34/2.69 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 14.34/2.69 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1)
% 14.34/2.69 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.34/2.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 14.34/2.69 (empty(v2) = v0))
% 14.34/2.69
% 14.34/2.69 Further assumptions not needed in the proof:
% 14.34/2.69 --------------------------------------------
% 14.34/2.69 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski, d5_tarski,
% 14.34/2.69 dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski,
% 14.34/2.69 dt_k2_xboole_0, dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1,
% 14.34/2.69 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0,
% 14.34/2.69 idempotence_k2_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0,
% 14.34/2.69 rc3_funct_1, t1_boole, t1_subset, t6_boole, t7_boole, t8_boole
% 14.34/2.69
% 14.34/2.69 Those formulas are unsatisfiable:
% 14.34/2.69 ---------------------------------
% 14.34/2.69
% 14.34/2.69 Begin of proof
% 14.34/2.69 |
% 14.34/2.69 | ALPHA: (cc2_funct_1) implies:
% 14.34/2.69 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 14.34/2.69 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 14.34/2.69 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 14.34/2.69 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 14.34/2.69 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 14.34/2.69 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 14.34/2.69 | ~ (v2 = 0) | v1 = 0)))
% 14.34/2.69 |
% 14.34/2.69 | ALPHA: (commutativity_k2_xboole_0) implies:
% 14.34/2.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 14.34/2.69 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 14.34/2.69 |
% 14.34/2.69 | ALPHA: (d1_relat_2) implies:
% 14.34/2.69 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 14.34/2.69 | (is_reflexive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) |
% 14.34/2.69 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 14.34/2.69 | ordered_pair(v3, v3) = v4 & in(v4, v0) = v5 & in(v3, v1) = 0 &
% 14.34/2.69 | $i(v4) & $i(v3)))
% 14.34/2.69 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.34/2.69 | (is_reflexive_in(v0, v1) = 0) | ~ (ordered_pair(v2, v2) = v3) | ~
% 14.34/2.69 | (relation(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 14.34/2.69 | : ? [v5: any] : (in(v3, v0) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) |
% 14.34/2.69 | v5 = 0)))
% 14.34/2.69 |
% 14.34/2.69 | ALPHA: (d6_relat_1) implies:
% 14.34/2.69 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 14.34/2.69 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_field(v0)
% 14.34/2.69 | = v1 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1 & $i(v3) &
% 14.34/2.69 | $i(v2) & $i(v1)))
% 14.34/2.70 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 14.34/2.70 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 14.34/2.70 | (relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4) =
% 14.34/2.70 | v5 & relation(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) |
% 14.34/2.70 | v5 = v1)))
% 14.34/2.70 |
% 14.34/2.70 | ALPHA: (d9_relat_2) implies:
% 14.34/2.70 | (8) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 14.34/2.70 | [v2: $i] : ? [v3: any] : (reflexive(v0) = v1 & relation_field(v0) =
% 14.34/2.70 | v2 & is_reflexive_in(v0, v2) = v3 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)
% 14.34/2.70 | & ( ~ (v1 = 0) | v3 = 0)))
% 14.34/2.70 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 14.34/2.70 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (reflexive(v0) = v3 &
% 14.34/2.70 | is_reflexive_in(v0, v1) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) |
% 14.34/2.70 | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0)))))
% 14.34/2.70 | (10) ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ?
