TSTP Solution File: SEU219+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU219+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:43:21 EDT 2023
% Result : Theorem 31.43s 5.03s
% Output : Proof 44.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU219+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 17:54:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/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 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 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 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
% 6.03/1.61 Prover 1: Preprocessing ...
% 6.03/1.66 Prover 4: Preprocessing ...
% 6.03/1.67 Prover 0: Preprocessing ...
% 6.03/1.67 Prover 2: Preprocessing ...
% 6.03/1.67 Prover 5: Preprocessing ...
% 6.03/1.67 Prover 3: Preprocessing ...
% 6.03/1.67 Prover 6: Preprocessing ...
% 18.86/3.33 Prover 1: Warning: ignoring some quantifiers
% 19.24/3.40 Prover 3: Warning: ignoring some quantifiers
% 19.96/3.45 Prover 3: Constructing countermodel ...
% 19.96/3.47 Prover 1: Constructing countermodel ...
% 20.25/3.50 Prover 5: Proving ...
% 20.58/3.54 Prover 6: Proving ...
% 24.64/4.13 Prover 2: Proving ...
% 25.55/4.29 Prover 4: Warning: ignoring some quantifiers
% 27.10/4.46 Prover 4: Constructing countermodel ...
% 30.65/4.92 Prover 0: Proving ...
% 31.43/5.03 Prover 3: proved (4394ms)
% 31.43/5.03
% 31.43/5.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.43/5.03
% 31.43/5.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 31.43/5.04 Prover 6: stopped
% 31.43/5.06 Prover 5: stopped
% 31.43/5.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 31.43/5.06 Prover 0: stopped
% 31.43/5.07 Prover 2: stopped
% 31.43/5.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 31.43/5.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 31.43/5.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.77/5.38 Prover 10: Preprocessing ...
% 34.38/5.39 Prover 13: Preprocessing ...
% 34.38/5.40 Prover 8: Preprocessing ...
% 34.38/5.40 Prover 11: Preprocessing ...
% 34.38/5.42 Prover 7: Preprocessing ...
% 35.44/5.74 Prover 10: Warning: ignoring some quantifiers
% 36.85/5.77 Prover 10: Constructing countermodel ...
% 38.36/5.92 Prover 7: Warning: ignoring some quantifiers
% 38.94/5.99 Prover 7: Constructing countermodel ...
% 38.94/6.00 Prover 13: Warning: ignoring some quantifiers
% 38.94/6.00 Prover 8: Warning: ignoring some quantifiers
% 38.94/6.04 Prover 8: Constructing countermodel ...
% 39.59/6.08 Prover 13: Constructing countermodel ...
% 42.80/6.55 Prover 10: Found proof (size 56)
% 42.80/6.55 Prover 10: proved (1475ms)
% 42.80/6.55 Prover 4: stopped
% 42.80/6.55 Prover 8: stopped
% 42.80/6.55 Prover 7: stopped
% 42.80/6.55 Prover 13: stopped
% 42.80/6.55 Prover 1: stopped
% 43.61/6.66 Prover 11: Warning: ignoring some quantifiers
% 43.61/6.72 Prover 11: Constructing countermodel ...
% 43.93/6.76 Prover 11: stopped
% 43.93/6.76
% 43.93/6.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.93/6.76
% 44.16/6.78 % SZS output start Proof for theBenchmark
% 44.16/6.80 Assumptions after simplification:
% 44.16/6.80 ---------------------------------
% 44.16/6.80
% 44.16/6.80 (d3_relat_1)
% 44.16/6.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 44.16/6.83 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 44.16/6.83 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) |
% 44.16/6.83 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 44.16/6.83 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i]
% 44.16/6.83 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 44.16/6.83 in(v4, v0) & ~ in(v4, v1)))
% 44.16/6.83
% 44.16/6.83 (d9_funct_1)
% 44.16/6.83 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 44.16/6.83 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | (relation_inverse(v0) =
% 44.16/6.83 v1 & $i(v1)))
% 44.16/6.83
% 44.16/6.83 (t25_relat_1)
% 44.16/6.83 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 44.16/6.83 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 44.16/6.83 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3)
% 44.16/6.83 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 44.16/6.83 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~
% 44.16/6.83 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) &
% 44.16/6.83 subset(v2, v5)))))
% 44.16/6.84
% 44.16/6.84 (t37_relat_1)
% 44.16/6.84 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse(v0) = v1) | ~ $i(v0) | ~
% 44.16/6.84 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_rng(v1) = v3 &
% 44.16/6.84 relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3 &
% 44.16/6.84 $i(v3) & $i(v2)))
% 44.16/6.84
% 44.16/6.84 (t46_relat_1)
% 44.16/6.84 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 44.16/6.84 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 44.16/6.84 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~
% 44.16/6.84 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4)
% 44.16/6.84 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5))))))
% 44.16/6.84
% 44.16/6.84 (t47_relat_1)
% 44.16/6.84 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 44.16/6.84 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 44.16/6.84 ! [v4: $i] : ( ~ (relation_composition(v3, v0) = v4) | ~ $i(v3) | ~
% 44.16/6.84 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_rng(v4)
% 44.16/6.84 = v1 & $i(v1)) | (relation_rng(v3) = v5 & $i(v5) & ~ subset(v2,
% 44.16/6.84 v5))))))
% 44.16/6.84
% 44.16/6.84 (t54_funct_1)
% 44.49/6.85 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 44.49/6.85 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 44.49/6.85 $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2) &
% 44.49/6.85 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v6 | ~
% 44.49/6.85 (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) =
% 44.49/6.85 v5) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) | ~ relation(v1) | ~
% 44.49/6.85 function(v1) | ~ in(v6, v3)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 44.49/6.85 : ! [v7: $i] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5)
% 44.49/6.85 = v6) | ~ (apply(v0, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) |
% 44.49/6.85 ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4: $i] : !
