TSTP Solution File: SEU252+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU252+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 : n018.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 17:43:40 EDT 2023
% Result : Theorem 12.63s 2.51s
% Output : Proof 18.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU252+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 13:05:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.84/1.07 Prover 1: Preprocessing ...
% 2.84/1.07 Prover 4: Preprocessing ...
% 2.84/1.11 Prover 5: Preprocessing ...
% 2.84/1.11 Prover 2: Preprocessing ...
% 2.84/1.11 Prover 3: Preprocessing ...
% 2.84/1.11 Prover 0: Preprocessing ...
% 2.84/1.11 Prover 6: Preprocessing ...
% 6.58/1.63 Prover 1: Warning: ignoring some quantifiers
% 6.58/1.64 Prover 3: Warning: ignoring some quantifiers
% 6.58/1.65 Prover 4: Warning: ignoring some quantifiers
% 6.58/1.66 Prover 1: Constructing countermodel ...
% 6.91/1.66 Prover 5: Proving ...
% 6.91/1.67 Prover 2: Proving ...
% 6.91/1.68 Prover 6: Proving ...
% 6.91/1.68 Prover 3: Constructing countermodel ...
% 6.91/1.69 Prover 4: Constructing countermodel ...
% 7.42/1.77 Prover 0: Proving ...
% 9.07/2.02 Prover 3: gave up
% 9.07/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.60/2.07 Prover 7: Preprocessing ...
% 9.89/2.13 Prover 1: gave up
% 9.89/2.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.89/2.19 Prover 7: Warning: ignoring some quantifiers
% 9.89/2.21 Prover 7: Constructing countermodel ...
% 9.89/2.22 Prover 8: Preprocessing ...
% 11.85/2.38 Prover 8: Warning: ignoring some quantifiers
% 11.85/2.39 Prover 8: Constructing countermodel ...
% 12.63/2.50 Prover 0: proved (1872ms)
% 12.63/2.50
% 12.63/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.63/2.51
% 12.63/2.51 Prover 2: stopped
% 12.63/2.51 Prover 5: stopped
% 12.63/2.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.63/2.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.63/2.52 Prover 6: stopped
% 12.63/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.63/2.52 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.12/2.54 Prover 11: Preprocessing ...
% 13.12/2.56 Prover 16: Preprocessing ...
% 13.12/2.56 Prover 10: Preprocessing ...
% 13.39/2.57 Prover 13: Preprocessing ...
% 13.39/2.63 Prover 16: Warning: ignoring some quantifiers
% 13.90/2.63 Prover 10: Warning: ignoring some quantifiers
% 13.90/2.64 Prover 16: Constructing countermodel ...
% 13.90/2.64 Prover 10: Constructing countermodel ...
% 14.14/2.67 Prover 13: Warning: ignoring some quantifiers
% 14.14/2.68 Prover 13: Constructing countermodel ...
% 14.14/2.73 Prover 10: gave up
% 14.14/2.73 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 14.65/2.73 Prover 11: Warning: ignoring some quantifiers
% 14.65/2.74 Prover 8: gave up
% 14.65/2.74 Prover 11: Constructing countermodel ...
% 14.65/2.76 Prover 19: Preprocessing ...
% 15.33/2.90 Prover 19: Warning: ignoring some quantifiers
% 15.33/2.92 Prover 19: Constructing countermodel ...
% 17.89/3.22 Prover 4: Found proof (size 177)
% 17.89/3.22 Prover 4: proved (2585ms)
% 17.89/3.22 Prover 7: stopped
% 17.89/3.22 Prover 11: stopped
% 17.89/3.22 Prover 16: stopped
% 17.89/3.22 Prover 19: stopped
% 17.89/3.22 Prover 13: stopped
% 17.89/3.22
% 17.89/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.89/3.22
% 17.89/3.25 % SZS output start Proof for theBenchmark
% 17.89/3.25 Assumptions after simplification:
% 17.89/3.25 ---------------------------------
% 17.89/3.25
% 17.89/3.25 (cc2_funct_1)
% 18.49/3.28 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 18.49/3.28 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 18.49/3.28 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 18.49/3.28 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 18.49/3.28 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 18.49/3.28 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 18.49/3.28 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 18.49/3.28 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 18.49/3.28 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 18.49/3.28 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 18.49/3.28 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 18.49/3.28 0)))
% 18.49/3.28
% 18.49/3.28 (d5_tarski)
% 18.49/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 18.49/3.28 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (singleton(v0) = v4 &
% 18.49/3.28 unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3 & $i(v4) &
% 18.49/3.28 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 18.49/3.28 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 18.49/3.28 [v4: $i] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 &
% 18.49/3.28 unordered_pair(v2, v4) = v3 & $i(v4) & $i(v3)))
% 18.49/3.28
% 18.49/3.28 (d6_relat_1)
% 18.49/3.29 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 18.49/3.29 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_field(v0) = v3
% 18.49/3.29 & relation_rng(v0) = v4 & set_union2(v1, v4) = v5 & relation(v0) = v2 &
% 18.49/3.29 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : !
% 18.49/3.29 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 18.49/3.29 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v3 &
% 18.49/3.29 relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 &
% 18.49/3.29 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : !
% 18.49/3.29 [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 18.49/3.29 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 18.49/3.29 relation_field(v0) = v3 & set_union2(v4, v1) = v5 & relation(v0) = v2 &
% 18.49/3.29 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : ( ~
% 18.49/3.29 (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 18.49/3.29 (relation_dom(v0) = v2 & relation_field(v0) = v1 & relation_rng(v0) = v3 &
% 18.49/3.29 set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 18.49/3.29
% 18.49/3.29 (d6_wellord1)
% 18.65/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 18.65/3.29 v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 18.65/3.29 (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2 & $i(v3) &
% 18.65/3.29 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 18.65/3.29 (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~
% 18.65/3.29 $i(v0) | ? [v3: $i] : (relation_restriction(v0, v1) = v3 &
% 18.65/3.29 set_intersection2(v0, v2) = v3 & $i(v3)))
% 18.65/3.29
% 18.65/3.29 (dt_k2_wellord1)
% 18.65/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 18.65/3.29 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2)
% 18.65/3.29 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 18.65/3.29
% 18.65/3.29 (l1_wellord1)
% 18.65/3.30 ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ? [v2:
% 18.65/3.30 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? [v7:
% 18.65/3.30 int] : (relation_field(v0) = v3 & relation(v0) = v2 & $i(v4) & $i(v3) & (
% 18.65/3.30 ~ (v2 = 0) | (( ~ (v1 = 0) | ( ! [v8: $i] : ! [v9: $i] : ( ~
% 18.65/3.30 (ordered_pair(v8, v8) = v9) | ~ $i(v8) | ? [v10: any] : ?
% 18.65/3.30 [v11: any] : (in(v9, v0) = v11 & in(v8, v3) = v10 & ( ~ (v10 =
% 18.65/3.30 0) | v11 = 0))) & ! [v8: $i] : ( ~ (in(v8, v3) = 0) | ~
% 18.65/3.30 $i(v8) | ? [v9: $i] : (ordered_pair(v8, v8) = v9 & in(v9, v0) =
% 18.65/3.30 0 & $i(v9))))) & (v1 = 0 | (v5 = 0 & ~ (v7 = 0) &
% 18.65/3.30 ordered_pair(v4, v4) = v6 & in(v6, v0) = v7 & in(v4, v3) = 0 &
% 18.65/3.30 $i(v6))))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0)
% 18.65/3.30 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 18.65/3.30 int] : ? [v6: $i] : ? [v7: int] : (reflexive(v0) = v3 & relation(v0) =
% 18.65/3.30 v2 & $i(v4) & ( ~ (v2 = 0) | (( ~ (v3 = 0) | ( ! [v8: $i] : ! [v9: $i] :
% 18.65/3.30 ( ~ (ordered_pair(v8, v8) = v9) | ~ $i(v8) | ? [v10: any] : ?
% 18.65/3.30 [v11: any] : (in(v9, v0) = v11 & in(v8, v1) = v10 & ( ~ (v10 =
% 18.65/3.30 0) | v11 = 0))) & ! [v8: $i] : ( ~ (in(v8, v1) = 0) | ~
% 18.65/3.30 $i(v8) | ? [v9: $i] : (ordered_pair(v8, v8) = v9 & in(v9, v0) =
% 18.65/3.30 0 & $i(v9))))) & (v3 = 0 | (v5 = 0 & ~ (v7 = 0) &
% 18.65/3.30 ordered_pair(v4, v4) = v6 & in(v6, v0) = v7 & in(v4, v1) = 0 &
% 18.65/3.30 $i(v6))))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) |
% 18.65/3.30 ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ?