% 14.34/2.70 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_field(v0) = v3 &
% 14.34/2.70 | is_reflexive_in(v0, v3) = v4 & relation(v0) = v2 & $i(v3) & ( ~
% 14.34/2.70 | (v2 = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0)))))
% 14.34/2.70 |
% 14.34/2.70 | ALPHA: (t2_subset) implies:
% 14.34/2.70 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 14.34/2.70 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 14.34/2.70 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 14.34/2.70 |
% 14.34/2.70 | ALPHA: (function-axioms) implies:
% 14.34/2.70 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.34/2.70 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 14.34/2.70 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.34/2.70 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 14.34/2.70 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.34/2.70 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 14.34/2.70 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.34/2.70 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 14.34/2.70 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.34/2.70 | : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0))
% 14.34/2.70 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.34/2.70 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 14.34/2.70 | v0))
% 14.34/2.70 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.34/2.70 | : ! [v3: $i] : (v1 = v0 | ~ (is_reflexive_in(v3, v2) = v1) | ~
% 14.34/2.70 | (is_reflexive_in(v3, v2) = v0))
% 14.34/2.70 |
% 14.34/2.70 | DELTA: instantiating (l1_wellord1) with fresh symbols all_34_0, all_34_1,
% 14.34/2.70 | all_34_2, all_34_3, all_34_4, all_34_5, all_34_6 gives:
% 14.34/2.71 | (19) reflexive(all_34_6) = all_34_5 & relation_field(all_34_6) = all_34_4 &
% 14.34/2.71 | relation(all_34_6) = 0 & $i(all_34_3) & $i(all_34_4) & $i(all_34_6) &
% 14.34/2.71 | ((all_34_2 = 0 & all_34_5 = 0 & ~ (all_34_0 = 0) &
% 14.34/2.71 | ordered_pair(all_34_3, all_34_3) = all_34_1 & in(all_34_1,
% 14.34/2.71 | all_34_6) = all_34_0 & in(all_34_3, all_34_4) = 0 &
% 14.34/2.71 | $i(all_34_1)) | ( ~ (all_34_5 = 0) & ! [v0: $i] : ! [v1: $i] : (
% 14.34/2.71 | ~ (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 14.34/2.71 | [v3: any] : (in(v1, all_34_6) = v3 & in(v0, all_34_4) = v2 & ( ~
% 14.34/2.71 | (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0, all_34_4) =
% 14.34/2.71 | 0) | ~ $i(v0) | ? [v1: $i] : (ordered_pair(v0, v0) = v1 &
% 14.34/2.71 | in(v1, all_34_6) = 0 & $i(v1)))))
% 14.34/2.71 |
% 14.34/2.71 | ALPHA: (19) implies:
% 14.34/2.71 | (20) $i(all_34_6)
% 14.34/2.71 | (21) $i(all_34_3)
% 14.34/2.71 | (22) relation(all_34_6) = 0
% 14.34/2.71 | (23) relation_field(all_34_6) = all_34_4
% 14.34/2.71 | (24) reflexive(all_34_6) = all_34_5
% 14.34/2.71 | (25) (all_34_2 = 0 & all_34_5 = 0 & ~ (all_34_0 = 0) &
% 14.34/2.71 | ordered_pair(all_34_3, all_34_3) = all_34_1 & in(all_34_1, all_34_6)
% 14.34/2.71 | = all_34_0 & in(all_34_3, all_34_4) = 0 & $i(all_34_1)) | ( ~
% 14.34/2.71 | (all_34_5 = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 14.34/2.71 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1,
% 14.34/2.71 | all_34_6) = v3 & in(v0, all_34_4) = v2 & ( ~ (v2 = 0) | v3 =
% 14.34/2.71 | 0))) & ! [v0: $i] : ( ~ (in(v0, all_34_4) = 0) | ~ $i(v0) |