% 44.49/6.85 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (relation_dom(v1) = v4) | ~
% 44.49/6.85 (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ $i(v6) | ~ $i(v5) |
% 44.49/6.85 ~ $i(v1) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5,
% 44.49/6.85 v2)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 44.49/6.85 (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) =
% 44.49/6.85 v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) | ~ relation(v1) | ~
% 44.49/6.85 function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4: $i] : (v4 = v2 | ~
% 44.49/6.85 (relation_dom(v1) = v4) | ~ $i(v1) | ~ relation(v1) | ~ function(v1))
% 44.49/6.85 & ! [v4: $i] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ $i(v4) | ~
% 44.49/6.85 relation(v4) | ~ function(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 44.49/6.85 : ? [v8: $i] : ($i(v6) & $i(v5) & ((v8 = v5 & apply(v0, v6) = v5 &
% 44.49/6.85 in(v6, v3) & ( ~ in(v5, v2) | ( ~ (v7 = v6) & apply(v4, v5) = v7 &
% 44.49/6.85 $i(v7)))) | (v7 = v6 & apply(v4, v5) = v6 & in(v5, v2) & ( ~
% 44.49/6.85 in(v6, v3) | ( ~ (v8 = v5) & apply(v0, v6) = v8 & $i(v8)))))))))
% 44.49/6.85
% 44.49/6.85 (t55_funct_1)
% 44.49/6.86 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 44.49/6.86 $i] : (function_inverse(v0) = v2 & $i(v2) & $i(v0) & one_to_one(v0) &
% 44.49/6.86 relation(v0) & function(v0) & (( ~ (v5 = v4) & relation_rng(v2) = v5 &
% 44.49/6.86 relation_dom(v0) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = v1) &
% 44.49/6.86 relation_rng(v0) = v1 & relation_dom(v2) = v3 & $i(v3) & $i(v1))))
% 44.49/6.86
% 44.49/6.86 (function-axioms)
% 44.49/6.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 44.49/6.87 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 44.49/6.87 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 44.49/6.87 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) =
% 44.49/6.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 44.49/6.87 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & !
% 44.49/6.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.49/6.87 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) =
% 44.49/6.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 44.49/6.87 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 44.49/6.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 44.49/6.87 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) &
% 44.49/6.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.49/6.87 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 44.49/6.87 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 44.49/6.87 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 44.49/6.87 : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 44.49/6.87 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 44.49/6.87 : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~
% 44.49/6.87 (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 44.49/6.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 44.49/6.87 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 44.49/6.87 ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~
% 44.49/6.87 (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 44.49/6.87 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1)
% 44.49/6.87 | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 44.49/6.87 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 44.49/6.87 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 44.49/6.87 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 44.49/6.87 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 44.49/6.87 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 44.49/6.87 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 44.49/6.87 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 44.49/6.87 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.49/6.87 (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i]
% 44.49/6.87 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~
% 44.49/6.87 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 44.49/6.87 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & !
% 44.49/6.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 44.49/6.87 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 44.49/6.87 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1:
% 44.49/6.87 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~
% 44.49/6.87 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 44.49/6.87 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i]
% 44.49/6.87 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 44.49/6.87 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 44.49/6.87 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1:
% 44.49/6.87 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) =
% 44.49/6.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.49/6.87 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 44.49/6.87
% 44.49/6.87 Further assumptions not needed in the proof:
% 44.49/6.87 --------------------------------------------
% 44.59/6.87 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1,
% 44.59/6.87 cc2_funct_1, commutativity_k2_tarski, commutativity_k2_xboole_0,
% 44.59/6.87 commutativity_k3_xboole_0, d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1,
% 44.59/6.87 d13_relat_1, d14_relat_1, d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0,
% 44.59/6.87 d1_zfmisc_1, d2_relat_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1,
% 44.59/6.87 d3_tarski, d3_xboole_0, d4_funct_1, d4_relat_1, d4_subset_1, d4_tarski,
% 44.59/6.87 d4_xboole_0, d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1,
% 44.59/6.87 d7_xboole_0, d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k10_relat_1,
% 44.59/6.87 dt_k1_funct_1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0,
% 44.59/6.87 dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski,
% 44.59/6.87 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski,
% 44.59/6.87 dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1,
% 44.59/6.87 dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1,
% 44.59/6.87 dt_k7_setfam_1, dt_k8_relat_1, dt_k9_relat_1, dt_m1_subset_1,
% 44.59/6.87 existence_m1_subset_1, fc10_relat_1, fc11_relat_1, fc12_relat_1, fc1_funct_1,
% 44.59/6.87 fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_relat_1,
% 44.59/6.87 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_subset_1, fc3_xboole_0,
% 44.59/6.87 fc4_relat_1, fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1,
% 44.59/6.87 fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 44.59/6.87 involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 44.59/6.87 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 44.59/6.87 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 44.59/6.87 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 44.59/6.87 rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1,
% 44.59/6.87 rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, redefinition_k5_setfam_1,
% 44.59/6.87 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski,
% 44.59/6.87 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1,
% 44.59/6.87 t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1,
% 44.59/6.87 t12_xboole_1, t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1,
% 44.59/6.87 t145_relat_1, t146_relat_1, t160_relat_1, t166_relat_1, t167_relat_1,
% 44.59/6.87 t174_relat_1, t178_relat_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset,
% 44.59/6.87 t1_xboole_1, t1_zfmisc_1, t20_relat_1, t21_funct_1, t21_relat_1, t22_funct_1,
% 44.59/6.87 t23_funct_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, t2_tarski,
% 44.59/6.87 t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1, t34_funct_1, t35_funct_1,
% 44.59/6.87 t36_xboole_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1,
% 44.59/6.87 t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1,
% 44.59/6.87 t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_setfam_1,
% 44.59/6.87 t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset,
% 44.59/6.87 t4_xboole_0, t50_subset_1, t54_subset_1, t56_relat_1, t5_subset, t60_relat_1,
% 44.59/6.87 t60_xboole_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1,
% 44.59/6.87 t69_enumset1, t6_boole, t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole,
% 44.59/6.87 t7_xboole_1, t83_xboole_1, t86_relat_1, t88_relat_1, t8_boole, t8_funct_1,
% 44.59/6.87 t8_xboole_1, t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1,