% 18.65/3.30 [v6: int] : (reflexive(v0) = v1 & relation_field(v0) = v2 & $i(v3) & $i(v2)
% 18.65/3.30 & ( ~ (v1 = 0) | ( ! [v7: $i] : ! [v8: $i] : ( ~ (ordered_pair(v7, v7) =
% 18.65/3.30 v8) | ~ $i(v7) | ? [v9: any] : ? [v10: any] : (in(v8, v0) = v10
% 18.65/3.30 & in(v7, v2) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7: $i] : ( ~
% 18.65/3.30 (in(v7, v2) = 0) | ~ $i(v7) | ? [v8: $i] : (ordered_pair(v7, v7) =
% 18.65/3.30 v8 & in(v8, v0) = 0 & $i(v8))))) & (v1 = 0 | (v4 = 0 & ~ (v6 = 0)
% 18.65/3.30 & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v2) = 0 &
% 18.65/3.30 $i(v5)))))
% 18.65/3.30
% 18.65/3.30 (t106_zfmisc_1)
% 18.65/3.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.65/3.30 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~
% 18.65/3.30 (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) |
% 18.65/3.30 ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = v8 &
% 18.65/3.30 in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1:
% 18.65/3.30 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 18.65/3.30 (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~
% 18.65/3.30 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1,
% 18.65/3.30 v3) = 0 & in(v0, v2) = 0))
% 18.65/3.30
% 18.65/3.30 (t16_wellord1)
% 18.65/3.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 18.65/3.30 (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ $i(v2) | ~
% 18.65/3.30 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8:
% 18.65/3.30 any] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) =
% 18.65/3.30 v8 & in(v0, v2) = v6 & $i(v7) & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0)
% 18.65/3.30 | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0))))))
% 18.65/3.30
% 18.65/3.30 (t19_wellord1)
% 18.65/3.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 18.65/3.30 (relation_restriction(v2, v1) = v3) | ~ (relation_field(v3) = v4) | ~
% 18.65/3.30 (in(v0, v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 18.65/3.30 [v6: $i] : ? [v7: any] : ? [v8: any] : (relation_field(v2) = v6 &
% 18.65/3.30 relation(v2) = v5 & in(v0, v6) = v7 & in(v0, v1) = v8 & $i(v6) & ( ~ (v5 =
% 18.65/3.30 0) | (v8 = 0 & v7 = 0))))
% 18.65/3.30
% 18.65/3.30 (t22_wellord1)
% 18.65/3.30 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 18.65/3.30 reflexive(v2) = v3 & reflexive(v1) = 0 & relation_restriction(v1, v0) = v2 &
% 18.65/3.30 relation(v1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 18.65/3.30
% 18.65/3.30 (t2_subset)
% 18.65/3.30 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 18.65/3.30 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 18.65/3.30 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 18.65/3.30 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 18.65/3.30 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 18.65/3.30
% 18.65/3.30 (function-axioms)
% 18.65/3.31 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 18.65/3.31 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 18.65/3.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.65/3.31 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) =
% 18.65/3.31 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 18.65/3.31 ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 18.65/3.31 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.65/3.31 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 18.65/3.31 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.65/3.31 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 18.65/3.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.65/3.31 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : !
% 18.65/3.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) =
% 18.65/3.31 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.65/3.31 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3,
% 18.65/3.31 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.65/3.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~
% 18.65/3.31 (reflexive(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 18.65/3.31 ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : !
% 18.65/3.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~
% 18.65/3.31 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 18.65/3.31 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i]
% 18.65/3.31 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 18.65/3.31 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.65/3.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 18.65/3.31 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.65/3.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 18.65/3.31 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.65/3.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 18.65/3.31 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.65/3.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 18.65/3.31 (empty(v2) = v0))
% 18.65/3.31
% 18.65/3.31 Further assumptions not needed in the proof:
% 18.65/3.31 --------------------------------------------
% 18.65/3.31 antisymmetry_r2_hidden, cc1_funct_1, commutativity_k2_tarski,
% 18.65/3.31 commutativity_k2_xboole_0, commutativity_k3_xboole_0, dt_k1_relat_1,
% 18.65/3.31 dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski, dt_k2_xboole_0,
% 18.65/3.31 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_xboole_0, dt_k4_tarski, dt_m1_subset_1,
% 18.65/3.31 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0,
% 18.65/3.31 idempotence_k2_xboole_0, idempotence_k3_xboole_0, rc1_funct_1, rc1_xboole_0,
% 18.65/3.31 rc2_funct_1, rc2_xboole_0, rc3_funct_1, t1_boole, t1_subset, t2_boole, t6_boole,
% 18.65/3.31 t7_boole, t8_boole
% 18.65/3.31
% 18.65/3.31 Those formulas are unsatisfiable:
% 18.65/3.31 ---------------------------------
% 18.65/3.31
% 18.65/3.31 Begin of proof
% 18.65/3.31 |
% 18.65/3.31 | ALPHA: (cc2_funct_1) implies:
% 18.65/3.31 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 18.65/3.31 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 &
% 18.65/3.31 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 18.65/3.31 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 18.65/3.31 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 18.65/3.31 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 18.65/3.31 | ~ (v2 = 0) | v1 = 0)))
% 18.65/3.31 |
% 18.65/3.31 | ALPHA: (d5_tarski) implies:
% 18.65/3.31 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 18.65/3.31 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 18.65/3.31 | (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 &
% 18.65/3.31 | unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2)))
% 18.65/3.31 |
% 18.65/3.31 | ALPHA: (d6_relat_1) implies:
% 18.65/3.31 | (4) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 18.65/3.31 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_field(v0)
% 18.65/3.31 | = v1 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1 & $i(v3) &
% 18.65/3.31 | $i(v2) & $i(v1)))
% 18.65/3.31 |
% 18.65/3.31 | ALPHA: (d6_wellord1) implies:
% 18.65/3.32 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0,
% 18.65/3.32 | v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 18.65/3.32 | [v3: $i] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0,
% 18.65/3.32 | v3) = v2 & $i(v3) & $i(v2)))
% 18.65/3.32 |
% 18.65/3.32 | ALPHA: (l1_wellord1) implies:
% 18.65/3.32 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 18.65/3.32 | [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int] :
% 18.65/3.32 | (reflexive(v0) = v1 & relation_field(v0) = v2 & $i(v3) & $i(v2) & ( ~
% 18.65/3.32 | (v1 = 0) | ( ! [v7: $i] : ! [v8: $i] : ( ~ (ordered_pair(v7, v7)
% 18.65/3.32 | = v8) | ~ $i(v7) | ? [v9: any] : ? [v10: any] : (in(v8,
% 18.65/3.32 | v0) = v10 & in(v7, v2) = v9 & ( ~ (v9 = 0) | v10 = 0))) &
% 18.65/3.32 | ! [v7: $i] : ( ~ (in(v7, v2) = 0) | ~ $i(v7) | ? [v8: $i] :
% 18.65/3.32 | (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0 & $i(v8))))) &
% 18.65/3.32 | (v1 = 0 | (v4 = 0 & ~ (v6 = 0) & ordered_pair(v3, v3) = v5 &
% 18.65/3.32 | in(v5, v0) = v6 & in(v3, v2) = 0 & $i(v5)))))
% 18.65/3.32 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) |
% 18.65/3.32 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: int] : ? [v6:
% 18.65/3.32 | $i] : ? [v7: int] : (reflexive(v0) = v3 & relation(v0) = v2 &
% 18.65/3.32 | $i(v4) & ( ~ (v2 = 0) | (( ~ (v3 = 0) | ( ! [v8: $i] : ! [v9: $i]
% 18.65/3.32 | : ( ~ (ordered_pair(v8, v8) = v9) | ~ $i(v8) | ? [v10:
% 18.65/3.32 | any] : ? [v11: any] : (in(v9, v0) = v11 & in(v8, v1) =
% 18.65/3.32 | v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8: $i] : ( ~
% 18.65/3.32 | (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: $i] :
% 18.65/3.32 | (ordered_pair(v8, v8) = v9 & in(v9, v0) = 0 & $i(v9)))))
% 18.65/3.32 | & (v3 = 0 | (v5 = 0 & ~ (v7 = 0) & ordered_pair(v4, v4) = v6 &
% 18.65/3.32 | in(v6, v0) = v7 & in(v4, v1) = 0 & $i(v6)))))))
% 18.65/3.32 | (8) ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ?