% 14.34/2.71 | ? [v1: $i] : (ordered_pair(v0, v0) = v1 & in(v1, all_34_6) = 0 &
% 14.34/2.71 | $i(v1))))
% 14.34/2.71 |
% 14.34/2.71 | GROUND_INST: instantiating (8) with all_34_6, simplifying with (20), (22)
% 14.34/2.71 | gives:
% 14.34/2.71 | (26) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (reflexive(all_34_6) = v0
% 14.34/2.71 | & relation_field(all_34_6) = v1 & is_reflexive_in(all_34_6, v1) = v2
% 14.34/2.71 | & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 14.34/2.71 |
% 14.34/2.71 | GROUND_INST: instantiating (6) with all_34_6, simplifying with (20), (22)
% 14.34/2.71 | gives:
% 14.34/2.71 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_34_6) = v1
% 14.34/2.71 | & relation_field(all_34_6) = v0 & relation_rng(all_34_6) = v2 &
% 14.34/2.71 | set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 14.34/2.71 |
% 14.34/2.71 | GROUND_INST: instantiating (1) with all_34_6, simplifying with (20), (22)
% 14.34/2.71 | gives:
% 14.34/2.71 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_34_6) =
% 14.34/2.71 | v2 & function(all_34_6) = v1 & empty(all_34_6) = v0 & ( ~ (v1 = 0) |
% 14.34/2.71 | ~ (v0 = 0) | v2 = 0))
% 14.34/2.71 |
% 14.34/2.71 | GROUND_INST: instantiating (7) with all_34_6, all_34_4, simplifying with (20),
% 14.34/2.71 | (23) gives:
% 14.34/2.71 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 14.34/2.71 | (relation_dom(all_34_6) = v1 & relation_rng(all_34_6) = v2 &
% 14.34/2.71 | set_union2(v1, v2) = v3 & relation(all_34_6) = v0 & $i(v3) & $i(v2)
% 14.34/2.71 | & $i(v1) & ( ~ (v0 = 0) | v3 = all_34_4))
% 14.34/2.71 |
% 14.34/2.71 | GROUND_INST: instantiating (9) with all_34_6, all_34_4, simplifying with (20),
% 14.34/2.71 | (23) gives:
% 14.34/2.71 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : (reflexive(all_34_6) = v1
% 14.34/2.71 | & is_reflexive_in(all_34_6, all_34_4) = v2 & relation(all_34_6) = v0
% 14.34/2.71 | & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))))
% 14.34/2.71 |
% 14.34/2.71 | GROUND_INST: instantiating (10) with all_34_6, all_34_5, simplifying with
% 14.34/2.71 | (20), (24) gives:
% 14.34/2.71 | (31) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_34_6)
% 14.34/2.71 | = v1 & is_reflexive_in(all_34_6, v1) = v2 & relation(all_34_6) = v0
% 14.34/2.71 | & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = 0) | all_34_5 = 0) & ( ~
% 14.34/2.71 | (all_34_5 = 0) | v2 = 0))))
% 14.34/2.71 |
% 14.34/2.71 | DELTA: instantiating (28) with fresh symbols all_44_0, all_44_1, all_44_2
% 14.34/2.71 | gives:
% 14.34/2.72 | (32) one_to_one(all_34_6) = all_44_0 & function(all_34_6) = all_44_1 &
% 14.34/2.72 | empty(all_34_6) = all_44_2 & ( ~ (all_44_1 = 0) | ~ (all_44_2 = 0) |
% 14.34/2.72 | all_44_0 = 0)
% 14.34/2.72 |
% 14.34/2.72 | ALPHA: (32) implies:
% 14.34/2.72 | (33) one_to_one(all_34_6) = all_44_0
% 14.34/2.72 |
% 14.34/2.72 | DELTA: instantiating (27) with fresh symbols all_64_0, all_64_1, all_64_2
% 14.34/2.72 | gives:
% 14.34/2.72 | (34) relation_dom(all_34_6) = all_64_1 & relation_field(all_34_6) =
% 14.34/2.72 | all_64_2 & relation_rng(all_34_6) = all_64_0 & set_union2(all_64_1,
% 14.34/2.72 | all_64_0) = all_64_2 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2)
% 14.34/2.72 |
% 14.34/2.72 | ALPHA: (34) implies:
% 14.34/2.72 | (35) relation_rng(all_34_6) = all_64_0
% 14.34/2.72 | (36) relation_field(all_34_6) = all_64_2
