TSTP Solution File: SEU225+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU225+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 : n005.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 17:43:27 EDT 2023
% Result : Theorem 138.21s 19.03s
% Output : Proof 138.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU225+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 17:19:08 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.64 ________ _____
% 0.21/0.64 ___ __ \_________(_)________________________________
% 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64
% 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.66 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.93/1.71 Prover 1: Preprocessing ...
% 6.56/1.73 Prover 4: Preprocessing ...
% 6.56/1.74 Prover 2: Preprocessing ...
% 6.56/1.74 Prover 5: Preprocessing ...
% 6.56/1.74 Prover 6: Preprocessing ...
% 6.56/1.74 Prover 3: Preprocessing ...
% 6.56/1.75 Prover 0: Preprocessing ...
% 19.19/3.42 Prover 1: Warning: ignoring some quantifiers
% 19.44/3.59 Prover 3: Warning: ignoring some quantifiers
% 19.44/3.64 Prover 1: Constructing countermodel ...
% 20.26/3.67 Prover 3: Constructing countermodel ...
% 20.26/3.69 Prover 5: Proving ...
% 20.26/3.69 Prover 6: Proving ...
% 23.55/4.07 Prover 2: Proving ...
% 26.31/4.39 Prover 4: Warning: ignoring some quantifiers
% 27.00/4.49 Prover 4: Constructing countermodel ...
% 28.59/4.74 Prover 0: Proving ...
% 74.04/10.67 Prover 2: stopped
% 74.04/10.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 75.61/10.89 Prover 7: Preprocessing ...
% 78.79/11.30 Prover 7: Warning: ignoring some quantifiers
% 79.37/11.33 Prover 7: Constructing countermodel ...
% 99.65/14.00 Prover 5: stopped
% 99.65/14.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.94/14.22 Prover 8: Preprocessing ...
% 103.49/14.63 Prover 8: Warning: ignoring some quantifiers
% 104.87/14.67 Prover 8: Constructing countermodel ...
% 114.23/16.01 Prover 1: stopped
% 114.23/16.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.91/16.13 Prover 9: Preprocessing ...
% 124.47/17.21 Prover 9: Warning: ignoring some quantifiers
% 124.47/17.25 Prover 9: Constructing countermodel ...
% 129.61/17.91 Prover 6: stopped
% 129.61/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.80/18.19 Prover 10: Preprocessing ...
% 132.98/18.38 Prover 10: Warning: ignoring some quantifiers
% 133.63/18.42 Prover 10: Constructing countermodel ...
% 137.90/18.98 Prover 10: Found proof (size 88)
% 137.90/18.99 Prover 10: proved (1067ms)
% 137.90/18.99 Prover 9: stopped
% 137.90/18.99 Prover 3: stopped
% 137.90/18.99 Prover 8: stopped
% 137.90/19.00 Prover 7: stopped
% 138.12/19.02 Prover 4: stopped
% 138.21/19.03 Prover 0: stopped
% 138.21/19.03
% 138.21/19.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 138.21/19.03
% 138.21/19.04 % SZS output start Proof for theBenchmark
% 138.21/19.05 Assumptions after simplification:
% 138.21/19.05 ---------------------------------
% 138.21/19.05
% 138.21/19.05 (d11_relat_1)
% 138.21/19.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 138.21/19.09 $i] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4)
% 138.21/19.09 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 138.21/19.09 relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0: $i] :
% 138.21/19.09 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 138.21/19.09 (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) |
% 138.21/19.09 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) |
% 138.21/19.09 ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0: $i] : ! [v1: $i] :
% 138.21/19.09 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 138.21/19.09 (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) |
% 138.21/19.09 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) |
% 138.21/19.09 ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0: $i]
% 138.21/19.09 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 138.21/19.09 (relation_dom_restriction(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 138.21/19.09 | ~ relation(v2) | ~ relation(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 138.21/19.09 $i] : (ordered_pair(v4, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ in(v6,
% 138.21/19.09 v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) &
% 138.21/19.09 in(v4, v1)))))
% 138.21/19.09
% 138.21/19.09 (d3_relat_1)
% 138.21/19.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 138.21/19.09 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 138.21/19.09 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) |
% 138.21/19.09 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 138.21/19.09 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i]
% 138.21/19.09 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 138.21/19.09 in(v4, v0) & ~ in(v4, v1)))
% 138.21/19.09
% 138.21/19.09 (d4_funct_1)
% 138.21/19.10 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 138.21/19.10 [v4: $i] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~
% 138.21/19.10 $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ~
% 138.21/19.10 in(v2, v1) | ? [v5: $i] : (( ~ in(v4, v0) | (v5 = v3 & apply(v0, v2) = v3))
% 138.21/19.10 & (in(v4, v0) | ( ~ (v5 = v3) & apply(v0, v2) = v5 & $i(v5))))) & ! [v0:
% 138.21/19.10 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~
% 138.21/19.10 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v3) | ~ $i(v2) |
% 138.21/19.10 ~ $i(v0) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0: $i] :
% 138.21/19.10 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set | ~
% 138.21/19.10 (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) |
% 138.21/19.10 ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 138.21/19.10
% 138.21/19.10 (d4_relat_1)
% 138.21/19.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 138.21/19.10 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~
% 138.21/19.10 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2,
% 138.21/19.10 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) =
% 138.21/19.10 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1)
% 138.21/19.10 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) &
% 138.21/19.10 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 138.21/19.10 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3:
% 138.21/19.10 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | !
% 138.21/19.10 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) |
% 138.21/19.10 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) &
% 138.21/19.10 in(v5, v1)))))
% 138.21/19.10
% 138.21/19.10 (dt_k7_relat_1)
% 138.21/19.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 138.21/19.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | relation(v2))
% 138.21/19.10
% 138.21/19.10 (fc4_funct_1)
% 138.21/19.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 138.21/19.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) |
% 138.21/19.10 relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 138.21/19.10 (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 138.21/19.10 relation(v0) | ~ function(v0) | function(v2))
% 138.21/19.10
% 138.21/19.10 (t23_funct_1)
% 138.21/19.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (apply(v1, v0) = v2) | ~ $i(v1)
% 138.21/19.10 | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v3: $i] :
% 138.21/19.10 (relation_dom(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 138.21/19.10 ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~
% 138.21/19.10 $i(v4) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | (apply(v4,
% 138.21/19.11 v2) = v6 & $i(v6)))))
% 138.21/19.11
% 138.21/19.11 (t25_relat_1)
% 138.21/19.11 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 138.21/19.11 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 138.21/19.11 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3)
% 138.21/19.11 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 138.21/19.11 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~
% 138.21/19.11 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) &
% 138.21/19.11 subset(v2, v5)))))
% 138.21/19.11
% 138.21/19.11 (t46_relat_1)
% 138.21/19.11 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 138.21/19.11 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 138.21/19.11 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~
% 138.21/19.11 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4)
% 138.21/19.11 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5))))))
% 138.21/19.11
% 138.21/19.11 (t47_relat_1)
% 138.21/19.11 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 138.21/19.11 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] :
% 138.21/19.11 ! [v4: $i] : ( ~ (relation_composition(v3, v0) = v4) | ~ $i(v3) | ~
% 138.21/19.11 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_rng(v4)
% 138.21/19.11 = v1 & $i(v1)) | (relation_rng(v3) = v5 & $i(v5) & ~ subset(v2,
% 138.21/19.11 v5))))))
% 138.21/19.11
% 138.21/19.11 (t70_funct_1)
% 138.21/19.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 138.21/19.11 (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~
% 138.21/19.11 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ function(v2) | ? [v5:
% 138.21/19.11 $i] : ? [v6: $i] : ((v6 = v4 & apply(v2, v1) = v4 & $i(v4)) |
% 138.21/19.11 (relation_dom(v3) = v5 & $i(v5) & ~ in(v1, v5))))
% 138.21/19.11
% 138.21/19.11 (t72_funct_1)
% 138.21/19.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 138.21/19.11 $i] : ( ~ (v5 = v4) & apply(v3, v1) = v4 & apply(v2, v1) = v5 &
% 138.21/19.11 relation_dom_restriction(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 138.21/19.11 $i(v1) & $i(v0) & relation(v2) & function(v2) & in(v1, v0))
% 138.21/19.11
% 138.21/19.11 (t88_relat_1)
% 138.21/19.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v1,
% 138.21/19.11 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | subset(v2, v1))
% 138.21/19.11
% 138.21/19.11 (t8_funct_1)
% 138.21/19.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 138.21/19.11 (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ $i(v2) | ~
% 138.21/19.12 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ function(v2) | ? [v5: $i] : (( ~
% 138.21/19.12 (v4 = v1) | in(v3, v2) | (relation_dom(v2) = v5 & $i(v5) & ~ in(v0,
% 138.21/19.12 v5))) & ( ~ in(v3, v2) | (v4 = v1 & relation_dom(v2) = v5 & $i(v5) &
% 138.21/19.12 in(v0, v5)))))
% 138.21/19.12
% 138.21/19.12 (t99_relat_1)
% 138.62/19.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v1,
% 138.62/19.12 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: $i] : ?
% 138.62/19.12 [v4: $i] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & $i(v4) & $i(v3)
% 138.62/19.12 & subset(v3, v4)))
% 138.62/19.12
% 138.62/19.12 (function-axioms)
% 138.62/19.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 138.62/19.13 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 138.62/19.13 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 138.62/19.13 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) =
% 138.62/19.13 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 138.62/19.13 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & !
% 138.62/19.13 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 138.62/19.13 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) =
% 138.62/19.13 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 138.62/19.13 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 138.62/19.13 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 138.62/19.13 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) &
% 138.62/19.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 138.62/19.13 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 138.62/19.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 138.62/19.13 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 138.62/19.13 : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 138.62/19.13 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 138.62/19.13 : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~
% 138.62/19.13 (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 138.62/19.13 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~
% 138.62/19.13 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 138.62/19.13 ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~
% 138.62/19.13 (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 138.62/19.13 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1)
% 138.62/19.13 | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 138.62/19.13 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~
% 138.62/19.13 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 138.62/19.13 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 138.62/19.13 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 138.62/19.13 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3,
% 138.62/19.13 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 138.62/19.13 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 138.62/19.13 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 138.62/19.13 (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i]
% 138.62/19.13 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~
% 138.62/19.13 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 138.62/19.13 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & !
% 138.62/19.13 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) |
% 138.62/19.13 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 138.62/19.13 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1:
% 138.62/19.13 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~
% 138.62/19.13 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 138.62/19.13 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i]
% 138.62/19.13 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 138.62/19.13 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 138.62/19.13 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1:
% 138.62/19.13 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) =
% 138.62/19.13 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 138.62/19.13 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 138.62/19.13
% 138.62/19.13 Further assumptions not needed in the proof:
% 138.62/19.13 --------------------------------------------
% 138.62/19.13 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1,
% 138.62/19.13 cc2_funct_1, commutativity_k2_tarski, commutativity_k2_xboole_0,
% 138.62/19.13 commutativity_k3_xboole_0, d10_relat_1, d10_xboole_0, d12_relat_1, d13_relat_1,
% 138.62/19.13 d14_relat_1, d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1,
% 138.62/19.13 d2_relat_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski,
% 138.62/19.13 d3_xboole_0, d4_subset_1, d4_tarski, d4_xboole_0, d5_relat_1, d5_subset_1,
% 138.62/19.13 d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, d8_funct_1, d8_relat_1,
% 138.62/19.13 d8_setfam_1, d8_xboole_0, d9_funct_1, dt_k10_relat_1, dt_k1_funct_1,
% 138.62/19.13 dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 138.62/19.13 dt_k2_funct_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0,
% 138.62/19.13 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0,
% 138.62/19.13 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1,
% 138.62/19.13 dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, dt_k8_relat_1,
% 138.62/19.13 dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1,
% 138.62/19.13 fc11_relat_1, fc12_relat_1, fc13_relat_1, fc1_funct_1, fc1_relat_1,
% 138.62/19.13 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_relat_1,
% 138.62/19.13 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_subset_1, fc3_xboole_0,
% 138.62/19.13 fc4_relat_1, fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1,
% 138.62/19.13 fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 138.62/19.13 involutiveness_k3_subset_1, involutiveness_k4_relat_1,
% 138.62/19.13 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1,
% 138.62/19.13 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1,
% 138.62/19.13 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1,
% 138.62/19.13 l82_funct_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1,
% 138.62/19.13 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1,
% 138.62/19.13 redefinition_k5_setfam_1, redefinition_k6_setfam_1, redefinition_k6_subset_1,
% 138.62/19.13 reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1,
% 138.62/19.13 t115_relat_1, t116_relat_1, t117_relat_1, t118_relat_1, t118_zfmisc_1,
% 138.62/19.13 t119_relat_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t140_relat_1,
% 138.62/19.13 t143_relat_1, t144_relat_1, t145_relat_1, t146_relat_1, t160_relat_1,
% 138.62/19.13 t166_relat_1, t167_relat_1, t174_relat_1, t178_relat_1, t17_xboole_1,
% 138.62/19.13 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1,
% 138.62/19.13 t21_funct_1, t21_relat_1, t22_funct_1, t26_xboole_1, t28_xboole_1, t2_boole,
% 138.62/19.13 t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1,
% 138.62/19.13 t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 138.62/19.13 t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0,
% 138.62/19.13 t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1,
% 138.62/19.13 t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole,
% 138.62/19.13 t4_subset, t4_xboole_0, t50_subset_1, t54_funct_1, t54_subset_1, t55_funct_1,
% 138.62/19.13 t56_relat_1, t57_funct_1, t5_subset, t60_relat_1, t60_xboole_1, t62_funct_1,
% 138.62/19.13 t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, t68_funct_1, t69_enumset1,
% 138.62/19.13 t6_boole, t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole, t7_xboole_1,
% 138.62/19.13 t83_xboole_1, t86_relat_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t90_relat_1,
% 138.62/19.13 t92_zfmisc_1, t94_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1
% 138.62/19.13
% 138.62/19.13 Those formulas are unsatisfiable:
% 138.62/19.13 ---------------------------------
% 138.62/19.13
% 138.62/19.13 Begin of proof
% 138.62/19.13 |
% 138.62/19.13 | ALPHA: (d11_relat_1) implies:
% 138.62/19.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 138.62/19.13 | ! [v5: $i] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~
% 138.62/19.13 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 138.62/19.13 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v0) | ~ in(v5,
% 138.62/19.13 | v0) | ~ in(v3, v1) | in(v5, v2))
% 138.62/19.13 |
% 138.62/19.13 | ALPHA: (d3_relat_1) implies:
% 138.62/19.13 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) |
% 138.62/19.13 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 138.62/19.13 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 138.62/19.13 | in(v4, v0) & ~ in(v4, v1)))
% 138.62/19.13 |
% 138.62/19.13 | ALPHA: (d4_funct_1) implies:
% 138.62/19.13 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set
% 138.62/19.13 | | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ $i(v2) |
% 138.62/19.13 | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 138.62/19.13 |
% 138.62/19.13 | ALPHA: (d4_relat_1) implies:
% 138.62/19.13 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = v1) |
% 138.62/19.13 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) |
% 138.62/19.13 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) &
% 138.62/19.13 | $i(v3) & in(v4, v0)))
% 138.62/19.13 |
% 138.62/19.13 | ALPHA: (fc4_funct_1) implies:
% 138.62/19.13 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 138.62/19.13 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 138.62/19.13 | relation(v0) | ~ function(v0) | function(v2))
% 138.62/19.13 |
% 138.62/19.13 | ALPHA: (function-axioms) implies:
% 138.62/19.14 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 138.62/19.14 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 138.62/19.14 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 138.62/19.14 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 138.62/19.14 |
% 138.62/19.14 | DELTA: instantiating (t72_funct_1) with fresh symbols all_245_0, all_245_1,
% 138.62/19.14 | all_245_2, all_245_3, all_245_4, all_245_5 gives:
% 138.62/19.14 | (8) ~ (all_245_0 = all_245_1) & apply(all_245_2, all_245_4) = all_245_1 &
% 138.62/19.14 | apply(all_245_3, all_245_4) = all_245_0 &
% 138.62/19.14 | relation_dom_restriction(all_245_3, all_245_5) = all_245_2 &
% 138.62/19.14 | $i(all_245_0) & $i(all_245_1) & $i(all_245_2) & $i(all_245_3) &
% 138.62/19.14 | $i(all_245_4) & $i(all_245_5) & relation(all_245_3) &
% 138.62/19.14 | function(all_245_3) & in(all_245_4, all_245_5)
% 138.62/19.14 |
% 138.62/19.14 | ALPHA: (8) implies:
% 138.62/19.14 | (9) ~ (all_245_0 = all_245_1)
% 138.62/19.14 | (10) in(all_245_4, all_245_5)
% 138.62/19.14 | (11) function(all_245_3)
% 138.62/19.14 | (12) relation(all_245_3)
% 138.62/19.14 | (13) $i(all_245_5)
% 138.62/19.14 | (14) $i(all_245_4)
% 138.62/19.14 | (15) $i(all_245_3)
% 138.62/19.14 | (16) $i(all_245_2)
% 138.62/19.14 | (17) relation_dom_restriction(all_245_3, all_245_5) = all_245_2
% 138.62/19.14 | (18) apply(all_245_3, all_245_4) = all_245_0
% 138.62/19.14 | (19) apply(all_245_2, all_245_4) = all_245_1
% 138.62/19.14 |
% 138.62/19.14 | GROUND_INST: instantiating (2) with all_245_3, all_245_3, simplifying with
% 138.62/19.14 | (12), (15) gives:
% 138.62/19.14 | (20) subset(all_245_3, all_245_3)
% 138.62/19.14 |
% 138.62/19.14 | GROUND_INST: instantiating (5) with all_245_3, all_245_5, all_245_2,
% 138.62/19.14 | simplifying with (11), (12), (13), (15), (17) gives:
% 138.62/19.14 | (21) function(all_245_2)
% 138.62/19.14 |
% 138.62/19.14 | GROUND_INST: instantiating (t88_relat_1) with all_245_5, all_245_3, all_245_2,
% 138.62/19.14 | simplifying with (12), (13), (15), (17) gives:
% 138.62/19.14 | (22) subset(all_245_2, all_245_3)
% 138.62/19.14 |
% 138.62/19.14 | GROUND_INST: instantiating (t99_relat_1) with all_245_5, all_245_3, all_245_2,
% 138.62/19.14 | simplifying with (12), (13), (15), (17) gives:
% 138.62/19.14 | (23) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_245_2) = v0 &
% 138.62/19.14 | relation_rng(all_245_3) = v1 & $i(v1) & $i(v0) & subset(v0, v1))
% 138.62/19.14 |
% 138.62/19.14 | GROUND_INST: instantiating (dt_k7_relat_1) with all_245_3, all_245_5,
% 138.62/19.14 | all_245_2, simplifying with (12), (13), (15), (17) gives:
% 138.62/19.14 | (24) relation(all_245_2)
% 138.62/19.14 |
% 138.62/19.14 | GROUND_INST: instantiating (t23_funct_1) with all_245_4, all_245_3, all_245_0,
% 138.62/19.14 | simplifying with (11), (12), (14), (15), (18) gives:
% 138.62/19.15 | (25) ? [v0: $i] : (relation_dom(all_245_3) = v0 & $i(v0) & ! [v1: $i] :
% 138.62/19.15 | ! [v2: $i] : ! [v3: $i] : ( ~ (relation_composition(all_245_3, v1)
% 138.62/19.15 | = v2) | ~ (apply(v2, all_245_4) = v3) | ~ $i(v1) | ~
% 138.62/19.15 | relation(v1) | ~ function(v1) | ~ in(all_245_4, v0) | (apply(v1,
% 138.62/19.15 | all_245_0) = v3 & $i(v3))))
% 138.62/19.15 |
% 138.62/19.15 | GROUND_INST: instantiating (t70_funct_1) with all_245_5, all_245_4, all_245_3,
% 138.62/19.15 | all_245_2, all_245_1, simplifying with (11), (12), (13), (14),
% 138.62/19.15 | (15), (17), (19) gives:
% 138.62/19.15 | (26) ? [v0: $i] : ? [v1: int] : ((v1 = all_245_1 & apply(all_245_3,
% 138.62/19.15 | all_245_4) = all_245_1 & $i(all_245_1)) |
% 138.62/19.15 | (relation_dom(all_245_2) = v0 & $i(v0) & ~ in(all_245_4, v0)))
% 138.62/19.15 |
% 138.62/19.15 | DELTA: instantiating (23) with fresh symbols all_281_0, all_281_1 gives:
% 138.62/19.15 | (27) relation_rng(all_245_2) = all_281_1 & relation_rng(all_245_3) =
% 138.62/19.15 | all_281_0 & $i(all_281_0) & $i(all_281_1) & subset(all_281_1,
% 138.62/19.15 | all_281_0)
% 138.62/19.15 |
% 138.62/19.15 | ALPHA: (27) implies:
% 138.62/19.15 | (28) relation_rng(all_245_3) = all_281_0
% 138.62/19.15 | (29) relation_rng(all_245_2) = all_281_1
% 138.62/19.15 |
% 138.62/19.15 | DELTA: instantiating (26) with fresh symbols all_283_0, all_283_1 gives:
% 138.62/19.15 | (30) (all_283_0 = all_245_1 & apply(all_245_3, all_245_4) = all_245_1 &
% 138.62/19.15 | $i(all_245_1)) | (relation_dom(all_245_2) = all_283_1 &
% 138.62/19.15 | $i(all_283_1) & ~ in(all_245_4, all_283_1))
% 138.62/19.15 |
% 138.62/19.15 | DELTA: instantiating (25) with fresh symbol all_284_0 gives:
% 138.62/19.15 | (31) relation_dom(all_245_3) = all_284_0 & $i(all_284_0) & ! [v0: $i] : !