% 18.65/3.32 | [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] :
% 18.65/3.32 | ? [v7: int] : (relation_field(v0) = v3 & relation(v0) = v2 & $i(v4) &
% 18.65/3.32 | $i(v3) & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ( ! [v8: $i] : ! [v9: $i]
% 18.65/3.32 | : ( ~ (ordered_pair(v8, v8) = v9) | ~ $i(v8) | ? [v10:
% 18.65/3.32 | any] : ? [v11: any] : (in(v9, v0) = v11 & in(v8, v3) =
% 18.65/3.32 | v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8: $i] : ( ~
% 18.65/3.32 | (in(v8, v3) = 0) | ~ $i(v8) | ? [v9: $i] :
% 18.65/3.32 | (ordered_pair(v8, v8) = v9 & in(v9, v0) = 0 & $i(v9)))))
% 18.65/3.32 | & (v1 = 0 | (v5 = 0 & ~ (v7 = 0) & ordered_pair(v4, v4) = v6 &
% 18.65/3.32 | in(v6, v0) = v7 & in(v4, v3) = 0 & $i(v6)))))))
% 18.65/3.32 |
% 18.65/3.32 | ALPHA: (t106_zfmisc_1) implies:
% 18.65/3.32 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.65/3.32 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) =
% 18.65/3.32 | v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~
% 18.65/3.32 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8:
% 18.65/3.32 | any] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 =
% 18.65/3.32 | 0))))
% 18.65/3.32 |
% 18.65/3.32 | ALPHA: (t2_subset) implies:
% 18.65/3.32 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 18.65/3.32 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 18.65/3.32 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 18.65/3.32 |
% 18.65/3.32 | ALPHA: (function-axioms) implies:
% 18.65/3.32 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 18.65/3.32 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 18.65/3.32 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.65/3.32 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 18.65/3.32 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 18.65/3.32 | : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0))
% 18.65/3.33 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 18.65/3.33 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 18.65/3.33 | v0))
% 18.65/3.33 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.65/3.33 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) =
% 18.65/3.33 | v0))
% 18.65/3.33 |
% 18.65/3.33 | DELTA: instantiating (t22_wellord1) with fresh symbols all_41_0, all_41_1,
% 18.65/3.33 | all_41_2, all_41_3 gives:
% 18.65/3.33 | (16) ~ (all_41_0 = 0) & reflexive(all_41_1) = all_41_0 &
% 18.65/3.33 | reflexive(all_41_2) = 0 & relation_restriction(all_41_2, all_41_3) =
% 18.65/3.33 | all_41_1 & relation(all_41_2) = 0 & $i(all_41_1) & $i(all_41_2) &
% 18.65/3.33 | $i(all_41_3)
% 18.65/3.33 |
% 18.65/3.33 | ALPHA: (16) implies:
% 18.65/3.33 | (17) ~ (all_41_0 = 0)
% 18.65/3.33 | (18) $i(all_41_3)
% 18.65/3.33 | (19) $i(all_41_2)
% 18.65/3.33 | (20) $i(all_41_1)
% 18.65/3.33 | (21) relation(all_41_2) = 0
% 18.65/3.33 | (22) relation_restriction(all_41_2, all_41_3) = all_41_1
% 18.65/3.33 | (23) reflexive(all_41_2) = 0
% 18.65/3.33 | (24) reflexive(all_41_1) = all_41_0
% 18.65/3.33 |
% 18.65/3.33 | GROUND_INST: instantiating (6) with all_41_2, simplifying with (19), (21)
% 18.65/3.33 | gives:
% 18.87/3.33 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i]
% 18.87/3.33 | : ? [v5: int] : (reflexive(all_41_2) = v0 & relation_field(all_41_2)
% 18.87/3.33 | = v1 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( ! [v6: $i] : ! [v7: $i] :
% 18.87/3.33 | ( ~ (ordered_pair(v6, v6) = v7) | ~ $i(v6) | ? [v8: any] : ?
% 18.87/3.33 | [v9: any] : (in(v7, all_41_2) = v9 & in(v6, v1) = v8 & ( ~ (v8
% 18.87/3.33 | = 0) | v9 = 0))) & ! [v6: $i] : ( ~ (in(v6, v1) = 0) |
% 18.87/3.33 | ~ $i(v6) | ? [v7: $i] : (ordered_pair(v6, v6) = v7 & in(v7,
% 18.87/3.33 | all_41_2) = 0 & $i(v7))))) & (v0 = 0 | (v3 = 0 & ~ (v5 =
% 18.87/3.33 | 0) & ordered_pair(v2, v2) = v4 & in(v4, all_41_2) = v5 &
% 18.87/3.33 | in(v2, v1) = 0 & $i(v4))))
% 18.87/3.33 |
% 18.87/3.33 | GROUND_INST: instantiating (4) with all_41_2, simplifying with (19), (21)
% 18.87/3.33 | gives:
% 18.87/3.33 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_41_2) = v1
% 18.87/3.33 | & relation_field(all_41_2) = v0 & relation_rng(all_41_2) = v2 &
% 18.87/3.33 | set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 18.87/3.33 |
% 18.87/3.33 | GROUND_INST: instantiating (1) with all_41_2, simplifying with (19), (21)
% 18.87/3.33 | gives:
% 18.87/3.33 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_41_2) =
% 18.87/3.33 | v2 & function(all_41_2) = v1 & empty(all_41_2) = v0 & ( ~ (v1 = 0) |
% 18.87/3.33 | ~ (v0 = 0) | v2 = 0))
% 18.87/3.33 |
% 18.87/3.33 | GROUND_INST: instantiating (5) with all_41_2, all_41_3, all_41_1, simplifying
% 18.87/3.33 | with (18), (19), (21), (22) gives:
% 18.87/3.33 | (28) ? [v0: $i] : (cartesian_product2(all_41_3, all_41_3) = v0 &
% 18.87/3.33 | set_intersection2(all_41_2, v0) = all_41_1 & $i(v0) & $i(all_41_1))
% 18.87/3.33 |
% 18.87/3.33 | GROUND_INST: instantiating (dt_k2_wellord1) with all_41_2, all_41_3, all_41_1,
% 18.87/3.33 | simplifying with (18), (19), (22) gives:
% 18.87/3.33 | (29) ? [v0: any] : ? [v1: any] : (relation(all_41_1) = v1 &
% 18.87/3.33 | relation(all_41_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 18.87/3.33 |
% 18.87/3.33 | GROUND_INST: instantiating (8) with all_41_2, 0, simplifying with (19), (23)
% 18.87/3.33 | gives:
% 18.87/3.34 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_field(all_41_2) =
% 18.87/3.34 | v1 & relation(all_41_2) = v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | ( !
% 18.87/3.34 | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v3, v3) = v4) | ~
% 18.87/3.34 | $i(v3) | ? [v5: any] : ? [v6: any] : (in(v4, all_41_2) = v6
% 18.87/3.34 | & in(v3, v1) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3: $i] :
% 18.87/3.34 | ( ~ (in(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] :
% 18.87/3.34 | (ordered_pair(v3, v3) = v4 & in(v4, all_41_2) = 0 &
% 18.87/3.34 | $i(v4))))))
% 18.87/3.34 |
% 18.87/3.34 | GROUND_INST: instantiating (8) with all_41_1, all_41_0, simplifying with (20),
% 18.87/3.34 | (24) gives:
% 18.87/3.34 | (31) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i]
% 18.87/3.34 | : ? [v5: int] : (relation_field(all_41_1) = v1 & relation(all_41_1) =
% 18.87/3.34 | v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_41_0 = 0) | ( ! [v6:
% 18.87/3.34 | $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v6) = v7) | ~
% 18.87/3.34 | $i(v6) | ? [v8: any] : ? [v9: any] : (in(v7, all_41_1) =
% 18.87/3.34 | v9 & in(v6, v1) = v8 & ( ~ (v8 = 0) | v9 = 0))) & !
% 18.87/3.34 | [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6) | ? [v7: $i] :
% 18.87/3.34 | (ordered_pair(v6, v6) = v7 & in(v7, all_41_1) = 0 &
% 18.87/3.34 | $i(v7))))) & (all_41_0 = 0 | (v3 = 0 & ~ (v5 = 0) &
% 18.87/3.34 | ordered_pair(v2, v2) = v4 & in(v4, all_41_1) = v5 & in(v2,
% 18.87/3.34 | v1) = 0 & $i(v4))))))
% 18.87/3.34 |
% 18.87/3.34 | DELTA: instantiating (29) with fresh symbols all_51_0, all_51_1 gives:
% 18.87/3.34 | (32) relation(all_41_1) = all_51_0 & relation(all_41_2) = all_51_1 & ( ~
% 18.87/3.34 | (all_51_1 = 0) | all_51_0 = 0)
% 18.87/3.34 |
% 18.87/3.34 | ALPHA: (32) implies:
% 18.87/3.34 | (33) relation(all_41_2) = all_51_1
% 18.87/3.34 | (34) relation(all_41_1) = all_51_0
% 18.87/3.34 | (35) ~ (all_51_1 = 0) | all_51_0 = 0
% 18.87/3.34 |
% 18.87/3.34 | DELTA: instantiating (28) with fresh symbol all_53_0 gives:
% 18.87/3.34 | (36) cartesian_product2(all_41_3, all_41_3) = all_53_0 &
% 18.87/3.34 | set_intersection2(all_41_2, all_53_0) = all_41_1 & $i(all_53_0) &
% 18.87/3.34 | $i(all_41_1)
% 18.87/3.34 |
% 18.87/3.34 | ALPHA: (36) implies:
% 18.91/3.34 | (37) cartesian_product2(all_41_3, all_41_3) = all_53_0
% 18.91/3.34 |
% 18.91/3.34 | DELTA: instantiating (27) with fresh symbols all_55_0, all_55_1, all_55_2
% 18.91/3.34 | gives:
% 18.91/3.34 | (38) one_to_one(all_41_2) = all_55_0 & function(all_41_2) = all_55_1 &
% 18.91/3.34 | empty(all_41_2) = all_55_2 & ( ~ (all_55_1 = 0) | ~ (all_55_2 = 0) |
% 18.91/3.34 | all_55_0 = 0)
% 18.91/3.34 |
% 18.91/3.34 | ALPHA: (38) implies:
% 18.91/3.34 | (39) one_to_one(all_41_2) = all_55_0
% 18.91/3.34 |
% 18.91/3.34 | DELTA: instantiating (26) with fresh symbols all_77_0, all_77_1, all_77_2
% 18.91/3.34 | gives:
% 18.91/3.34 | (40) relation_dom(all_41_2) = all_77_1 & relation_field(all_41_2) =
% 18.91/3.34 | all_77_2 & relation_rng(all_41_2) = all_77_0 & set_union2(all_77_1,
% 18.91/3.34 | all_77_0) = all_77_2 & $i(all_77_0) & $i(all_77_1) & $i(all_77_2)
% 18.91/3.34 |
% 18.91/3.34 | ALPHA: (40) implies:
% 18.91/3.34 | (41) relation_field(all_41_2) = all_77_2
% 18.91/3.34 |
% 18.91/3.34 | DELTA: instantiating (30) with fresh symbols all_83_0, all_83_1, all_83_2
% 18.91/3.34 | gives:
% 18.91/3.34 | (42) relation_field(all_41_2) = all_83_1 & relation(all_41_2) = all_83_2 &
% 18.91/3.34 | $i(all_83_0) & $i(all_83_1) & ( ~ (all_83_2 = 0) | ( ! [v0: $i] : !