% 44.59/6.87 t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 44.59/6.87
% 44.59/6.87 Those formulas are unsatisfiable:
% 44.59/6.87 ---------------------------------
% 44.59/6.87
% 44.59/6.87 Begin of proof
% 44.59/6.87 |
% 44.59/6.87 | ALPHA: (d3_relat_1) implies:
% 44.59/6.87 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 44.59/6.87 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 44.59/6.87 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 44.59/6.87 | in(v4, v0) & ~ in(v4, v1)))
% 44.59/6.87 |
% 44.59/6.87 | ALPHA: (function-axioms) implies:
% 44.59/6.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.59/6.88 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 44.59/6.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.59/6.88 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 44.59/6.88 |
% 44.59/6.88 | DELTA: instantiating (t55_funct_1) with fresh symbols all_243_0, all_243_1,
% 44.59/6.88 | all_243_2, all_243_3, all_243_4, all_243_5 gives:
% 44.59/6.88 | (4) function_inverse(all_243_5) = all_243_3 & $i(all_243_3) & $i(all_243_5)
% 44.59/6.88 | & one_to_one(all_243_5) & relation(all_243_5) & function(all_243_5) &
% 44.59/6.88 | (( ~ (all_243_0 = all_243_1) & relation_rng(all_243_3) = all_243_0 &
% 44.59/6.88 | relation_dom(all_243_5) = all_243_1 & $i(all_243_0) &
% 44.59/6.88 | $i(all_243_1)) | ( ~ (all_243_2 = all_243_4) &
% 44.59/6.88 | relation_rng(all_243_5) = all_243_4 & relation_dom(all_243_3) =
% 44.59/6.88 | all_243_2 & $i(all_243_2) & $i(all_243_4)))
% 44.59/6.88 |
% 44.59/6.88 | ALPHA: (4) implies:
% 44.59/6.88 | (5) function(all_243_5)
% 44.59/6.88 | (6) relation(all_243_5)
% 44.59/6.88 | (7) one_to_one(all_243_5)
% 44.59/6.88 | (8) $i(all_243_5)
% 44.59/6.88 | (9) function_inverse(all_243_5) = all_243_3
% 44.59/6.88 | (10) ( ~ (all_243_0 = all_243_1) & relation_rng(all_243_3) = all_243_0 &
% 44.59/6.88 | relation_dom(all_243_5) = all_243_1 & $i(all_243_0) & $i(all_243_1))
% 44.59/6.88 | | ( ~ (all_243_2 = all_243_4) & relation_rng(all_243_5) = all_243_4 &
% 44.59/6.88 | relation_dom(all_243_3) = all_243_2 & $i(all_243_2) & $i(all_243_4))
% 44.59/6.88 |
% 44.59/6.88 | GROUND_INST: instantiating (1) with all_243_5, all_243_5, simplifying with
% 44.59/6.88 | (6), (8) gives:
% 44.59/6.88 | (11) subset(all_243_5, all_243_5)
% 44.59/6.88 |
% 44.59/6.88 | GROUND_INST: instantiating (t54_funct_1) with all_243_5, all_243_3,
% 44.59/6.88 | simplifying with (5), (6), (7), (8), (9) gives:
% 44.59/6.89 | (12) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_243_5) = v0 &
% 44.59/6.89 | relation_dom(all_243_5) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 44.59/6.89 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 44.59/6.89 | (relation_dom(all_243_3) = v2) | ~ (apply(all_243_3, v3) = v5) |
% 44.59/6.89 | ~ (apply(all_243_5, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 44.59/6.89 | $i(all_243_3) | ~ relation(all_243_3) | ~ function(all_243_3) |
% 44.59/6.89 | ~ in(v4, v1)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 44.59/6.89 | $i] : (v5 = v3 | ~ (relation_dom(all_243_3) = v2) | ~
% 44.59/6.89 | (apply(all_243_3, v3) = v4) | ~ (apply(all_243_5, v4) = v5) | ~
% 44.59/6.89 | $i(v4) | ~ $i(v3) | ~ $i(all_243_3) | ~ relation(all_243_3) |
% 44.59/6.89 | ~ function(all_243_3) | ~ in(v3, v0)) & ! [v2: $i] : ! [v3: $i]
% 44.59/6.89 | : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(all_243_3) = v2) |
% 44.59/6.89 | ~ (apply(all_243_3, v3) = v5) | ~ (apply(all_243_5, v4) = v3) |
% 44.59/6.89 | ~ $i(v4) | ~ $i(v3) | ~ $i(all_243_3) | ~ relation(all_243_3) |
% 44.59/6.89 | ~ function(all_243_3) | ~ in(v4, v1) | in(v3, v0)) & ! [v2: $i]
% 44.59/6.89 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 44.59/6.89 | (relation_dom(all_243_3) = v2) | ~ (apply(all_243_3, v3) = v4) |
% 44.59/6.89 | ~ (apply(all_243_5, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 44.59/6.89 | $i(all_243_3) | ~ relation(all_243_3) | ~ function(all_243_3) |
% 44.59/6.89 | ~ in(v3, v0) | in(v4, v1)) & ! [v2: $i] : (v2 = v0 | ~
% 44.59/6.89 | (relation_dom(all_243_3) = v2) | ~ $i(all_243_3) | ~
% 44.59/6.89 | relation(all_243_3) | ~ function(all_243_3)) & ! [v2: any] : (v2
% 44.59/6.89 | = all_243_3 | ~ (relation_dom(v2) = v0) | ~ $i(v2) | ~
% 44.59/6.89 | relation(v2) | ~ function(v2) | ? [v3: $i] : ? [v4: $i] : ?