% 138.62/19.15 | [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(all_245_3, v0) =
% 138.62/19.15 | v1) | ~ (apply(v1, all_245_4) = v2) | ~ $i(v0) | ~ relation(v0)
% 138.62/19.15 | | ~ function(v0) | ~ in(all_245_4, all_284_0) | (apply(v0,
% 138.62/19.15 | all_245_0) = v2 & $i(v2)))
% 138.62/19.15 |
% 138.62/19.15 | ALPHA: (31) implies:
% 138.62/19.15 | (32) relation_dom(all_245_3) = all_284_0
% 138.62/19.15 |
% 138.62/19.15 | BETA: splitting (30) gives:
% 138.62/19.15 |
% 138.62/19.15 | Case 1:
% 138.62/19.15 | |
% 138.62/19.15 | | (33) all_283_0 = all_245_1 & apply(all_245_3, all_245_4) = all_245_1 &
% 138.62/19.15 | | $i(all_245_1)
% 138.62/19.15 | |
% 138.62/19.15 | | ALPHA: (33) implies:
% 138.62/19.15 | | (34) apply(all_245_3, all_245_4) = all_245_1
% 138.62/19.15 | |
% 138.62/19.15 | | GROUND_INST: instantiating (7) with all_245_0, all_245_1, all_245_4,
% 138.62/19.15 | | all_245_3, simplifying with (18), (34) gives:
% 138.62/19.15 | | (35) all_245_0 = all_245_1
% 138.62/19.15 | |
% 138.62/19.15 | | REDUCE: (9), (35) imply:
% 138.62/19.15 | | (36) $false
% 138.62/19.15 | |
% 138.62/19.15 | | CLOSE: (36) is inconsistent.
% 138.62/19.15 | |
% 138.62/19.15 | Case 2:
% 138.62/19.15 | |
% 138.62/19.15 | | (37) relation_dom(all_245_2) = all_283_1 & $i(all_283_1) & ~
% 138.62/19.15 | | in(all_245_4, all_283_1)
% 138.62/19.15 | |
% 138.62/19.15 | | ALPHA: (37) implies:
% 138.62/19.15 | | (38) ~ in(all_245_4, all_283_1)
% 138.62/19.15 | | (39) relation_dom(all_245_2) = all_283_1
% 138.62/19.15 | |
% 138.62/19.15 | | GROUND_INST: instantiating (3) with all_245_3, all_284_0, all_245_4,
% 138.62/19.15 | | all_245_0, simplifying with (11), (12), (14), (15), (18), (32)
% 138.62/19.15 | | gives:
% 138.62/19.15 | | (40) all_245_0 = empty_set | in(all_245_4, all_284_0)
% 138.62/19.15 | |
% 138.62/19.15 | | GROUND_INST: instantiating (3) with all_245_2, all_283_1, all_245_4,
% 138.62/19.15 | | all_245_1, simplifying with (14), (16), (19), (21), (24), (38),
% 138.62/19.15 | | (39) gives:
% 138.62/19.15 | | (41) all_245_1 = empty_set
% 138.62/19.15 | |
% 138.62/19.15 | | GROUND_INST: instantiating (t47_relat_1) with all_245_3, all_281_0,
% 138.62/19.15 | | simplifying with (12), (15), (28) gives:
% 138.62/19.16 | | (42) ? [v0: $i] : (relation_dom(all_245_3) = v0 & $i(v0) & ! [v1: $i] :
% 138.62/19.16 | | ! [v2: $i] : ( ~ (relation_composition(v1, all_245_3) = v2) | ~
% 138.62/19.16 | | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 =
% 138.62/19.16 | | all_281_0 & relation_rng(v2) = all_281_0 & $i(all_281_0)) |
% 138.62/19.16 | | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3)))))
% 138.62/19.16 | |
% 138.62/19.16 | | GROUND_INST: instantiating (t46_relat_1) with all_245_3, all_281_0,
% 138.62/19.16 | | simplifying with (12), (15), (28) gives:
% 138.62/19.16 | | (43) ? [v0: $i] : (relation_dom(all_245_3) = v0 & $i(v0) & ! [v1: $i] :
% 138.62/19.16 | | ! [v2: $i] : ( ~ (relation_composition(all_245_3, v1) = v2) | ~
% 138.62/19.16 | | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0
% 138.62/19.16 | | & relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) &
% 138.62/19.16 | | ~ subset(all_281_0, v3)))))
% 138.62/19.16 | |
% 138.62/19.16 | | GROUND_INST: instantiating (t25_relat_1) with all_245_3, all_281_0,
% 138.62/19.16 | | simplifying with (12), (15), (28) gives:
% 138.62/19.16 | | (44) ? [v0: $i] : (relation_dom(all_245_3) = v0 & $i(v0) & ! [v1: $i] :
% 138.62/19.16 | | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 138.62/19.16 | | subset(all_245_3, v1) | ~ relation(v1) | subset(all_281_0, v2))
% 138.62/19.16 | | & ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~
% 138.62/19.16 | | $i(v1) | ~ subset(all_245_3, v1) | ~ relation(v1) | ? [v3:
% 138.62/19.16 | | $i] : (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 138.62/19.16 | |
% 138.62/19.16 | | GROUND_INST: instantiating (t25_relat_1) with all_245_2, all_281_1,
% 138.62/19.16 | | simplifying with (16), (24), (29) gives:
% 138.62/19.16 | | (45) ? [v0: $i] : (relation_dom(all_245_2) = v0 & $i(v0) & ! [v1: $i] :
% 138.62/19.16 | | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~
% 138.62/19.16 | | subset(all_245_2, v1) | ~ relation(v1) | subset(all_281_1, v2))
% 138.62/19.16 | | & ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~
% 138.62/19.16 | | $i(v1) | ~ subset(all_245_2, v1) | ~ relation(v1) | ? [v3:
% 138.62/19.16 | | $i] : (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3))))