% 18.91/3.34 | [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2:
% 18.91/3.34 | any] : ? [v3: any] : (in(v1, all_41_2) = v3 & in(v0,
% 18.91/3.34 | all_83_1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : (
% 18.91/3.34 | ~ (in(v0, all_83_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.34 | (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 & $i(v1)))))
% 18.91/3.34 |
% 18.91/3.34 | ALPHA: (42) implies:
% 18.91/3.34 | (43) relation(all_41_2) = all_83_2
% 18.91/3.34 | (44) relation_field(all_41_2) = all_83_1
% 18.91/3.34 | (45) ~ (all_83_2 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 18.91/3.34 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1,
% 18.91/3.34 | all_41_2) = v3 & in(v0, all_83_1) = v2 & ( ~ (v2 = 0) | v3 =
% 18.91/3.34 | 0))) & ! [v0: $i] : ( ~ (in(v0, all_83_1) = 0) | ~ $i(v0) |
% 18.91/3.34 | ? [v1: $i] : (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 &
% 18.91/3.34 | $i(v1))))
% 18.91/3.34 |
% 18.91/3.34 | DELTA: instantiating (25) with fresh symbols all_89_0, all_89_1, all_89_2,
% 18.91/3.34 | all_89_3, all_89_4, all_89_5 gives:
% 18.91/3.35 | (46) reflexive(all_41_2) = all_89_5 & relation_field(all_41_2) = all_89_4 &
% 18.91/3.35 | $i(all_89_3) & $i(all_89_4) & ( ~ (all_89_5 = 0) | ( ! [v0: $i] : !
% 18.91/3.35 | [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2:
% 18.91/3.35 | any] : ? [v3: any] : (in(v1, all_41_2) = v3 & in(v0,
% 18.91/3.35 | all_89_4) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : (
% 18.91/3.35 | ~ (in(v0, all_89_4) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.35 | (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 & $i(v1))))) &
% 18.91/3.35 | (all_89_5 = 0 | (all_89_2 = 0 & ~ (all_89_0 = 0) &
% 18.91/3.35 | ordered_pair(all_89_3, all_89_3) = all_89_1 & in(all_89_1,
% 18.91/3.35 | all_41_2) = all_89_0 & in(all_89_3, all_89_4) = 0 &
% 18.91/3.35 | $i(all_89_1)))
% 18.91/3.35 |
% 18.91/3.35 | ALPHA: (46) implies:
% 18.91/3.35 | (47) relation_field(all_41_2) = all_89_4
% 18.91/3.35 | (48) reflexive(all_41_2) = all_89_5
% 18.91/3.35 | (49) ~ (all_89_5 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 18.91/3.35 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1,
% 18.91/3.35 | all_41_2) = v3 & in(v0, all_89_4) = v2 & ( ~ (v2 = 0) | v3 =
% 18.91/3.35 | 0))) & ! [v0: $i] : ( ~ (in(v0, all_89_4) = 0) | ~ $i(v0) |
% 18.91/3.35 | ? [v1: $i] : (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 &
% 18.91/3.35 | $i(v1))))
% 18.91/3.35 |
% 18.91/3.35 | DELTA: instantiating (31) with fresh symbols all_93_0, all_93_1, all_93_2,
% 18.91/3.35 | all_93_3, all_93_4, all_93_5 gives:
% 18.91/3.35 | (50) relation_field(all_41_1) = all_93_4 & relation(all_41_1) = all_93_5 &
% 18.91/3.35 | $i(all_93_3) & $i(all_93_4) & ( ~ (all_93_5 = 0) | (( ~ (all_41_0 = 0)
% 18.91/3.35 | | ( ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) |
% 18.91/3.35 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, all_41_1)
% 18.91/3.35 | = v3 & in(v0, all_93_4) = v2 & ( ~ (v2 = 0) | v3 = 0))) &
% 18.91/3.35 | ! [v0: $i] : ( ~ (in(v0, all_93_4) = 0) | ~ $i(v0) | ? [v1:
% 18.91/3.35 | $i] : (ordered_pair(v0, v0) = v1 & in(v1, all_41_1) = 0 &
% 18.91/3.35 | $i(v1))))) & (all_41_0 = 0 | (all_93_2 = 0 & ~ (all_93_0
% 18.91/3.35 | = 0) & ordered_pair(all_93_3, all_93_3) = all_93_1 &
% 18.91/3.35 | in(all_93_1, all_41_1) = all_93_0 & in(all_93_3, all_93_4) = 0
% 18.91/3.35 | & $i(all_93_1)))))
% 18.91/3.35 |
% 18.91/3.35 | ALPHA: (50) implies:
% 18.91/3.35 | (51) $i(all_93_3)
% 18.91/3.35 | (52) relation(all_41_1) = all_93_5
% 18.91/3.35 | (53) relation_field(all_41_1) = all_93_4
% 18.91/3.35 | (54) ~ (all_93_5 = 0) | (( ~ (all_41_0 = 0) | ( ! [v0: $i] : ! [v1: $i] :
% 18.91/3.35 | ( ~ (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 18.91/3.35 | [v3: any] : (in(v1, all_41_1) = v3 & in(v0, all_93_4) = v2 & (
% 18.91/3.35 | ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (in(v0,
% 18.91/3.35 | all_93_4) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.35 | (ordered_pair(v0, v0) = v1 & in(v1, all_41_1) = 0 & $i(v1)))))
% 18.91/3.35 | & (all_41_0 = 0 | (all_93_2 = 0 & ~ (all_93_0 = 0) &
% 18.91/3.35 | ordered_pair(all_93_3, all_93_3) = all_93_1 & in(all_93_1,
% 18.91/3.35 | all_41_1) = all_93_0 & in(all_93_3, all_93_4) = 0 &
% 18.91/3.35 | $i(all_93_1))))
% 18.91/3.35 |
% 18.91/3.35 | GROUND_INST: instantiating (11) with 0, all_83_2, all_41_2, simplifying with
% 18.91/3.35 | (21), (43) gives:
% 18.91/3.35 | (55) all_83_2 = 0
% 18.91/3.35 |
% 18.91/3.35 | GROUND_INST: instantiating (11) with all_51_1, all_83_2, all_41_2, simplifying
% 18.91/3.35 | with (33), (43) gives:
% 18.91/3.35 | (56) all_83_2 = all_51_1
% 18.91/3.35 |
% 18.91/3.35 | GROUND_INST: instantiating (11) with all_51_0, all_93_5, all_41_1, simplifying
% 18.91/3.35 | with (34), (52) gives:
% 18.91/3.35 | (57) all_93_5 = all_51_0
% 18.91/3.35 |
% 18.91/3.35 | GROUND_INST: instantiating (12) with all_83_1, all_89_4, all_41_2, simplifying
% 18.91/3.35 | with (44), (47) gives:
% 18.91/3.35 | (58) all_89_4 = all_83_1
% 18.91/3.35 |
% 18.91/3.35 | GROUND_INST: instantiating (12) with all_77_2, all_89_4, all_41_2, simplifying
% 18.91/3.35 | with (41), (47) gives:
% 18.91/3.35 | (59) all_89_4 = all_77_2
% 18.91/3.35 |
% 18.91/3.35 | GROUND_INST: instantiating (13) with 0, all_89_5, all_41_2, simplifying with
% 18.91/3.35 | (23), (48) gives:
% 18.91/3.35 | (60) all_89_5 = 0
% 18.91/3.35 |
% 18.91/3.35 | COMBINE_EQS: (58), (59) imply:
% 18.91/3.35 | (61) all_83_1 = all_77_2
% 18.91/3.35 |
% 18.91/3.35 | SIMP: (61) implies:
% 18.91/3.35 | (62) all_83_1 = all_77_2
% 18.91/3.35 |
% 18.91/3.35 | COMBINE_EQS: (55), (56) imply:
% 18.91/3.35 | (63) all_51_1 = 0
% 18.91/3.35 |
% 18.91/3.35 | BETA: splitting (35) gives:
% 18.91/3.35 |
% 18.91/3.35 | Case 1:
% 18.91/3.35 | |
% 18.91/3.35 | | (64) ~ (all_51_1 = 0)
% 18.91/3.35 | |
% 18.91/3.35 | | REDUCE: (63), (64) imply:
% 18.91/3.35 | | (65) $false
% 18.91/3.35 | |
% 18.91/3.35 | | CLOSE: (65) is inconsistent.