% 44.59/6.89 | [v5: $i] : ? [v6: $i] : ($i(v4) & $i(v3) & ((v6 = v3 &
% 44.59/6.89 | apply(all_243_5, v4) = v3 & in(v4, v1) & ( ~ in(v3, v0) | (
% 44.59/6.89 | ~ (v5 = v4) & apply(v2, v3) = v5 & $i(v5)))) | (v5 = v4
% 44.59/6.89 | & apply(v2, v3) = v4 & in(v3, v0) & ( ~ in(v4, v1) | ( ~ (v6
% 44.59/6.89 | = v3) & apply(all_243_5, v4) = v6 & $i(v6))))))))
% 44.59/6.89 |
% 44.59/6.89 | GROUND_INST: instantiating (d9_funct_1) with all_243_5, all_243_3, simplifying
% 44.59/6.89 | with (5), (6), (7), (8), (9) gives:
% 44.59/6.89 | (13) relation_inverse(all_243_5) = all_243_3 & $i(all_243_3)
% 44.59/6.89 |
% 44.59/6.89 | ALPHA: (13) implies:
% 44.59/6.89 | (14) relation_inverse(all_243_5) = all_243_3
% 44.59/6.89 |
% 44.59/6.89 | DELTA: instantiating (12) with fresh symbols all_280_0, all_280_1 gives:
% 44.59/6.89 | (15) relation_rng(all_243_5) = all_280_1 & relation_dom(all_243_5) =
% 44.59/6.89 | all_280_0 & $i(all_280_0) & $i(all_280_1) & ! [v0: $i] : ! [v1: $i]
% 44.59/6.89 | : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (relation_dom(all_243_3) =
% 44.59/6.89 | v0) | ~ (apply(all_243_3, v1) = v3) | ~ (apply(all_243_5, v2) =
% 44.59/6.89 | v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(all_243_3) | ~
% 44.59/6.89 | relation(all_243_3) | ~ function(all_243_3) | ~ in(v2, all_280_0))
% 44.59/6.89 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 |
% 44.59/6.89 | ~ (relation_dom(all_243_3) = v0) | ~ (apply(all_243_3, v1) = v2) |
% 44.59/6.89 | ~ (apply(all_243_5, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 44.59/6.89 | $i(all_243_3) | ~ relation(all_243_3) | ~ function(all_243_3) | ~
% 44.59/6.89 | in(v1, all_280_1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 44.59/6.89 | [v3: $i] : ( ~ (relation_dom(all_243_3) = v0) | ~ (apply(all_243_3,
% 44.59/6.89 | v1) = v3) | ~ (apply(all_243_5, v2) = v1) | ~ $i(v2) | ~
% 44.59/6.89 | $i(v1) | ~ $i(all_243_3) | ~ relation(all_243_3) | ~
% 44.59/6.89 | function(all_243_3) | ~ in(v2, all_280_0) | in(v1, all_280_1)) & !
% 44.59/6.89 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 44.59/6.89 | (relation_dom(all_243_3) = v0) | ~ (apply(all_243_3, v1) = v2) | ~
% 44.59/6.89 | (apply(all_243_5, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 44.59/6.89 | $i(all_243_3) | ~ relation(all_243_3) | ~ function(all_243_3) | ~
% 44.59/6.89 | in(v1, all_280_1) | in(v2, all_280_0)) & ! [v0: int] : (v0 =
% 44.59/6.89 | all_280_1 | ~ (relation_dom(all_243_3) = v0) | ~ $i(all_243_3) |
% 44.59/6.89 | ~ relation(all_243_3) | ~ function(all_243_3)) & ! [v0: any] : (v0
% 44.59/6.89 | = all_243_3 | ~ (relation_dom(v0) = all_280_1) | ~ $i(v0) | ~
% 44.59/6.89 | relation(v0) | ~ function(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3:
% 44.59/6.89 | $i] : ? [v4: $i] : ($i(v2) & $i(v1) & ((v4 = v1 &
% 44.59/6.89 | apply(all_243_5, v2) = v1 & in(v2, all_280_0) & ( ~ in(v1,
% 44.59/6.89 | all_280_1) | ( ~ (v3 = v2) & apply(v0, v1) = v3 &
% 44.59/6.89 | $i(v3)))) | (v3 = v2 & apply(v0, v1) = v2 & in(v1,
% 44.59/6.89 | all_280_1) & ( ~ in(v2, all_280_0) | ( ~ (v4 = v1) &
% 44.59/6.89 | apply(all_243_5, v2) = v4 & $i(v4)))))))
% 44.59/6.89 |
% 44.59/6.89 | ALPHA: (15) implies:
% 44.59/6.89 | (16) relation_dom(all_243_5) = all_280_0
% 44.59/6.89 | (17) relation_rng(all_243_5) = all_280_1
% 44.59/6.89 |
% 44.59/6.90 | GROUND_INST: instantiating (t47_relat_1) with all_243_5, all_280_1,
% 44.59/6.90 | simplifying with (6), (8), (17) gives:
% 44.59/6.90 | (18) ? [v0: $i] : (relation_dom(all_243_5) = v0 & $i(v0) & ! [v1: $i] :
% 44.59/6.90 | ! [v2: $i] : ( ~ (relation_composition(v1, all_243_5) = v2) | ~