% 138.62/19.16 | |
% 138.62/19.16 | | DELTA: instantiating (43) with fresh symbol all_312_0 gives:
% 138.62/19.16 | | (46) relation_dom(all_245_3) = all_312_0 & $i(all_312_0) & ! [v0: $i] :
% 138.62/19.16 | | ! [v1: $i] : ( ~ (relation_composition(all_245_3, v0) = v1) | ~
% 138.62/19.16 | | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 =
% 138.62/19.16 | | all_312_0 & relation_dom(v1) = all_312_0) | (relation_dom(v0)
% 138.62/19.16 | | = v2 & $i(v2) & ~ subset(all_281_0, v2))))
% 138.62/19.16 | |
% 138.62/19.16 | | ALPHA: (46) implies:
% 138.62/19.16 | | (47) $i(all_312_0)
% 138.62/19.16 | | (48) relation_dom(all_245_3) = all_312_0
% 138.62/19.16 | |
% 138.62/19.16 | | DELTA: instantiating (42) with fresh symbol all_321_0 gives:
% 138.62/19.16 | | (49) relation_dom(all_245_3) = all_321_0 & $i(all_321_0) & ! [v0: $i] :
% 138.62/19.16 | | ! [v1: $i] : ( ~ (relation_composition(v0, all_245_3) = v1) | ~
% 138.62/19.16 | | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 =
% 138.62/19.16 | | all_281_0 & relation_rng(v1) = all_281_0 & $i(all_281_0)) |
% 138.62/19.16 | | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_321_0, v2))))
% 138.62/19.16 | |
% 138.62/19.16 | | ALPHA: (49) implies:
% 138.62/19.16 | | (50) relation_dom(all_245_3) = all_321_0
% 138.62/19.16 | |
% 138.62/19.16 | | DELTA: instantiating (45) with fresh symbol all_324_0 gives:
% 138.62/19.16 | | (51) relation_dom(all_245_2) = all_324_0 & $i(all_324_0) & ! [v0: $i] :
% 138.62/19.16 | | ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 138.62/19.16 | | subset(all_245_2, v0) | ~ relation(v0) | subset(all_281_1, v1)) &
% 138.62/19.16 | | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0)
% 138.62/19.16 | | | ~ subset(all_245_2, v0) | ~ relation(v0) | ? [v2: $i] :
% 138.62/19.16 | | (relation_dom(v0) = v2 & $i(v2) & subset(all_324_0, v2)))
% 138.62/19.16 | |
% 138.62/19.16 | | ALPHA: (51) implies:
% 138.62/19.16 | | (52) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0)
% 138.62/19.16 | | | ~ subset(all_245_2, v0) | ~ relation(v0) | ? [v2: $i] :
% 138.62/19.16 | | (relation_dom(v0) = v2 & $i(v2) & subset(all_324_0, v2)))
% 138.62/19.16 | |
% 138.62/19.16 | | GROUND_INST: instantiating (52) with all_245_3, all_281_0, simplifying with
% 138.62/19.16 | | (12), (15), (22), (28) gives:
% 138.62/19.16 | | (53) ? [v0: $i] : (relation_dom(all_245_3) = v0 & $i(v0) &
% 138.62/19.16 | | subset(all_324_0, v0))
% 138.62/19.16 | |
% 138.62/19.16 | | DELTA: instantiating (44) with fresh symbol all_327_0 gives:
% 138.62/19.16 | | (54) relation_dom(all_245_3) = all_327_0 & $i(all_327_0) & ! [v0: $i] :
% 138.62/19.16 | | ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 138.62/19.16 | | subset(all_245_3, v0) | ~ relation(v0) | subset(all_281_0, v1)) &
% 138.62/19.16 | | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0)
% 138.62/19.16 | | | ~ subset(all_245_3, v0) | ~ relation(v0) | ? [v2: $i] :
% 138.62/19.16 | | (relation_dom(v0) = v2 & $i(v2) & subset(all_327_0, v2)))
% 138.62/19.16 | |
% 138.62/19.16 | | ALPHA: (54) implies:
% 138.62/19.16 | | (55) relation_dom(all_245_3) = all_327_0
% 138.62/19.16 | | (56) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0)
% 138.62/19.16 | | | ~ subset(all_245_3, v0) | ~ relation(v0) | ? [v2: $i] :
% 138.62/19.16 | | (relation_dom(v0) = v2 & $i(v2) & subset(all_327_0, v2)))
% 138.62/19.16 | |
% 138.62/19.17 | | GROUND_INST: instantiating (56) with all_245_3, all_281_0, simplifying with
% 138.62/19.17 | | (12), (15), (20), (28) gives:
% 138.62/19.17 | | (57) ? [v0: $i] : (relation_dom(all_245_3) = v0 & $i(v0) &
% 138.62/19.17 | | subset(all_327_0, v0))
% 138.62/19.17 | |
% 138.62/19.17 | | DELTA: instantiating (53) with fresh symbol all_331_0 gives:
% 138.62/19.17 | | (58) relation_dom(all_245_3) = all_331_0 & $i(all_331_0) &
% 138.62/19.17 | | subset(all_324_0, all_331_0)
% 138.62/19.17 | |
% 138.62/19.17 | | ALPHA: (58) implies:
% 138.62/19.17 | | (59) relation_dom(all_245_3) = all_331_0
% 138.62/19.17 | |
% 138.62/19.17 | | DELTA: instantiating (57) with fresh symbol all_333_0 gives:
% 138.62/19.17 | | (60) relation_dom(all_245_3) = all_333_0 & $i(all_333_0) &
% 138.62/19.17 | | subset(all_327_0, all_333_0)
% 138.62/19.17 | |
% 138.62/19.17 | | ALPHA: (60) implies:
% 138.62/19.17 | | (61) relation_dom(all_245_3) = all_333_0
% 138.62/19.17 | |
% 138.62/19.17 | | REDUCE: (9), (41) imply:
% 138.62/19.17 | | (62) ~ (all_245_0 = empty_set)