% 18.91/3.35 | |
% 18.91/3.35 | Case 2:
% 18.91/3.35 | |
% 18.91/3.35 | | (66) all_51_0 = 0
% 18.91/3.35 | |
% 18.91/3.35 | | COMBINE_EQS: (57), (66) imply:
% 18.91/3.35 | | (67) all_93_5 = 0
% 18.91/3.35 | |
% 18.91/3.35 | | BETA: splitting (45) gives:
% 18.91/3.35 | |
% 18.91/3.35 | | Case 1:
% 18.91/3.35 | | |
% 18.91/3.35 | | | (68) ~ (all_83_2 = 0)
% 18.91/3.35 | | |
% 18.91/3.35 | | | REDUCE: (55), (68) imply:
% 18.91/3.35 | | | (69) $false
% 18.91/3.35 | | |
% 18.91/3.35 | | | CLOSE: (69) is inconsistent.
% 18.91/3.35 | | |
% 18.91/3.35 | | Case 2:
% 18.91/3.35 | | |
% 18.91/3.36 | | | (70) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) | ~
% 18.91/3.36 | | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, all_41_2) = v3 &
% 18.91/3.36 | | | in(v0, all_83_1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i]
% 18.91/3.36 | | | : ( ~ (in(v0, all_83_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.36 | | | (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 & $i(v1)))
% 18.91/3.36 | | |
% 18.91/3.36 | | | ALPHA: (70) implies:
% 18.91/3.36 | | | (71) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) | ~
% 18.91/3.36 | | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, all_41_2) = v3 &
% 18.91/3.36 | | | in(v0, all_83_1) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 18.91/3.36 | | |
% 18.91/3.36 | | | BETA: splitting (54) gives:
% 18.91/3.36 | | |
% 18.91/3.36 | | | Case 1:
% 18.91/3.36 | | | |
% 18.91/3.36 | | | | (72) ~ (all_93_5 = 0)
% 18.91/3.36 | | | |
% 18.91/3.36 | | | | REDUCE: (67), (72) imply:
% 18.91/3.36 | | | | (73) $false
% 18.91/3.36 | | | |
% 18.91/3.36 | | | | CLOSE: (73) is inconsistent.
% 18.91/3.36 | | | |
% 18.91/3.36 | | | Case 2:
% 18.91/3.36 | | | |
% 18.91/3.36 | | | | (74) ( ~ (all_41_0 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 18.91/3.36 | | | | (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 18.91/3.36 | | | | ? [v3: any] : (in(v1, all_41_1) = v3 & in(v0, all_93_4) =
% 18.91/3.36 | | | | v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 18.91/3.36 | | | | (in(v0, all_93_4) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.36 | | | | (ordered_pair(v0, v0) = v1 & in(v1, all_41_1) = 0 &
% 18.91/3.36 | | | | $i(v1))))) & (all_41_0 = 0 | (all_93_2 = 0 & ~
% 18.91/3.36 | | | | (all_93_0 = 0) & ordered_pair(all_93_3, all_93_3) = all_93_1
% 18.91/3.36 | | | | & in(all_93_1, all_41_1) = all_93_0 & in(all_93_3, all_93_4)
% 18.91/3.36 | | | | = 0 & $i(all_93_1)))
% 18.91/3.36 | | | |
% 18.91/3.36 | | | | ALPHA: (74) implies:
% 18.91/3.36 | | | | (75) all_41_0 = 0 | (all_93_2 = 0 & ~ (all_93_0 = 0) &
% 18.91/3.36 | | | | ordered_pair(all_93_3, all_93_3) = all_93_1 & in(all_93_1,
% 18.91/3.36 | | | | all_41_1) = all_93_0 & in(all_93_3, all_93_4) = 0 &
% 18.91/3.36 | | | | $i(all_93_1))
% 18.91/3.36 | | | |
% 18.91/3.36 | | | | BETA: splitting (49) gives:
% 18.91/3.36 | | | |
% 18.91/3.36 | | | | Case 1:
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | | (76) ~ (all_89_5 = 0)
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | | REDUCE: (60), (76) imply:
% 18.91/3.36 | | | | | (77) $false
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | | CLOSE: (77) is inconsistent.
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | Case 2:
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | | (78) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) |
% 18.91/3.36 | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, all_41_2) =
% 18.91/3.36 | | | | | v3 & in(v0, all_89_4) = v2 & ( ~ (v2 = 0) | v3 = 0))) & !
% 18.91/3.36 | | | | | [v0: $i] : ( ~ (in(v0, all_89_4) = 0) | ~ $i(v0) | ? [v1:
% 18.91/3.36 | | | | | $i] : (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 &
% 18.91/3.36 | | | | | $i(v1)))
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | | ALPHA: (78) implies:
% 18.91/3.36 | | | | | (79) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) |
% 18.91/3.36 | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1, all_41_2) =
% 18.91/3.36 | | | | | v3 & in(v0, all_89_4) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | | BETA: splitting (75) gives:
% 18.91/3.36 | | | | |
% 18.91/3.36 | | | | | Case 1:
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | (80) all_41_0 = 0
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | REDUCE: (17), (80) imply:
% 18.91/3.36 | | | | | | (81) $false
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | CLOSE: (81) is inconsistent.
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | Case 2:
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | (82) all_93_2 = 0 & ~ (all_93_0 = 0) & ordered_pair(all_93_3,
% 18.91/3.36 | | | | | | all_93_3) = all_93_1 & in(all_93_1, all_41_1) = all_93_0 &
% 18.91/3.36 | | | | | | in(all_93_3, all_93_4) = 0 & $i(all_93_1)
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | ALPHA: (82) implies:
% 18.91/3.36 | | | | | | (83) ~ (all_93_0 = 0)
% 18.91/3.36 | | | | | | (84) $i(all_93_1)
% 18.91/3.36 | | | | | | (85) in(all_93_3, all_93_4) = 0
% 18.91/3.36 | | | | | | (86) in(all_93_1, all_41_1) = all_93_0
% 18.91/3.36 | | | | | | (87) ordered_pair(all_93_3, all_93_3) = all_93_1
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | GROUND_INST: instantiating (t16_wellord1) with all_93_1, all_41_3,
% 18.91/3.36 | | | | | | all_41_2, all_41_1, all_93_0, simplifying with (18),
% 18.91/3.36 | | | | | | (19), (22), (84), (86) gives:
% 18.91/3.36 | | | | | | (88) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 18.91/3.36 | | | | | | (cartesian_product2(all_41_3, all_41_3) = v2 &
% 18.91/3.36 | | | | | | relation(all_41_2) = v0 & in(all_93_1, v2) = v3 &
% 18.91/3.36 | | | | | | in(all_93_1, all_41_2) = v1 & $i(v2) & ( ~ (v0 = 0) | (( ~
% 18.91/3.36 | | | | | | (v3 = 0) | ~ (v1 = 0) | all_93_0 = 0) & ( ~
% 18.91/3.36 | | | | | | (all_93_0 = 0) | (v3 = 0 & v1 = 0)))))
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | GROUND_INST: instantiating (2) with all_41_2, all_55_0, simplifying
% 18.91/3.36 | | | | | | with (19), (39) gives:
% 18.91/3.36 | | | | | | (89) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 18.91/3.36 | | | | | | (relation(all_41_2) = v0 & function(all_41_2) = v2 &
% 18.91/3.36 | | | | | | empty(all_41_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 18.91/3.36 | | | | | | = 0) | all_55_0 = 0))
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | GROUND_INST: instantiating (79) with all_93_3, all_93_1, simplifying
% 18.91/3.36 | | | | | | with (51), (87) gives:
% 18.91/3.36 | | | | | | (90) ? [v0: any] : ? [v1: any] : (in(all_93_1, all_41_2) = v1 &
% 18.91/3.36 | | | | | | in(all_93_3, all_89_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | GROUND_INST: instantiating (71) with all_93_3, all_93_1, simplifying
% 18.91/3.36 | | | | | | with (51), (87) gives:
% 18.91/3.36 | | | | | | (91) ? [v0: any] : ? [v1: any] : (in(all_93_1, all_41_2) = v1 &
% 18.91/3.36 | | | | | | in(all_93_3, all_83_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | GROUND_INST: instantiating (3) with all_93_3, all_93_3, all_93_1,
% 18.91/3.36 | | | | | | simplifying with (51), (87) gives:
% 18.91/3.36 | | | | | | (92) ? [v0: $i] : ? [v1: $i] : (singleton(all_93_3) = v1 &
% 18.91/3.36 | | | | | | unordered_pair(v0, v1) = all_93_1 &
% 18.91/3.36 | | | | | | unordered_pair(all_93_3, all_93_3) = v0 & $i(v1) & $i(v0)
% 18.91/3.36 | | | | | | & $i(all_93_1))
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | GROUND_INST: instantiating (7) with all_41_2, all_77_2, simplifying
% 18.91/3.36 | | | | | | with (19), (41) gives:
% 18.91/3.36 | | | | | | (93) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] :
% 18.91/3.36 | | | | | | ? [v4: $i] : ? [v5: int] : (reflexive(all_41_2) = v1 &
% 18.91/3.36 | | | | | | relation(all_41_2) = v0 & $i(v2) & ( ~ (v0 = 0) | (( ~ (v1
% 18.91/3.36 | | | | | | = 0) | ( ! [v6: $i] : ! [v7: $i] : ( ~
% 18.91/3.36 | | | | | | (ordered_pair(v6, v6) = v7) | ~ $i(v6) | ?