% 44.59/6.90 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 =
% 44.59/6.90 | all_280_1 & relation_rng(v2) = all_280_1 & $i(all_280_1)) |
% 44.59/6.90 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3)))))
% 44.59/6.90 |
% 44.59/6.90 | GROUND_INST: instantiating (t46_relat_1) with all_243_5, all_280_1,
% 44.59/6.90 | simplifying with (6), (8), (17) gives:
% 44.59/6.90 | (19) ? [v0: $i] : (relation_dom(all_243_5) = v0 & $i(v0) & ! [v1: $i] :
% 44.59/6.90 | ! [v2: $i] : ( ~ (relation_composition(all_243_5, v1) = v2) | ~
% 44.59/6.90 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 &
% 44.59/6.90 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~
% 44.59/6.90 | subset(all_280_1, v3)))))
% 44.59/6.90 |
% 44.59/6.90 | GROUND_INST: instantiating (t25_relat_1) with all_243_5, all_280_1,
% 44.59/6.90 | simplifying with (6), (8), (17) gives:
% 44.59/6.90 | (20) ? [v0: $i] : (relation_dom(all_243_5) = v0 & $i(v0) & ! [v1: $i] :
% 44.59/6.90 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 44.59/6.90 | subset(all_243_5, v1) | ~ relation(v1) | subset(all_280_1, v2)) &
% 44.59/6.90 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1)
% 44.59/6.90 | | ~ subset(all_243_5, v1) | ~ relation(v1) | ? [v3: $i] :
% 44.59/6.90 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 44.59/6.90 |
% 44.59/6.90 | GROUND_INST: instantiating (t37_relat_1) with all_243_5, all_243_3,
% 44.59/6.90 | simplifying with (6), (8), (14) gives:
% 44.59/6.90 | (21) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_243_3) = v1 &
% 44.59/6.90 | relation_rng(all_243_5) = v0 & relation_dom(all_243_3) = v0 &
% 44.59/6.90 | relation_dom(all_243_5) = v1 & $i(v1) & $i(v0))
% 44.59/6.90 |
% 44.59/6.90 | DELTA: instantiating (21) with fresh symbols all_293_0, all_293_1 gives:
% 44.59/6.90 | (22) relation_rng(all_243_3) = all_293_0 & relation_rng(all_243_5) =
% 44.59/6.90 | all_293_1 & relation_dom(all_243_3) = all_293_1 &
% 44.59/6.90 | relation_dom(all_243_5) = all_293_0 & $i(all_293_0) & $i(all_293_1)
% 44.59/6.90 |
% 44.59/6.90 | ALPHA: (22) implies:
% 44.59/6.90 | (23) relation_dom(all_243_5) = all_293_0
% 44.59/6.90 | (24) relation_dom(all_243_3) = all_293_1
% 44.59/6.90 | (25) relation_rng(all_243_5) = all_293_1
% 44.59/6.90 | (26) relation_rng(all_243_3) = all_293_0
% 44.59/6.90 |
% 44.59/6.90 | DELTA: instantiating (19) with fresh symbol all_296_0 gives:
% 44.59/6.90 | (27) relation_dom(all_243_5) = all_296_0 & $i(all_296_0) & ! [v0: $i] : !
% 44.59/6.90 | [v1: $i] : ( ~ (relation_composition(all_243_5, v0) = v1) | ~ $i(v0)
% 44.59/6.90 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_296_0 &
% 44.59/6.90 | relation_dom(v1) = all_296_0) | (relation_dom(v0) = v2 & $i(v2)
% 44.59/6.90 | & ~ subset(all_280_1, v2))))
% 44.59/6.90 |
% 44.59/6.90 | ALPHA: (27) implies:
% 44.59/6.90 | (28) relation_dom(all_243_5) = all_296_0
% 44.59/6.90 |
% 44.59/6.90 | DELTA: instantiating (18) with fresh symbol all_299_0 gives:
% 44.59/6.90 | (29) relation_dom(all_243_5) = all_299_0 & $i(all_299_0) & ! [v0: $i] : !
% 44.59/6.90 | [v1: $i] : ( ~ (relation_composition(v0, all_243_5) = v1) | ~ $i(v0)
% 44.59/6.90 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_280_1 &
% 44.59/6.90 | relation_rng(v1) = all_280_1 & $i(all_280_1)) |
% 44.59/6.90 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_299_0, v2))))
% 44.59/6.90 |
% 44.59/6.90 | ALPHA: (29) implies:
% 44.59/6.90 | (30) relation_dom(all_243_5) = all_299_0
% 44.59/6.90 |
% 44.59/6.90 | DELTA: instantiating (20) with fresh symbol all_302_0 gives:
% 44.59/6.91 | (31) relation_dom(all_243_5) = all_302_0 & $i(all_302_0) & ! [v0: $i] : !