% 14.34/2.72 | (37) relation_dom(all_34_6) = all_64_1
% 14.34/2.72 |
% 14.34/2.72 | DELTA: instantiating (26) with fresh symbols all_74_0, all_74_1, all_74_2
% 14.34/2.72 | gives:
% 14.34/2.72 | (38) reflexive(all_34_6) = all_74_2 & relation_field(all_34_6) = all_74_1 &
% 14.34/2.72 | is_reflexive_in(all_34_6, all_74_1) = all_74_0 & $i(all_74_1) & ( ~
% 14.34/2.72 | (all_74_0 = 0) | all_74_2 = 0) & ( ~ (all_74_2 = 0) | all_74_0 = 0)
% 14.34/2.72 |
% 14.34/2.72 | ALPHA: (38) implies:
% 14.34/2.72 | (39) is_reflexive_in(all_34_6, all_74_1) = all_74_0
% 14.34/2.72 | (40) relation_field(all_34_6) = all_74_1
% 14.34/2.72 | (41) reflexive(all_34_6) = all_74_2
% 14.34/2.72 | (42) ~ (all_74_2 = 0) | all_74_0 = 0
% 14.34/2.72 | (43) ~ (all_74_0 = 0) | all_74_2 = 0
% 14.34/2.72 |
% 14.34/2.72 | DELTA: instantiating (30) with fresh symbols all_76_0, all_76_1, all_76_2
% 14.34/2.72 | gives:
% 14.34/2.72 | (44) reflexive(all_34_6) = all_76_1 & is_reflexive_in(all_34_6, all_34_4) =
% 14.34/2.72 | all_76_0 & relation(all_34_6) = all_76_2 & ( ~ (all_76_2 = 0) | (( ~
% 14.34/2.72 | (all_76_0 = 0) | all_76_1 = 0) & ( ~ (all_76_1 = 0) | all_76_0 =
% 14.34/2.72 | 0)))
% 14.34/2.72 |
% 14.34/2.72 | ALPHA: (44) implies:
% 14.34/2.72 | (45) relation(all_34_6) = all_76_2
% 14.34/2.72 | (46) is_reflexive_in(all_34_6, all_34_4) = all_76_0
% 14.34/2.72 | (47) reflexive(all_34_6) = all_76_1
% 14.34/2.72 |
% 14.34/2.72 | DELTA: instantiating (29) with fresh symbols all_82_0, all_82_1, all_82_2,
% 14.34/2.72 | all_82_3 gives:
% 14.34/2.72 | (48) relation_dom(all_34_6) = all_82_2 & relation_rng(all_34_6) = all_82_1
% 14.34/2.72 | & set_union2(all_82_2, all_82_1) = all_82_0 & relation(all_34_6) =
% 14.34/2.72 | all_82_3 & $i(all_82_0) & $i(all_82_1) & $i(all_82_2) & ( ~ (all_82_3
% 14.34/2.72 | = 0) | all_82_0 = all_34_4)
% 14.34/2.72 |
% 14.34/2.72 | ALPHA: (48) implies:
% 14.34/2.72 | (49) $i(all_82_2)
% 14.34/2.72 | (50) $i(all_82_1)
% 14.34/2.72 | (51) relation(all_34_6) = all_82_3
% 14.34/2.72 | (52) set_union2(all_82_2, all_82_1) = all_82_0
% 14.34/2.72 | (53) relation_rng(all_34_6) = all_82_1
% 14.34/2.72 | (54) relation_dom(all_34_6) = all_82_2
% 14.34/2.72 | (55) ~ (all_82_3 = 0) | all_82_0 = all_34_4
% 14.34/2.72 |
% 14.34/2.72 | DELTA: instantiating (31) with fresh symbols all_84_0, all_84_1, all_84_2
% 14.34/2.72 | gives:
% 14.34/2.72 | (56) relation_field(all_34_6) = all_84_1 & is_reflexive_in(all_34_6,
% 14.34/2.72 | all_84_1) = all_84_0 & relation(all_34_6) = all_84_2 & $i(all_84_1)
% 14.34/2.72 | & ( ~ (all_84_2 = 0) | (( ~ (all_84_0 = 0) | all_34_5 = 0) & ( ~
% 14.34/2.72 | (all_34_5 = 0) | all_84_0 = 0)))
% 14.34/2.72 |
% 14.34/2.72 | ALPHA: (56) implies:
% 14.34/2.72 | (57) relation(all_34_6) = all_84_2
% 14.34/2.72 | (58) is_reflexive_in(all_34_6, all_84_1) = all_84_0
% 14.34/2.72 | (59) relation_field(all_34_6) = all_84_1
% 14.34/2.72 |
% 14.34/2.72 | GROUND_INST: instantiating (12) with 0, all_84_2, all_34_6, simplifying with
% 14.34/2.72 | (22), (57) gives:
% 14.34/2.72 | (60) all_84_2 = 0
% 14.34/2.72 |
% 14.34/2.72 | GROUND_INST: instantiating (12) with all_82_3, all_84_2, all_34_6, simplifying
% 14.34/2.72 | with (51), (57) gives:
% 14.34/2.72 | (61) all_84_2 = all_82_3
% 14.34/2.72 |
% 14.34/2.72 | GROUND_INST: instantiating (12) with all_76_2, all_84_2, all_34_6, simplifying
% 14.34/2.72 | with (45), (57) gives:
% 14.34/2.72 | (62) all_84_2 = all_76_2
% 14.34/2.72 |
% 14.34/2.72 | GROUND_INST: instantiating (13) with all_64_0, all_82_1, all_34_6, simplifying
% 14.34/2.72 | with (35), (53) gives:
% 14.34/2.72 | (63) all_82_1 = all_64_0
% 14.34/2.72 |
% 14.34/2.73 | GROUND_INST: instantiating (14) with all_34_4, all_84_1, all_34_6, simplifying
% 14.34/2.73 | with (23), (59) gives:
% 14.34/2.73 | (64) all_84_1 = all_34_4
% 14.34/2.73 |
% 14.34/2.73 | GROUND_INST: instantiating (14) with all_74_1, all_84_1, all_34_6, simplifying
% 14.34/2.73 | with (40), (59) gives:
% 14.34/2.73 | (65) all_84_1 = all_74_1
% 14.34/2.73 |
% 14.34/2.73 | GROUND_INST: instantiating (14) with all_64_2, all_84_1, all_34_6, simplifying
% 14.34/2.73 | with (36), (59) gives:
% 14.34/2.73 | (66) all_84_1 = all_64_2
% 14.34/2.73 |
% 14.34/2.73 | GROUND_INST: instantiating (15) with all_64_1, all_82_2, all_34_6, simplifying
% 14.34/2.73 | with (37), (54) gives:
% 14.34/2.73 | (67) all_82_2 = all_64_1
% 14.34/2.73 |
% 14.34/2.73 | GROUND_INST: instantiating (16) with all_34_5, all_76_1, all_34_6, simplifying
% 14.34/2.73 | with (24), (47) gives:
% 14.34/2.73 | (68) all_76_1 = all_34_5
% 14.34/2.73 |
% 14.34/2.73 | GROUND_INST: instantiating (16) with all_74_2, all_76_1, all_34_6, simplifying
% 14.34/2.73 | with (41), (47) gives:
% 14.34/2.73 | (69) all_76_1 = all_74_2
% 14.34/2.73 |
% 14.34/2.73 | COMBINE_EQS: (64), (65) imply:
% 14.34/2.73 | (70) all_74_1 = all_34_4
% 14.34/2.73 |
% 14.34/2.73 | COMBINE_EQS: (65), (66) imply:
% 14.34/2.73 | (71) all_74_1 = all_64_2
% 14.34/2.73 |
% 14.34/2.73 | COMBINE_EQS: (60), (61) imply:
% 14.34/2.73 | (72) all_82_3 = 0
% 14.34/2.73 |
% 14.34/2.73 | COMBINE_EQS: (61), (62) imply:
% 14.34/2.73 | (73) all_82_3 = all_76_2
% 14.34/2.73 |
% 14.34/2.73 | COMBINE_EQS: (72), (73) imply:
% 14.34/2.73 | (74) all_76_2 = 0
% 14.34/2.73 |
% 14.34/2.73 | SIMP: (74) implies:
% 14.34/2.73 | (75) all_76_2 = 0
% 14.34/2.73 |
% 14.34/2.73 | COMBINE_EQS: (68), (69) imply:
% 14.34/2.73 | (76) all_74_2 = all_34_5
% 14.34/2.73 |
% 14.34/2.73 | COMBINE_EQS: (70), (71) imply:
% 14.34/2.73 | (77) all_64_2 = all_34_4
% 14.34/2.73 |
% 14.34/2.73 | REDUCE: (58), (64) imply:
% 14.34/2.73 | (78) is_reflexive_in(all_34_6, all_34_4) = all_84_0
% 14.34/2.73 |
% 14.34/2.73 | REDUCE: (39), (70) imply:
% 14.34/2.73 | (79) is_reflexive_in(all_34_6, all_34_4) = all_74_0
% 14.34/2.73 |
% 14.34/2.73 | REDUCE: (52), (63), (67) imply:
% 14.34/2.73 | (80) set_union2(all_64_1, all_64_0) = all_82_0
% 14.34/2.73 |
% 14.34/2.73 | REDUCE: (50), (63) imply:
% 14.34/2.73 | (81) $i(all_64_0)
% 14.34/2.73 |
% 14.34/2.73 | REDUCE: (49), (67) imply:
% 14.34/2.73 | (82) $i(all_64_1)
% 14.34/2.73 |
% 14.34/2.73 | BETA: splitting (55) gives:
% 14.34/2.73 |
% 14.34/2.73 | Case 1:
% 14.34/2.73 | |
% 14.34/2.73 | | (83) ~ (all_82_3 = 0)
% 14.34/2.73 | |
% 14.34/2.73 | | REDUCE: (72), (83) imply:
% 14.34/2.73 | | (84) $false
% 14.34/2.73 | |
% 14.34/2.73 | | CLOSE: (84) is inconsistent.
% 14.34/2.73 | |
% 14.34/2.73 | Case 2:
% 14.34/2.73 | |
% 14.34/2.73 | | (85) all_82_0 = all_34_4
% 14.34/2.73 | |
% 14.34/2.73 | | REDUCE: (80), (85) imply:
% 14.34/2.73 | | (86) set_union2(all_64_1, all_64_0) = all_34_4
% 14.34/2.73 | |
% 14.34/2.73 | | GROUND_INST: instantiating (18) with all_76_0, all_84_0, all_34_4, all_34_6,
% 14.34/2.73 | | simplifying with (46), (78) gives:
% 14.34/2.73 | | (87) all_84_0 = all_76_0
% 14.34/2.73 | |
% 14.34/2.73 | | GROUND_INST: instantiating (18) with all_74_0, all_84_0, all_34_4, all_34_6,
% 14.34/2.73 | | simplifying with (78), (79) gives:
% 14.34/2.73 | | (88) all_84_0 = all_74_0
% 14.34/2.73 | |
% 14.34/2.73 | | COMBINE_EQS: (87), (88) imply:
% 14.34/2.73 | | (89) all_76_0 = all_74_0
% 14.34/2.73 | |
% 14.34/2.73 | | SIMP: (89) implies:
% 14.34/2.73 | | (90) all_76_0 = all_74_0
% 14.34/2.73 | |
% 14.34/2.73 | | GROUND_INST: instantiating (2) with all_34_6, all_44_0, simplifying with
% 14.34/2.73 | | (20), (33) gives:
% 14.34/2.73 | | (91) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_34_6) =
% 14.34/2.73 | | v0 & function(all_34_6) = v2 & empty(all_34_6) = v1 & ( ~ (v2 = 0)
% 14.34/2.73 | | | ~ (v1 = 0) | ~ (v0 = 0) | all_44_0 = 0))
% 14.34/2.73 | |
% 14.34/2.73 | | GROUND_INST: instantiating (3) with all_64_0, all_64_1, all_34_4,
% 14.34/2.73 | | simplifying with (81), (82), (86) gives:
% 14.34/2.74 | | (92) set_union2(all_64_0, all_64_1) = all_34_4 & $i(all_34_4)
% 14.34/2.74 | |
% 14.34/2.74 | | ALPHA: (92) implies:
% 14.34/2.74 | | (93) $i(all_34_4)
% 14.34/2.74 | |
% 14.34/2.74 | | GROUND_INST: instantiating (4) with all_34_6, all_34_4, all_74_0,
% 14.34/2.74 | | simplifying with (20), (22), (79), (93) gives:
% 14.34/2.74 | | (94) all_74_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 =
% 14.34/2.74 | | 0) & ordered_pair(v0, v0) = v1 & in(v1, all_34_6) = v2 & in(v0,
% 14.34/2.74 | | all_34_4) = 0 & $i(v1) & $i(v0))
% 14.34/2.74 | |
% 14.34/2.74 | | DELTA: instantiating (91) with fresh symbols all_128_0, all_128_1, all_128_2
% 14.34/2.74 | | gives:
% 14.34/2.74 | | (95) relation(all_34_6) = all_128_2 & function(all_34_6) = all_128_0 &
% 14.34/2.74 | | empty(all_34_6) = all_128_1 & ( ~ (all_128_0 = 0) | ~ (all_128_1 =
% 14.34/2.74 | | 0) | ~ (all_128_2 = 0) | all_44_0 = 0)
% 14.34/2.74 | |
% 14.34/2.74 | | ALPHA: (95) implies:
% 14.34/2.74 | | (96) relation(all_34_6) = all_128_2
% 14.34/2.74 | |
% 14.34/2.74 | | GROUND_INST: instantiating (12) with 0, all_128_2, all_34_6, simplifying
% 14.34/2.74 | | with (22), (96) gives:
% 14.34/2.74 | | (97) all_128_2 = 0
% 14.34/2.74 | |
% 14.34/2.74 | | BETA: splitting (25) gives:
% 14.34/2.74 | |
% 14.34/2.74 | | Case 1:
% 14.34/2.74 | | |
% 14.34/2.74 | | | (98) all_34_2 = 0 & all_34_5 = 0 & ~ (all_34_0 = 0) &
% 14.34/2.74 | | | ordered_pair(all_34_3, all_34_3) = all_34_1 & in(all_34_1,
% 14.34/2.74 | | | all_34_6) = all_34_0 & in(all_34_3, all_34_4) = 0 & $i(all_34_1)
% 14.34/2.74 | | |
% 14.34/2.74 | | | ALPHA: (98) implies:
% 14.34/2.74 | | | (99) all_34_5 = 0
% 14.34/2.74 | | | (100) ~ (all_34_0 = 0)
% 14.34/2.74 | | | (101) in(all_34_3, all_34_4) = 0
% 14.34/2.74 | | | (102) in(all_34_1, all_34_6) = all_34_0
% 14.34/2.74 | | | (103) ordered_pair(all_34_3, all_34_3) = all_34_1
% 14.34/2.74 | | |
% 14.34/2.74 | | | COMBINE_EQS: (76), (99) imply:
% 14.34/2.74 | | | (104) all_74_2 = 0
% 14.34/2.74 | | |
% 14.34/2.74 | | | BETA: splitting (42) gives:
% 14.34/2.74 | | |
% 14.34/2.74 | | | Case 1:
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | (105) ~ (all_74_2 = 0)
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | REDUCE: (104), (105) imply:
% 14.34/2.74 | | | | (106) $false
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | CLOSE: (106) is inconsistent.