% 138.62/19.17 | |
% 138.62/19.17 | | REDUCE: (19), (41) imply:
% 138.62/19.17 | | (63) apply(all_245_2, all_245_4) = empty_set
% 138.62/19.17 | |
% 138.62/19.17 | | BETA: splitting (40) gives:
% 138.62/19.17 | |
% 138.62/19.17 | | Case 1:
% 138.62/19.17 | | |
% 138.62/19.17 | | | (64) in(all_245_4, all_284_0)
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (6) with all_284_0, all_331_0, all_245_3,
% 138.62/19.17 | | | simplifying with (32), (59) gives:
% 138.62/19.17 | | | (65) all_331_0 = all_284_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (6) with all_327_0, all_331_0, all_245_3,
% 138.62/19.17 | | | simplifying with (55), (59) gives:
% 138.62/19.17 | | | (66) all_331_0 = all_327_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (6) with all_321_0, all_331_0, all_245_3,
% 138.62/19.17 | | | simplifying with (50), (59) gives:
% 138.62/19.17 | | | (67) all_331_0 = all_321_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (6) with all_321_0, all_333_0, all_245_3,
% 138.62/19.17 | | | simplifying with (50), (61) gives:
% 138.62/19.17 | | | (68) all_333_0 = all_321_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (6) with all_312_0, all_333_0, all_245_3,
% 138.62/19.17 | | | simplifying with (48), (61) gives:
% 138.62/19.17 | | | (69) all_333_0 = all_312_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | COMBINE_EQS: (68), (69) imply:
% 138.62/19.17 | | | (70) all_321_0 = all_312_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | SIMP: (70) implies:
% 138.62/19.17 | | | (71) all_321_0 = all_312_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | COMBINE_EQS: (65), (66) imply:
% 138.62/19.17 | | | (72) all_327_0 = all_284_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | COMBINE_EQS: (66), (67) imply:
% 138.62/19.17 | | | (73) all_327_0 = all_321_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | COMBINE_EQS: (72), (73) imply:
% 138.62/19.17 | | | (74) all_321_0 = all_284_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | SIMP: (74) implies:
% 138.62/19.17 | | | (75) all_321_0 = all_284_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | COMBINE_EQS: (71), (75) imply:
% 138.62/19.17 | | | (76) all_312_0 = all_284_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | REDUCE: (47), (76) imply:
% 138.62/19.17 | | | (77) $i(all_284_0)
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (4) with all_245_3, all_284_0, all_245_4,
% 138.62/19.17 | | | simplifying with (12), (14), (15), (32), (64), (77) gives:
% 138.62/19.17 | | | (78) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_245_4, v0) = v1 &
% 138.62/19.17 | | | $i(v1) & $i(v0) & in(v1, all_245_3))
% 138.62/19.17 | | |
% 138.62/19.17 | | | DELTA: instantiating (78) with fresh symbols all_375_0, all_375_1 gives:
% 138.62/19.17 | | | (79) ordered_pair(all_245_4, all_375_1) = all_375_0 & $i(all_375_0) &
% 138.62/19.17 | | | $i(all_375_1) & in(all_375_0, all_245_3)
% 138.62/19.17 | | |
% 138.62/19.17 | | | ALPHA: (79) implies:
% 138.62/19.17 | | | (80) in(all_375_0, all_245_3)
% 138.62/19.17 | | | (81) $i(all_375_1)
% 138.62/19.17 | | | (82) ordered_pair(all_245_4, all_375_1) = all_375_0
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (1) with all_245_3, all_245_5, all_245_2,
% 138.62/19.17 | | | all_245_4, all_375_1, all_375_0, simplifying with (10), (12),
% 138.62/19.17 | | | (13), (14), (15), (16), (17), (24), (80), (81), (82) gives:
% 138.62/19.17 | | | (83) in(all_375_0, all_245_2)
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (t8_funct_1) with all_245_4, all_375_1,
% 138.62/19.17 | | | all_245_2, all_375_0, empty_set, simplifying with (14), (16),
% 138.62/19.17 | | | (21), (24), (63), (81), (82) gives:
% 138.62/19.17 | | | (84) ? [v0: $i] : (( ~ (all_375_1 = empty_set) | in(all_375_0,
% 138.62/19.17 | | | all_245_2) | (relation_dom(all_245_2) = v0 & $i(v0) & ~
% 138.62/19.17 | | | in(all_245_4, v0))) & ( ~ in(all_375_0, all_245_2) |
% 138.62/19.17 | | | (all_375_1 = empty_set & relation_dom(all_245_2) = v0 & $i(v0)
% 138.62/19.17 | | | & in(all_245_4, v0))))
% 138.62/19.17 | | |
% 138.62/19.17 | | | GROUND_INST: instantiating (t8_funct_1) with all_245_4, all_375_1,
% 138.62/19.17 | | | all_245_3, all_375_0, all_245_0, simplifying with (11), (12),
% 138.62/19.17 | | | (14), (15), (18), (81), (82) gives:
% 138.62/19.17 | | | (85) ? [v0: $i] : (( ~ (all_375_1 = all_245_0) | in(all_375_0,
% 138.62/19.17 | | | all_245_3) | (relation_dom(all_245_3) = v0 & $i(v0) & ~