% 44.59/6.91 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 44.59/6.91 | subset(all_243_5, v0) | ~ relation(v0) | subset(all_280_1, v1)) &
% 44.59/6.91 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 44.59/6.91 | ~ subset(all_243_5, v0) | ~ relation(v0) | ? [v2: $i] :
% 44.59/6.91 | (relation_dom(v0) = v2 & $i(v2) & subset(all_302_0, v2)))
% 44.59/6.91 |
% 44.59/6.91 | ALPHA: (31) implies:
% 44.59/6.91 | (32) relation_dom(all_243_5) = all_302_0
% 44.59/6.91 | (33) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 44.59/6.91 | ~ subset(all_243_5, v0) | ~ relation(v0) | ? [v2: $i] :
% 44.59/6.91 | (relation_dom(v0) = v2 & $i(v2) & subset(all_302_0, v2)))
% 44.59/6.91 |
% 44.59/6.91 | GROUND_INST: instantiating (33) with all_243_5, all_280_1, simplifying with
% 44.59/6.91 | (6), (8), (11), (17) gives:
% 44.59/6.91 | (34) ? [v0: $i] : (relation_dom(all_243_5) = v0 & $i(v0) &
% 44.59/6.91 | subset(all_302_0, v0))
% 44.59/6.91 |
% 44.59/6.91 | DELTA: instantiating (34) with fresh symbol all_306_0 gives:
% 44.59/6.91 | (35) relation_dom(all_243_5) = all_306_0 & $i(all_306_0) &
% 44.59/6.91 | subset(all_302_0, all_306_0)
% 44.59/6.91 |
% 44.59/6.91 | ALPHA: (35) implies:
% 44.59/6.91 | (36) relation_dom(all_243_5) = all_306_0
% 44.59/6.91 |
% 44.59/6.91 | GROUND_INST: instantiating (2) with all_280_0, all_299_0, all_243_5,
% 44.59/6.91 | simplifying with (16), (30) gives:
% 44.59/6.91 | (37) all_299_0 = all_280_0
% 44.59/6.91 |
% 44.59/6.91 | GROUND_INST: instantiating (2) with all_296_0, all_299_0, all_243_5,
% 44.59/6.91 | simplifying with (28), (30) gives:
% 44.59/6.91 | (38) all_299_0 = all_296_0
% 44.59/6.91 |
% 44.59/6.91 | GROUND_INST: instantiating (2) with all_299_0, all_302_0, all_243_5,
% 44.59/6.91 | simplifying with (30), (32) gives:
% 44.59/6.91 | (39) all_302_0 = all_299_0
% 44.59/6.91 |
% 44.59/6.91 | GROUND_INST: instantiating (2) with all_302_0, all_306_0, all_243_5,
% 44.59/6.91 | simplifying with (32), (36) gives:
% 44.59/6.91 | (40) all_306_0 = all_302_0
% 44.59/6.91 |
% 44.59/6.91 | GROUND_INST: instantiating (2) with all_293_0, all_306_0, all_243_5,
% 44.59/6.91 | simplifying with (23), (36) gives:
% 44.59/6.91 | (41) all_306_0 = all_293_0
% 44.59/6.91 |
% 44.59/6.91 | GROUND_INST: instantiating (3) with all_280_1, all_293_1, all_243_5,
% 44.59/6.91 | simplifying with (17), (25) gives:
% 44.59/6.91 | (42) all_293_1 = all_280_1
% 44.59/6.91 |
% 44.59/6.91 | COMBINE_EQS: (40), (41) imply:
% 44.59/6.91 | (43) all_302_0 = all_293_0
% 44.59/6.91 |
% 44.59/6.91 | SIMP: (43) implies:
% 44.59/6.91 | (44) all_302_0 = all_293_0
% 44.59/6.91 |
% 44.59/6.91 | COMBINE_EQS: (39), (44) imply:
% 44.59/6.91 | (45) all_299_0 = all_293_0
% 44.59/6.91 |
% 44.59/6.91 | SIMP: (45) implies:
% 44.59/6.91 | (46) all_299_0 = all_293_0
% 44.59/6.91 |
% 44.59/6.91 | COMBINE_EQS: (38), (46) imply:
% 44.59/6.91 | (47) all_296_0 = all_293_0
% 44.59/6.91 |
% 44.59/6.91 | COMBINE_EQS: (37), (38) imply:
% 44.59/6.91 | (48) all_296_0 = all_280_0
% 44.59/6.91 |
% 44.59/6.91 | COMBINE_EQS: (47), (48) imply:
% 44.59/6.91 | (49) all_293_0 = all_280_0
% 44.59/6.91 |
% 44.59/6.91 | REDUCE: (26), (49) imply:
% 44.59/6.91 | (50) relation_rng(all_243_3) = all_280_0
% 44.59/6.91 |
% 44.59/6.91 | REDUCE: (24), (42) imply:
% 44.59/6.91 | (51) relation_dom(all_243_3) = all_280_1
% 44.59/6.91 |
% 44.59/6.91 | BETA: splitting (10) gives:
% 44.59/6.91 |
% 44.59/6.91 | Case 1:
% 44.59/6.91 | |
% 44.59/6.91 | | (52) ~ (all_243_0 = all_243_1) & relation_rng(all_243_3) = all_243_0 &
% 44.59/6.91 | | relation_dom(all_243_5) = all_243_1 & $i(all_243_0) & $i(all_243_1)
% 44.59/6.91 | |
% 44.59/6.91 | | ALPHA: (52) implies:
% 44.59/6.91 | | (53) ~ (all_243_0 = all_243_1)
% 44.59/6.91 | | (54) relation_dom(all_243_5) = all_243_1
% 44.59/6.91 | | (55) relation_rng(all_243_3) = all_243_0
% 44.59/6.91 | |
% 44.59/6.92 | | GROUND_INST: instantiating (2) with all_280_0, all_243_1, all_243_5,
% 44.59/6.92 | | simplifying with (16), (54) gives:
% 44.59/6.92 | | (56) all_280_0 = all_243_1
% 44.59/6.92 | |
% 44.59/6.92 | | GROUND_INST: instantiating (3) with all_243_0, all_280_0, all_243_3,
% 44.59/6.92 | | simplifying with (50), (55) gives:
% 44.59/6.92 | | (57) all_280_0 = all_243_0
% 44.59/6.92 | |
% 44.59/6.92 | | COMBINE_EQS: (56), (57) imply:
% 44.59/6.92 | | (58) all_243_0 = all_243_1
% 44.59/6.92 | |
% 44.59/6.92 | | REDUCE: (53), (58) imply:
% 44.59/6.92 | | (59) $false
% 44.59/6.92 | |
% 44.59/6.92 | | CLOSE: (59) is inconsistent.
% 44.59/6.92 | |
% 44.59/6.92 | Case 2:
% 44.59/6.92 | |
% 44.83/6.92 | | (60) ~ (all_243_2 = all_243_4) & relation_rng(all_243_5) = all_243_4 &
% 44.83/6.92 | | relation_dom(all_243_3) = all_243_2 & $i(all_243_2) & $i(all_243_4)
% 44.83/6.92 | |
% 44.83/6.92 | | ALPHA: (60) implies:
% 44.83/6.92 | | (61) ~ (all_243_2 = all_243_4)
% 44.83/6.92 | | (62) relation_dom(all_243_3) = all_243_2
% 44.83/6.92 | | (63) relation_rng(all_243_5) = all_243_4
% 44.83/6.92 | |
% 44.83/6.92 | | GROUND_INST: instantiating (2) with all_243_2, all_280_1, all_243_3,
% 44.83/6.92 | | simplifying with (51), (62) gives:
% 44.83/6.92 | | (64) all_280_1 = all_243_2
% 44.83/6.92 | |
% 44.83/6.92 | | GROUND_INST: instantiating (3) with all_280_1, all_243_4, all_243_5,
% 44.83/6.92 | | simplifying with (17), (63) gives:
% 44.83/6.92 | | (65) all_280_1 = all_243_4
% 44.83/6.92 | |
% 44.83/6.92 | | COMBINE_EQS: (64), (65) imply:
% 44.83/6.92 | | (66) all_243_2 = all_243_4
% 44.83/6.92 | |
% 44.83/6.92 | | SIMP: (66) implies:
% 44.83/6.92 | | (67) all_243_2 = all_243_4
% 44.83/6.92 | |
% 44.83/6.92 | | REDUCE: (61), (67) imply:
% 44.83/6.92 | | (68) $false
% 44.83/6.92 | |
% 44.83/6.92 | | CLOSE: (68) is inconsistent.
% 44.83/6.92 | |
% 44.83/6.92 | End of split
% 44.83/6.92 |
% 44.83/6.92 End of proof
% 44.83/6.92 % SZS output end Proof for theBenchmark
% 44.83/6.92
% 44.83/6.92 6322ms
%------------------------------------------------------------------------------