% 18.91/3.36 | | | | | | [v8: any] : ? [v9: any] : (in(v7, all_41_2) =
% 18.91/3.36 | | | | | | v9 & in(v6, all_77_2) = v8 & ( ~ (v8 = 0) | v9
% 18.91/3.36 | | | | | | = 0))) & ! [v6: $i] : ( ~ (in(v6, all_77_2)
% 18.91/3.36 | | | | | | = 0) | ~ $i(v6) | ? [v7: $i] :
% 18.91/3.36 | | | | | | (ordered_pair(v6, v6) = v7 & in(v7, all_41_2) =
% 18.91/3.36 | | | | | | 0 & $i(v7))))) & (v1 = 0 | (v3 = 0 & ~ (v5 =
% 18.91/3.36 | | | | | | 0) & ordered_pair(v2, v2) = v4 & in(v4,
% 18.91/3.36 | | | | | | all_41_2) = v5 & in(v2, all_77_2) = 0 &
% 18.91/3.36 | | | | | | $i(v4))))))
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | GROUND_INST: instantiating (t19_wellord1) with all_93_3, all_41_3,
% 18.91/3.36 | | | | | | all_41_2, all_41_1, all_93_4, simplifying with (18),
% 18.91/3.36 | | | | | | (19), (22), (51), (53), (85) gives:
% 18.91/3.36 | | | | | | (94) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 18.91/3.36 | | | | | | (relation_field(all_41_2) = v1 & relation(all_41_2) = v0 &
% 18.91/3.36 | | | | | | in(all_93_3, v1) = v2 & in(all_93_3, all_41_3) = v3 &
% 18.91/3.36 | | | | | | $i(v1) & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 18.91/3.36 | | | | | |
% 18.91/3.36 | | | | | | DELTA: instantiating (91) with fresh symbols all_155_0, all_155_1
% 18.91/3.36 | | | | | | gives:
% 18.91/3.37 | | | | | | (95) in(all_93_1, all_41_2) = all_155_0 & in(all_93_3, all_83_1)
% 18.91/3.37 | | | | | | = all_155_1 & ( ~ (all_155_1 = 0) | all_155_0 = 0)
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | ALPHA: (95) implies:
% 18.91/3.37 | | | | | | (96) in(all_93_3, all_83_1) = all_155_1
% 18.91/3.37 | | | | | | (97) in(all_93_1, all_41_2) = all_155_0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | DELTA: instantiating (90) with fresh symbols all_161_0, all_161_1
% 18.91/3.37 | | | | | | gives:
% 18.91/3.37 | | | | | | (98) in(all_93_1, all_41_2) = all_161_0 & in(all_93_3, all_89_4)
% 18.91/3.37 | | | | | | = all_161_1 & ( ~ (all_161_1 = 0) | all_161_0 = 0)
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | ALPHA: (98) implies:
% 18.91/3.37 | | | | | | (99) in(all_93_3, all_89_4) = all_161_1
% 18.91/3.37 | | | | | | (100) in(all_93_1, all_41_2) = all_161_0
% 18.91/3.37 | | | | | | (101) ~ (all_161_1 = 0) | all_161_0 = 0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | DELTA: instantiating (92) with fresh symbols all_175_0, all_175_1
% 18.91/3.37 | | | | | | gives:
% 18.91/3.37 | | | | | | (102) singleton(all_93_3) = all_175_0 & unordered_pair(all_175_1,
% 18.91/3.37 | | | | | | all_175_0) = all_93_1 & unordered_pair(all_93_3,
% 18.91/3.37 | | | | | | all_93_3) = all_175_1 & $i(all_175_0) & $i(all_175_1) &
% 18.91/3.37 | | | | | | $i(all_93_1)
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | DELTA: instantiating (89) with fresh symbols all_179_0, all_179_1,
% 18.91/3.37 | | | | | | all_179_2 gives:
% 18.91/3.37 | | | | | | (103) relation(all_41_2) = all_179_2 & function(all_41_2) =
% 18.91/3.37 | | | | | | all_179_0 & empty(all_41_2) = all_179_1 & ( ~ (all_179_0 =
% 18.91/3.37 | | | | | | 0) | ~ (all_179_1 = 0) | ~ (all_179_2 = 0) | all_55_0
% 18.91/3.37 | | | | | | = 0)
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | ALPHA: (103) implies:
% 18.91/3.37 | | | | | | (104) relation(all_41_2) = all_179_2
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | DELTA: instantiating (94) with fresh symbols all_185_0, all_185_1,
% 18.91/3.37 | | | | | | all_185_2, all_185_3 gives:
% 18.91/3.37 | | | | | | (105) relation_field(all_41_2) = all_185_2 & relation(all_41_2) =
% 18.91/3.37 | | | | | | all_185_3 & in(all_93_3, all_185_2) = all_185_1 &
% 18.91/3.37 | | | | | | in(all_93_3, all_41_3) = all_185_0 & $i(all_185_2) & ( ~
% 18.91/3.37 | | | | | | (all_185_3 = 0) | (all_185_0 = 0 & all_185_1 = 0))
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | ALPHA: (105) implies:
% 18.91/3.37 | | | | | | (106) in(all_93_3, all_41_3) = all_185_0
% 18.91/3.37 | | | | | | (107) in(all_93_3, all_185_2) = all_185_1
% 18.91/3.37 | | | | | | (108) relation(all_41_2) = all_185_3
% 18.91/3.37 | | | | | | (109) relation_field(all_41_2) = all_185_2
% 18.91/3.37 | | | | | | (110) ~ (all_185_3 = 0) | (all_185_0 = 0 & all_185_1 = 0)
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | DELTA: instantiating (88) with fresh symbols all_189_0, all_189_1,
% 18.91/3.37 | | | | | | all_189_2, all_189_3 gives:
% 18.91/3.37 | | | | | | (111) cartesian_product2(all_41_3, all_41_3) = all_189_1 &
% 18.91/3.37 | | | | | | relation(all_41_2) = all_189_3 & in(all_93_1, all_189_1) =
% 18.91/3.37 | | | | | | all_189_0 & in(all_93_1, all_41_2) = all_189_2 &
% 18.91/3.37 | | | | | | $i(all_189_1) & ( ~ (all_189_3 = 0) | (( ~ (all_189_0 = 0)
% 18.91/3.37 | | | | | | | ~ (all_189_2 = 0) | all_93_0 = 0) & ( ~ (all_93_0
% 18.91/3.37 | | | | | | = 0) | (all_189_0 = 0 & all_189_2 = 0))))
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | ALPHA: (111) implies:
% 18.91/3.37 | | | | | | (112) $i(all_189_1)
% 18.91/3.37 | | | | | | (113) in(all_93_1, all_41_2) = all_189_2
% 18.91/3.37 | | | | | | (114) in(all_93_1, all_189_1) = all_189_0
% 18.91/3.37 | | | | | | (115) relation(all_41_2) = all_189_3
% 18.91/3.37 | | | | | | (116) cartesian_product2(all_41_3, all_41_3) = all_189_1
% 18.91/3.37 | | | | | | (117) ~ (all_189_3 = 0) | (( ~ (all_189_0 = 0) | ~ (all_189_2 =
% 18.91/3.37 | | | | | | 0) | all_93_0 = 0) & ( ~ (all_93_0 = 0) | (all_189_0
% 18.91/3.37 | | | | | | = 0 & all_189_2 = 0)))
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | DELTA: instantiating (93) with fresh symbols all_195_0, all_195_1,
% 18.91/3.37 | | | | | | all_195_2, all_195_3, all_195_4, all_195_5 gives:
% 18.91/3.37 | | | | | | (118) reflexive(all_41_2) = all_195_4 & relation(all_41_2) =
% 18.91/3.37 | | | | | | all_195_5 & $i(all_195_3) & ( ~ (all_195_5 = 0) | (( ~
% 18.91/3.37 | | | | | | (all_195_4 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 18.91/3.37 | | | | | | (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2:
% 18.91/3.37 | | | | | | any] : ? [v3: any] : (in(v1, all_41_2) = v3 &
% 18.91/3.37 | | | | | | in(v0, all_77_2) = v2 & ( ~ (v2 = 0) | v3 =
% 18.91/3.37 | | | | | | 0))) & ! [v0: $i] : ( ~ (in(v0, all_77_2) =
% 18.91/3.37 | | | | | | 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.37 | | | | | | (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0
% 18.91/3.37 | | | | | | & $i(v1))))) & (all_195_4 = 0 | (all_195_2 = 0
% 18.91/3.37 | | | | | | & ~ (all_195_0 = 0) & ordered_pair(all_195_3,
% 18.91/3.37 | | | | | | all_195_3) = all_195_1 & in(all_195_1, all_41_2)
% 18.91/3.37 | | | | | | = all_195_0 & in(all_195_3, all_77_2) = 0 &
% 18.91/3.37 | | | | | | $i(all_195_1)))))
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | ALPHA: (118) implies:
% 18.91/3.37 | | | | | | (119) relation(all_41_2) = all_195_5
% 18.91/3.37 | | | | | | (120) reflexive(all_41_2) = all_195_4
% 18.91/3.37 | | | | | | (121) ~ (all_195_5 = 0) | (( ~ (all_195_4 = 0) | ( ! [v0: $i] :
% 18.91/3.37 | | | | | | ! [v1: $i] : ( ~ (ordered_pair(v0, v0) = v1) | ~
% 18.91/3.37 | | | | | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v1,
% 18.91/3.37 | | | | | | all_41_2) = v3 & in(v0, all_77_2) = v2 & ( ~
% 18.91/3.37 | | | | | | (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 18.91/3.37 | | | | | | (in(v0, all_77_2) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.37 | | | | | | (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 &
% 18.91/3.37 | | | | | | $i(v1))))) & (all_195_4 = 0 | (all_195_2 = 0 & ~