% 14.34/2.74 | | | |
% 14.34/2.74 | | | Case 2:
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | (107) all_74_0 = 0
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | REDUCE: (79), (107) imply:
% 14.34/2.74 | | | | (108) is_reflexive_in(all_34_6, all_34_4) = 0
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | GROUND_INST: instantiating (5) with all_34_6, all_34_4, all_34_3,
% 14.34/2.74 | | | | all_34_1, simplifying with (20), (21), (22), (93), (103),
% 14.34/2.74 | | | | (108) gives:
% 14.34/2.74 | | | | (109) ? [v0: any] : ? [v1: any] : (in(all_34_1, all_34_6) = v1 &
% 14.34/2.74 | | | | in(all_34_3, all_34_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | DELTA: instantiating (109) with fresh symbols all_223_0, all_223_1
% 14.34/2.74 | | | | gives:
% 14.34/2.74 | | | | (110) in(all_34_1, all_34_6) = all_223_0 & in(all_34_3, all_34_4) =
% 14.34/2.74 | | | | all_223_1 & ( ~ (all_223_1 = 0) | all_223_0 = 0)
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | ALPHA: (110) implies:
% 14.34/2.74 | | | | (111) in(all_34_3, all_34_4) = all_223_1
% 14.34/2.74 | | | | (112) in(all_34_1, all_34_6) = all_223_0
% 14.34/2.74 | | | | (113) ~ (all_223_1 = 0) | all_223_0 = 0
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | GROUND_INST: instantiating (17) with 0, all_223_1, all_34_4, all_34_3,
% 14.34/2.74 | | | | simplifying with (101), (111) gives:
% 14.34/2.74 | | | | (114) all_223_1 = 0
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | GROUND_INST: instantiating (17) with all_34_0, all_223_0, all_34_6,
% 14.34/2.74 | | | | all_34_1, simplifying with (102), (112) gives:
% 14.34/2.74 | | | | (115) all_223_0 = all_34_0
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | BETA: splitting (113) gives:
% 14.34/2.74 | | | |
% 14.34/2.74 | | | | Case 1:
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | | (116) ~ (all_223_1 = 0)
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | | REDUCE: (114), (116) imply:
% 14.34/2.74 | | | | | (117) $false
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | | CLOSE: (117) is inconsistent.
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | Case 2:
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | | (118) all_223_0 = 0
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | | COMBINE_EQS: (115), (118) imply:
% 14.34/2.74 | | | | | (119) all_34_0 = 0
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | | REDUCE: (100), (119) imply:
% 14.34/2.74 | | | | | (120) $false
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | | CLOSE: (120) is inconsistent.
% 14.34/2.74 | | | | |
% 14.34/2.74 | | | | End of split
% 14.34/2.74 | | | |
% 14.34/2.74 | | | End of split
% 14.34/2.74 | | |
% 14.34/2.74 | | Case 2:
% 14.34/2.74 | | |
% 14.34/2.74 | | | (121) ~ (all_34_5 = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 14.34/2.74 | | | (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 14.34/2.74 | | | [v3: any] : (in(v1, all_34_6) = v3 & in(v0, all_34_4) = v2 & (
% 14.34/2.74 | | | ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 14.34/2.74 | | | all_34_4) = 0) | ~ $i(v0) | ? [v1: $i] :
% 14.34/2.74 | | | (ordered_pair(v0, v0) = v1 & in(v1, all_34_6) = 0 & $i(v1)))
% 14.34/2.74 | | |
% 14.34/2.74 | | | ALPHA: (121) implies:
% 14.34/2.74 | | | (122) ~ (all_34_5 = 0)
% 14.34/2.75 | | | (123) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) | ~
% 14.34/2.75 | | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, all_34_6) = v3 &
% 14.34/2.75 | | | in(v0, all_34_4) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 14.34/2.75 | | |
% 14.34/2.75 | | | BETA: splitting (43) gives:
% 14.34/2.75 | | |
% 14.34/2.75 | | | Case 1:
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | (124) ~ (all_74_0 = 0)
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | BETA: splitting (94) gives:
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | Case 1:
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | (125) all_74_0 = 0
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | REDUCE: (124), (125) imply:
% 14.34/2.75 | | | | | (126) $false
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | CLOSE: (126) is inconsistent.