% 138.62/19.17 | | | in(all_245_4, v0))) & ( ~ in(all_375_0, all_245_3) |
% 138.62/19.17 | | | (all_375_1 = all_245_0 & relation_dom(all_245_3) = v0 & $i(v0)
% 138.62/19.17 | | | & in(all_245_4, v0))))
% 138.62/19.17 | | |
% 138.62/19.17 | | | DELTA: instantiating (85) with fresh symbol all_441_0 gives:
% 138.62/19.17 | | | (86) ( ~ (all_375_1 = all_245_0) | in(all_375_0, all_245_3) |
% 138.62/19.17 | | | (relation_dom(all_245_3) = all_441_0 & $i(all_441_0) & ~
% 138.62/19.17 | | | in(all_245_4, all_441_0))) & ( ~ in(all_375_0, all_245_3) |
% 138.62/19.17 | | | (all_375_1 = all_245_0 & relation_dom(all_245_3) = all_441_0 &
% 138.62/19.17 | | | $i(all_441_0) & in(all_245_4, all_441_0)))
% 138.62/19.17 | | |
% 138.62/19.17 | | | ALPHA: (86) implies:
% 138.62/19.17 | | | (87) ~ in(all_375_0, all_245_3) | (all_375_1 = all_245_0 &
% 138.62/19.17 | | | relation_dom(all_245_3) = all_441_0 & $i(all_441_0) &
% 138.62/19.17 | | | in(all_245_4, all_441_0))
% 138.62/19.17 | | |
% 138.62/19.17 | | | DELTA: instantiating (84) with fresh symbol all_442_0 gives:
% 138.62/19.17 | | | (88) ( ~ (all_375_1 = empty_set) | in(all_375_0, all_245_2) |
% 138.62/19.17 | | | (relation_dom(all_245_2) = all_442_0 & $i(all_442_0) & ~
% 138.62/19.17 | | | in(all_245_4, all_442_0))) & ( ~ in(all_375_0, all_245_2) |
% 138.62/19.17 | | | (all_375_1 = empty_set & relation_dom(all_245_2) = all_442_0 &
% 138.62/19.17 | | | $i(all_442_0) & in(all_245_4, all_442_0)))
% 138.62/19.17 | | |
% 138.62/19.17 | | | ALPHA: (88) implies:
% 138.62/19.18 | | | (89) ~ in(all_375_0, all_245_2) | (all_375_1 = empty_set &
% 138.62/19.18 | | | relation_dom(all_245_2) = all_442_0 & $i(all_442_0) &
% 138.62/19.18 | | | in(all_245_4, all_442_0))
% 138.62/19.18 | | |
% 138.62/19.18 | | | BETA: splitting (89) gives:
% 138.62/19.18 | | |
% 138.62/19.18 | | | Case 1:
% 138.62/19.18 | | | |
% 138.62/19.18 | | | | (90) ~ in(all_375_0, all_245_2)
% 138.62/19.18 | | | |
% 138.62/19.18 | | | | PRED_UNIFY: (83), (90) imply:
% 138.62/19.18 | | | | (91) $false
% 138.62/19.18 | | | |
% 138.62/19.18 | | | | CLOSE: (91) is inconsistent.
% 138.62/19.18 | | | |
% 138.62/19.18 | | | Case 2:
% 138.62/19.18 | | | |
% 138.62/19.18 | | | | (92) all_375_1 = empty_set & relation_dom(all_245_2) = all_442_0 &
% 138.62/19.18 | | | | $i(all_442_0) & in(all_245_4, all_442_0)
% 138.62/19.18 | | | |
% 138.62/19.18 | | | | ALPHA: (92) implies:
% 138.62/19.18 | | | | (93) all_375_1 = empty_set
% 138.62/19.18 | | | |
% 138.62/19.18 | | | | BETA: splitting (87) gives:
% 138.62/19.18 | | | |
% 138.62/19.18 | | | | Case 1:
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | (94) ~ in(all_375_0, all_245_3)
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | PRED_UNIFY: (80), (94) imply:
% 138.62/19.18 | | | | | (95) $false
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | CLOSE: (95) is inconsistent.
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | Case 2:
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | (96) all_375_1 = all_245_0 & relation_dom(all_245_3) = all_441_0 &
% 138.62/19.18 | | | | | $i(all_441_0) & in(all_245_4, all_441_0)
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | ALPHA: (96) implies:
% 138.62/19.18 | | | | | (97) all_375_1 = all_245_0
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | COMBINE_EQS: (93), (97) imply:
% 138.62/19.18 | | | | | (98) all_245_0 = empty_set
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | SIMP: (98) implies:
% 138.62/19.18 | | | | | (99) all_245_0 = empty_set
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | REDUCE: (62), (99) imply:
% 138.62/19.18 | | | | | (100) $false
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | | CLOSE: (100) is inconsistent.
% 138.62/19.18 | | | | |
% 138.62/19.18 | | | | End of split
% 138.62/19.18 | | | |
% 138.62/19.18 | | | End of split
% 138.62/19.18 | | |
% 138.62/19.18 | | Case 2:
% 138.62/19.18 | | |
% 138.62/19.18 | | | (101) all_245_0 = empty_set
% 138.62/19.18 | | |
% 138.62/19.18 | | | REDUCE: (62), (101) imply:
% 138.62/19.18 | | | (102) $false
% 138.62/19.18 | | |
% 138.62/19.18 | | | CLOSE: (102) is inconsistent.
% 138.62/19.18 | | |
% 138.62/19.18 | | End of split
% 138.62/19.18 | |
% 138.62/19.18 | End of split
% 138.62/19.18 |
% 138.62/19.18 End of proof
% 138.62/19.18 % SZS output end Proof for theBenchmark
% 138.62/19.18
% 138.62/19.18 18534ms
%------------------------------------------------------------------------------