% 18.91/3.37 | | | | | | (all_195_0 = 0) & ordered_pair(all_195_3, all_195_3)
% 18.91/3.37 | | | | | | = all_195_1 & in(all_195_1, all_41_2) = all_195_0 &
% 18.91/3.37 | | | | | | in(all_195_3, all_77_2) = 0 & $i(all_195_1))))
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | REDUCE: (59), (99) imply:
% 18.91/3.37 | | | | | | (122) in(all_93_3, all_77_2) = all_161_1
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | REDUCE: (62), (96) imply:
% 18.91/3.37 | | | | | | (123) in(all_93_3, all_77_2) = all_155_1
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (14) with all_155_1, all_161_1, all_77_2,
% 18.91/3.37 | | | | | | all_93_3, simplifying with (122), (123) gives:
% 18.91/3.37 | | | | | | (124) all_161_1 = all_155_1
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (14) with all_161_0, all_189_2, all_41_2,
% 18.91/3.37 | | | | | | all_93_1, simplifying with (100), (113) gives:
% 18.91/3.37 | | | | | | (125) all_189_2 = all_161_0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (14) with all_155_0, all_189_2, all_41_2,
% 18.91/3.37 | | | | | | all_93_1, simplifying with (97), (113) gives:
% 18.91/3.37 | | | | | | (126) all_189_2 = all_155_0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (11) with all_185_3, all_189_3, all_41_2,
% 18.91/3.37 | | | | | | simplifying with (108), (115) gives:
% 18.91/3.37 | | | | | | (127) all_189_3 = all_185_3
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (11) with all_179_2, all_189_3, all_41_2,
% 18.91/3.37 | | | | | | simplifying with (104), (115) gives:
% 18.91/3.37 | | | | | | (128) all_189_3 = all_179_2
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (11) with 0, all_195_5, all_41_2,
% 18.91/3.37 | | | | | | simplifying with (21), (119) gives:
% 18.91/3.37 | | | | | | (129) all_195_5 = 0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (11) with all_185_3, all_195_5, all_41_2,
% 18.91/3.37 | | | | | | simplifying with (108), (119) gives:
% 18.91/3.37 | | | | | | (130) all_195_5 = all_185_3
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (12) with all_77_2, all_185_2, all_41_2,
% 18.91/3.37 | | | | | | simplifying with (41), (109) gives:
% 18.91/3.37 | | | | | | (131) all_185_2 = all_77_2
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (15) with all_53_0, all_189_1, all_41_3,
% 18.91/3.37 | | | | | | all_41_3, simplifying with (37), (116) gives:
% 18.91/3.37 | | | | | | (132) all_189_1 = all_53_0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | GROUND_INST: instantiating (13) with 0, all_195_4, all_41_2,
% 18.91/3.37 | | | | | | simplifying with (23), (120) gives:
% 18.91/3.37 | | | | | | (133) all_195_4 = 0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | COMBINE_EQS: (129), (130) imply:
% 18.91/3.37 | | | | | | (134) all_185_3 = 0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | SIMP: (134) implies:
% 18.91/3.37 | | | | | | (135) all_185_3 = 0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | COMBINE_EQS: (125), (126) imply:
% 18.91/3.37 | | | | | | (136) all_161_0 = all_155_0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | COMBINE_EQS: (127), (128) imply:
% 18.91/3.37 | | | | | | (137) all_185_3 = all_179_2
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | SIMP: (137) implies:
% 18.91/3.37 | | | | | | (138) all_185_3 = all_179_2
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | COMBINE_EQS: (135), (138) imply:
% 18.91/3.37 | | | | | | (139) all_179_2 = 0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | COMBINE_EQS: (128), (139) imply:
% 18.91/3.37 | | | | | | (140) all_189_3 = 0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | REDUCE: (114), (132) imply:
% 18.91/3.37 | | | | | | (141) in(all_93_1, all_53_0) = all_189_0
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | REDUCE: (107), (131) imply:
% 18.91/3.37 | | | | | | (142) in(all_93_3, all_77_2) = all_185_1
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | REDUCE: (112), (132) imply:
% 18.91/3.37 | | | | | | (143) $i(all_53_0)
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | BETA: splitting (110) gives:
% 18.91/3.37 | | | | | |
% 18.91/3.37 | | | | | | Case 1:
% 18.91/3.37 | | | | | | |
% 18.91/3.37 | | | | | | | (144) ~ (all_185_3 = 0)
% 18.91/3.37 | | | | | | |
% 18.91/3.37 | | | | | | | REDUCE: (135), (144) imply:
% 18.91/3.38 | | | | | | | (145) $false
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | | CLOSE: (145) is inconsistent.
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | Case 2:
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | | (146) all_185_0 = 0 & all_185_1 = 0
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | | ALPHA: (146) implies:
% 18.91/3.38 | | | | | | | (147) all_185_1 = 0
% 18.91/3.38 | | | | | | | (148) all_185_0 = 0
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | | REDUCE: (142), (147) imply:
% 18.91/3.38 | | | | | | | (149) in(all_93_3, all_77_2) = 0
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | | REDUCE: (106), (148) imply:
% 18.91/3.38 | | | | | | | (150) in(all_93_3, all_41_3) = 0
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | | BETA: splitting (121) gives:
% 18.91/3.38 | | | | | | |
% 18.91/3.38 | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | | (151) ~ (all_195_5 = 0)
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | | REDUCE: (129), (151) imply:
% 18.91/3.38 | | | | | | | | (152) $false
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | | CLOSE: (152) is inconsistent.
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | | (153) ( ~ (all_195_4 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 18.91/3.38 | | | | | | | | (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2:
% 18.91/3.38 | | | | | | | | any] : ? [v3: any] : (in(v1, all_41_2) = v3 &
% 18.91/3.38 | | | | | | | | in(v0, all_77_2) = v2 & ( ~ (v2 = 0) | v3 =
% 18.91/3.38 | | | | | | | | 0))) & ! [v0: $i] : ( ~ (in(v0, all_77_2) =
% 18.91/3.38 | | | | | | | | 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.38 | | | | | | | | (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0
% 18.91/3.38 | | | | | | | | & $i(v1))))) & (all_195_4 = 0 | (all_195_2 = 0
% 18.91/3.38 | | | | | | | | & ~ (all_195_0 = 0) & ordered_pair(all_195_3,
% 18.91/3.38 | | | | | | | | all_195_3) = all_195_1 & in(all_195_1, all_41_2)
% 18.91/3.38 | | | | | | | | = all_195_0 & in(all_195_3, all_77_2) = 0 &
% 18.91/3.38 | | | | | | | | $i(all_195_1)))
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | | ALPHA: (153) implies:
% 18.91/3.38 | | | | | | | | (154) ~ (all_195_4 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( ~
% 18.91/3.38 | | | | | | | | (ordered_pair(v0, v0) = v1) | ~ $i(v0) | ? [v2:
% 18.91/3.38 | | | | | | | | any] : ? [v3: any] : (in(v1, all_41_2) = v3 &
% 18.91/3.38 | | | | | | | | in(v0, all_77_2) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 18.91/3.38 | | | | | | | | & ! [v0: $i] : ( ~ (in(v0, all_77_2) = 0) | ~
% 18.91/3.38 | | | | | | | | $i(v0) | ? [v1: $i] : (ordered_pair(v0, v0) = v1 &
% 18.91/3.38 | | | | | | | | in(v1, all_41_2) = 0 & $i(v1))))
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | | BETA: splitting (154) gives:
% 18.91/3.38 | | | | | | | |
% 18.91/3.38 | | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | (155) ~ (all_195_4 = 0)
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | REDUCE: (133), (155) imply:
% 18.91/3.38 | | | | | | | | | (156) $false
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | CLOSE: (156) is inconsistent.