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | Case 2:
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | (127) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 14.34/2.75 | | | | | ordered_pair(v0, v0) = v1 & in(v1, all_34_6) = v2 & in(v0,
% 14.34/2.75 | | | | | all_34_4) = 0 & $i(v1) & $i(v0))
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | DELTA: instantiating (127) with fresh symbols all_202_0, all_202_1,
% 14.34/2.75 | | | | | all_202_2 gives:
% 14.34/2.75 | | | | | (128) ~ (all_202_0 = 0) & ordered_pair(all_202_2, all_202_2) =
% 14.34/2.75 | | | | | all_202_1 & in(all_202_1, all_34_6) = all_202_0 &
% 14.34/2.75 | | | | | in(all_202_2, all_34_4) = 0 & $i(all_202_1) & $i(all_202_2)
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | ALPHA: (128) implies:
% 14.34/2.75 | | | | | (129) ~ (all_202_0 = 0)
% 14.34/2.75 | | | | | (130) $i(all_202_2)
% 14.34/2.75 | | | | | (131) $i(all_202_1)
% 14.34/2.75 | | | | | (132) in(all_202_2, all_34_4) = 0
% 14.34/2.75 | | | | | (133) in(all_202_1, all_34_6) = all_202_0
% 14.34/2.75 | | | | | (134) ordered_pair(all_202_2, all_202_2) = all_202_1
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | GROUND_INST: instantiating (11) with all_202_1, all_34_6, all_202_0,
% 14.34/2.75 | | | | | simplifying with (20), (131), (133) gives:
% 14.34/2.75 | | | | | (135) all_202_0 = 0 | ? [v0: any] : ? [v1: any] :
% 14.34/2.75 | | | | | (element(all_202_1, all_34_6) = v0 & empty(all_34_6) = v1 & (
% 14.34/2.75 | | | | | ~ (v0 = 0) | v1 = 0))
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | GROUND_INST: instantiating (123) with all_202_2, all_202_1,
% 14.34/2.75 | | | | | simplifying with (130), (134) gives:
% 14.34/2.75 | | | | | (136) ? [v0: any] : ? [v1: any] : (in(all_202_1, all_34_6) = v1 &
% 14.34/2.75 | | | | | in(all_202_2, all_34_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | DELTA: instantiating (136) with fresh symbols all_240_0, all_240_1
% 14.34/2.75 | | | | | gives:
% 14.34/2.75 | | | | | (137) in(all_202_1, all_34_6) = all_240_0 & in(all_202_2, all_34_4)
% 14.34/2.75 | | | | | = all_240_1 & ( ~ (all_240_1 = 0) | all_240_0 = 0)
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | ALPHA: (137) implies:
% 14.34/2.75 | | | | | (138) in(all_202_2, all_34_4) = all_240_1
% 14.34/2.75 | | | | | (139) in(all_202_1, all_34_6) = all_240_0
% 14.34/2.75 | | | | | (140) ~ (all_240_1 = 0) | all_240_0 = 0
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | BETA: splitting (135) gives:
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | | Case 1:
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | | (141) all_202_0 = 0
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | | REDUCE: (129), (141) imply:
% 14.34/2.75 | | | | | | (142) $false
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | | CLOSE: (142) is inconsistent.
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | Case 2:
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | | GROUND_INST: instantiating (17) with 0, all_240_1, all_34_4,
% 14.34/2.75 | | | | | | all_202_2, simplifying with (132), (138) gives:
% 14.34/2.75 | | | | | | (143) all_240_1 = 0
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | | GROUND_INST: instantiating (17) with all_202_0, all_240_0, all_34_6,
% 14.34/2.75 | | | | | | all_202_1, simplifying with (133), (139) gives:
% 14.34/2.75 | | | | | | (144) all_240_0 = all_202_0
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | | BETA: splitting (140) gives:
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | | Case 1:
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | | (145) ~ (all_240_1 = 0)
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | | REDUCE: (143), (145) imply:
% 14.34/2.75 | | | | | | | (146) $false
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | | CLOSE: (146) is inconsistent.
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | Case 2:
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | | (147) all_240_0 = 0
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | | COMBINE_EQS: (144), (147) imply:
% 14.34/2.75 | | | | | | | (148) all_202_0 = 0
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | | REDUCE: (129), (148) imply:
% 14.34/2.75 | | | | | | | (149) $false
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | | CLOSE: (149) is inconsistent.
% 14.34/2.75 | | | | | | |
% 14.34/2.75 | | | | | | End of split
% 14.34/2.75 | | | | | |
% 14.34/2.75 | | | | | End of split
% 14.34/2.75 | | | | |
% 14.34/2.75 | | | | End of split
% 14.34/2.75 | | | |
% 14.34/2.75 | | | Case 2:
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | (150) all_74_2 = 0
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | COMBINE_EQS: (76), (150) imply:
% 14.34/2.75 | | | | (151) all_34_5 = 0
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | SIMP: (151) implies:
% 14.34/2.75 | | | | (152) all_34_5 = 0
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | REDUCE: (122), (152) imply:
% 14.34/2.75 | | | | (153) $false
% 14.34/2.75 | | | |
% 14.34/2.75 | | | | CLOSE: (153) is inconsistent.
% 14.34/2.75 | | | |
% 14.34/2.75 | | | End of split
% 14.34/2.75 | | |
% 14.34/2.75 | | End of split
% 14.34/2.75 | |
% 14.34/2.75 | End of split
% 14.34/2.75 |
% 14.34/2.75 End of proof
% 14.34/2.75 % SZS output end Proof for theBenchmark
% 14.34/2.75
% 14.34/2.75 2145ms
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