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | (157) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0)
% 18.91/3.38 | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 18.91/3.38 | | | | | | | | | (in(v1, all_41_2) = v3 & in(v0, all_77_2) = v2 & (
% 18.91/3.38 | | | | | | | | | ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 18.91/3.38 | | | | | | | | | (in(v0, all_77_2) = 0) | ~ $i(v0) | ? [v1: $i] :
% 18.91/3.38 | | | | | | | | | (ordered_pair(v0, v0) = v1 & in(v1, all_41_2) = 0 &
% 18.91/3.38 | | | | | | | | | $i(v1)))
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | ALPHA: (157) implies:
% 18.91/3.38 | | | | | | | | | (158) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v0)
% 18.91/3.38 | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 18.91/3.38 | | | | | | | | | (in(v1, all_41_2) = v3 & in(v0, all_77_2) = v2 & (
% 18.91/3.38 | | | | | | | | | ~ (v2 = 0) | v3 = 0)))
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | GROUND_INST: instantiating (158) with all_93_3, all_93_1,
% 18.91/3.38 | | | | | | | | | simplifying with (51), (87) gives:
% 18.91/3.38 | | | | | | | | | (159) ? [v0: any] : ? [v1: any] : (in(all_93_1, all_41_2)
% 18.91/3.38 | | | | | | | | | = v1 & in(all_93_3, all_77_2) = v0 & ( ~ (v0 = 0) |
% 18.91/3.38 | | | | | | | | | v1 = 0))
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_238_0,
% 18.91/3.38 | | | | | | | | | all_238_1 gives:
% 18.91/3.38 | | | | | | | | | (160) in(all_93_1, all_41_2) = all_238_0 & in(all_93_3,
% 18.91/3.38 | | | | | | | | | all_77_2) = all_238_1 & ( ~ (all_238_1 = 0) |
% 18.91/3.38 | | | | | | | | | all_238_0 = 0)
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | ALPHA: (160) implies:
% 18.91/3.38 | | | | | | | | | (161) in(all_93_3, all_77_2) = all_238_1
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | GROUND_INST: instantiating (14) with all_155_1, all_238_1,
% 18.91/3.38 | | | | | | | | | all_77_2, all_93_3, simplifying with (123), (161)
% 18.91/3.38 | | | | | | | | | gives:
% 18.91/3.38 | | | | | | | | | (162) all_238_1 = all_155_1
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_238_1, all_77_2,
% 18.91/3.38 | | | | | | | | | all_93_3, simplifying with (149), (161) gives:
% 18.91/3.38 | | | | | | | | | (163) all_238_1 = 0
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | COMBINE_EQS: (162), (163) imply:
% 18.91/3.38 | | | | | | | | | (164) all_155_1 = 0
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | SIMP: (164) implies:
% 18.91/3.38 | | | | | | | | | (165) all_155_1 = 0
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | COMBINE_EQS: (124), (165) imply:
% 18.91/3.38 | | | | | | | | | (166) all_161_1 = 0
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | BETA: splitting (101) gives:
% 18.91/3.38 | | | | | | | | |
% 18.91/3.38 | | | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | (167) ~ (all_161_1 = 0)
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | REDUCE: (166), (167) imply:
% 18.91/3.38 | | | | | | | | | | (168) $false
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | CLOSE: (168) is inconsistent.
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | (169) all_161_0 = 0
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | COMBINE_EQS: (136), (169) imply:
% 18.91/3.38 | | | | | | | | | | (170) all_155_0 = 0
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | SIMP: (170) implies:
% 18.91/3.38 | | | | | | | | | | (171) all_155_0 = 0
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | COMBINE_EQS: (126), (171) imply:
% 18.91/3.38 | | | | | | | | | | (172) all_189_2 = 0
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | BETA: splitting (117) gives:
% 18.91/3.38 | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | (173) ~ (all_189_3 = 0)
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | REDUCE: (140), (173) imply:
% 18.91/3.38 | | | | | | | | | | | (174) $false
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | (175) ( ~ (all_189_0 = 0) | ~ (all_189_2 = 0) |
% 18.91/3.38 | | | | | | | | | | | all_93_0 = 0) & ( ~ (all_93_0 = 0) | (all_189_0
% 18.91/3.38 | | | | | | | | | | | = 0 & all_189_2 = 0))
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | ALPHA: (175) implies:
% 18.91/3.38 | | | | | | | | | | | (176) ~ (all_189_0 = 0) | ~ (all_189_2 = 0) | all_93_0
% 18.91/3.38 | | | | | | | | | | | = 0
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | BETA: splitting (176) gives:
% 18.91/3.38 | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | (177) ~ (all_189_0 = 0)
% 18.91/3.38 | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_93_3, all_93_3,
% 18.91/3.38 | | | | | | | | | | | | all_41_3, all_41_3, all_93_1, all_53_0, all_189_0,
% 18.91/3.38 | | | | | | | | | | | | simplifying with (18), (37), (51), (87), (141)
% 18.91/3.38 | | | | | | | | | | | | gives:
% 18.91/3.38 | | | | | | | | | | | | (178) all_189_0 = 0 | ? [v0: any] : ? [v1: any] :
% 18.91/3.38 | | | | | | | | | | | | (in(all_93_3, all_41_3) = v1 & in(all_93_3,
% 18.91/3.38 | | | | | | | | | | | | all_41_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 18.91/3.38 | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_93_1, all_53_0,
% 18.91/3.38 | | | | | | | | | | | | all_189_0, simplifying with (84), (141), (143)
% 18.91/3.38 | | | | | | | | | | | | gives:
% 18.91/3.38 | | | | | | | | | | | | (179) all_189_0 = 0 | ? [v0: any] : ? [v1: any] :
% 18.91/3.38 | | | | | | | | | | | | (element(all_93_1, all_53_0) = v0 &
% 18.91/3.38 | | | | | | | | | | | | empty(all_53_0) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 18.91/3.38 | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | BETA: splitting (178) gives:
% 18.91/3.38 | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | (180) all_189_0 = 0
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | REDUCE: (177), (180) imply:
% 18.91/3.38 | | | | | | | | | | | | | (181) $false
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | (182) ? [v0: any] : ? [v1: any] : (in(all_93_3,
% 18.91/3.38 | | | | | | | | | | | | | all_41_3) = v1 & in(all_93_3, all_41_3) = v0 &
% 18.91/3.38 | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0)))
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbols all_356_0,
% 18.91/3.38 | | | | | | | | | | | | | all_356_1 gives:
% 18.91/3.38 | | | | | | | | | | | | | (183) in(all_93_3, all_41_3) = all_356_0 & in(all_93_3,
% 18.91/3.38 | | | | | | | | | | | | | all_41_3) = all_356_1 & ( ~ (all_356_0 = 0) | ~
% 18.91/3.38 | | | | | | | | | | | | | (all_356_1 = 0))
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | ALPHA: (183) implies:
% 18.91/3.38 | | | | | | | | | | | | | (184) in(all_93_3, all_41_3) = all_356_1
% 18.91/3.38 | | | | | | | | | | | | | (185) in(all_93_3, all_41_3) = all_356_0
% 18.91/3.38 | | | | | | | | | | | | | (186) ~ (all_356_0 = 0) | ~ (all_356_1 = 0)
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | BETA: splitting (179) gives:
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | (187) all_189_0 = 0
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | REDUCE: (177), (187) imply:
% 18.91/3.38 | | | | | | | | | | | | | | (188) $false
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_356_0, all_41_3,
% 18.91/3.38 | | | | | | | | | | | | | | all_93_3, simplifying with (150), (185) gives:
% 18.91/3.38 | | | | | | | | | | | | | | (189) all_356_0 = 0
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_356_1, all_356_0,
% 18.91/3.38 | | | | | | | | | | | | | | all_41_3, all_93_3, simplifying with (184), (185)
% 18.91/3.38 | | | | | | | | | | | | | | gives:
% 18.91/3.38 | | | | | | | | | | | | | | (190) all_356_0 = all_356_1
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | COMBINE_EQS: (189), (190) imply:
% 18.91/3.38 | | | | | | | | | | | | | | (191) all_356_1 = 0
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | Case 1:
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | | (192) ~ (all_356_0 = 0)
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | | REDUCE: (189), (192) imply:
% 18.91/3.38 | | | | | | | | | | | | | | | (193) $false
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | | CLOSE: (193) is inconsistent.
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | | (194) ~ (all_356_1 = 0)
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | | REDUCE: (191), (194) imply:
% 18.91/3.38 | | | | | | | | | | | | | | | (195) $false
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 18.91/3.38 | | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | | End of split
% 18.91/3.38 | | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | | End of split
% 18.91/3.38 | | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | | End of split
% 18.91/3.38 | | | | | | | | | | | |
% 18.91/3.38 | | | | | | | | | | | Case 2:
% 18.91/3.38 | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | (196) ~ (all_189_2 = 0) | all_93_0 = 0
% 18.91/3.39 | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | BETA: splitting (196) gives:
% 18.91/3.39 | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | Case 1:
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | | (197) ~ (all_189_2 = 0)
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | | REDUCE: (172), (197) imply:
% 18.91/3.39 | | | | | | | | | | | | | (198) $false
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | | CLOSE: (198) is inconsistent.
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | Case 2:
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | | (199) all_93_0 = 0
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | | REDUCE: (83), (199) imply:
% 18.91/3.39 | | | | | | | | | | | | | (200) $false
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | | CLOSE: (200) is inconsistent.
% 18.91/3.39 | | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | | End of split
% 18.91/3.39 | | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | | End of split
% 18.91/3.39 | | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | | End of split
% 18.91/3.39 | | | | | | | | | |
% 18.91/3.39 | | | | | | | | | End of split
% 18.91/3.39 | | | | | | | | |
% 18.91/3.39 | | | | | | | | End of split
% 18.91/3.39 | | | | | | | |
% 18.91/3.39 | | | | | | | End of split
% 18.91/3.39 | | | | | | |
% 18.91/3.39 | | | | | | End of split
% 18.91/3.39 | | | | | |
% 18.91/3.39 | | | | | End of split
% 18.91/3.39 | | | | |
% 18.91/3.39 | | | | End of split
% 18.91/3.39 | | | |
% 18.91/3.39 | | | End of split
% 18.91/3.39 | | |
% 18.91/3.39 | | End of split
% 18.91/3.39 | |
% 18.91/3.39 | End of split
% 18.91/3.39 |
% 18.91/3.39 End of proof
% 18.91/3.39 % SZS output end Proof for theBenchmark
% 18.91/3.39
% 18.91/3.39 2773ms
%------------------------------------------------------------------------------