TSTP Solution File: TOP026+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : TOP026+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 : Fri Sep 1 05:58:50 EDT 2023
% Result : Theorem 17.71s 3.19s
% Output : Proof 28.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP026+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 23:30:17 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.64/1.29 Prover 4: Preprocessing ...
% 3.64/1.29 Prover 1: Preprocessing ...
% 4.01/1.33 Prover 3: Preprocessing ...
% 4.01/1.33 Prover 5: Preprocessing ...
% 4.01/1.33 Prover 2: Preprocessing ...
% 4.01/1.33 Prover 0: Preprocessing ...
% 4.01/1.33 Prover 6: Preprocessing ...
% 9.68/2.10 Prover 5: Proving ...
% 9.68/2.19 Prover 1: Warning: ignoring some quantifiers
% 9.68/2.25 Prover 1: Constructing countermodel ...
% 11.16/2.33 Prover 2: Proving ...
% 11.44/2.36 Prover 6: Proving ...
% 11.44/2.39 Prover 3: Warning: ignoring some quantifiers
% 11.44/2.42 Prover 3: Constructing countermodel ...
% 14.82/2.85 Prover 4: Warning: ignoring some quantifiers
% 14.82/2.89 Prover 4: Constructing countermodel ...
% 16.91/3.07 Prover 0: Proving ...
% 17.71/3.18 Prover 5: proved (2544ms)
% 17.71/3.18
% 17.71/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.71/3.19
% 17.71/3.19 Prover 3: stopped
% 17.71/3.19 Prover 6: stopped
% 17.71/3.19 Prover 2: stopped
% 17.71/3.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.71/3.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.71/3.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.71/3.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.11/3.23 Prover 0: stopped
% 18.11/3.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.87/3.34 Prover 10: Preprocessing ...
% 18.87/3.36 Prover 7: Preprocessing ...
% 19.22/3.39 Prover 13: Preprocessing ...
% 19.22/3.40 Prover 11: Preprocessing ...
% 19.22/3.41 Prover 8: Preprocessing ...
% 20.04/3.52 Prover 10: Warning: ignoring some quantifiers
% 20.04/3.55 Prover 7: Warning: ignoring some quantifiers
% 20.04/3.56 Prover 10: Constructing countermodel ...
% 20.04/3.57 Prover 7: Constructing countermodel ...
% 20.04/3.64 Prover 13: Warning: ignoring some quantifiers
% 21.34/3.67 Prover 13: Constructing countermodel ...
% 21.34/3.68 Prover 8: Warning: ignoring some quantifiers
% 21.34/3.69 Prover 8: Constructing countermodel ...
% 24.77/4.26 Prover 11: Warning: ignoring some quantifiers
% 24.77/4.29 Prover 11: Constructing countermodel ...
% 26.74/4.45 Prover 10: Found proof (size 145)
% 26.74/4.45 Prover 10: proved (1261ms)
% 26.74/4.45 Prover 13: stopped
% 26.74/4.45 Prover 7: stopped
% 26.74/4.45 Prover 1: stopped
% 26.74/4.45 Prover 8: stopped
% 26.74/4.45 Prover 11: stopped
% 26.74/4.46 Prover 4: stopped
% 26.74/4.46
% 26.74/4.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.74/4.46
% 27.20/4.49 % SZS output start Proof for theBenchmark
% 27.20/4.50 Assumptions after simplification:
% 27.20/4.50 ---------------------------------
% 27.20/4.50
% 27.20/4.50 (cc1_tops_1)
% 27.20/4.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.52 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 27.20/4.52 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~
% 27.20/4.52 m1_subset_1(v3, v2) | v3_pre_topc(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) |
% 27.20/4.52 ~ v1_xboole_0(v3) | ~ m1_subset_1(v3, v2) | v4_pre_topc(v3, v0))))
% 27.20/4.53
% 27.20/4.53 (cc2_tops_1)
% 27.20/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.53 l1_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i]
% 27.20/4.53 : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~ m1_subset_1(v3, v2) | v2_tops_1(v3,
% 27.20/4.53 v0))))
% 27.20/4.53
% 27.20/4.53 (cc3_tops_1)
% 27.20/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.53 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 27.20/4.53 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~
% 27.20/4.53 m1_subset_1(v3, v2) | v3_tops_1(v3, v0))))
% 27.20/4.53
% 27.20/4.53 (cc4_tops_1)
% 27.20/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.53 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 27.20/4.53 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~
% 27.20/4.53 m1_subset_1(v3, v2) | v2_tops_1(v3, v0))))
% 27.20/4.53
% 27.20/4.53 (cc5_tops_1)
% 27.20/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.53 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 27.20/4.53 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v4_pre_topc(v3, v0) | ~
% 27.20/4.53 v2_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v3_tops_1(v3, v0))))
% 27.20/4.53
% 27.20/4.53 (cc6_tops_1)
% 27.20/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.54 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 27.20/4.54 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~
% 27.20/4.54 v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v1_xboole_0(v3)) & ! [v3:
% 27.20/4.54 $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~
% 27.20/4.54 m1_subset_1(v3, v2) | v4_pre_topc(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) |
% 27.20/4.54 ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) |
% 27.20/4.54 v2_tops_1(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) |
% 27.20/4.54 ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v5_membered(v3)) & !
% 27.20/4.54 [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~
% 27.20/4.54 m1_subset_1(v3, v2) | v4_membered(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 27.20/4.54 v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) |
% 27.20/4.54 v3_membered(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) |
% 27.20/4.54 ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v2_membered(v3)) & !
% 27.20/4.54 [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~
% 27.20/4.54 m1_subset_1(v3, v2) | v1_membered(v3))))
% 27.20/4.54
% 27.20/4.54 (dt_k3_tex_4)
% 27.20/4.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_tex_4(v0, v1) = v2) | ~
% 27.20/4.54 $i(v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | v3_struct_0(v0) | ? [v3: $i] : ?
% 27.20/4.54 [v4: $i] : (u1_struct_0(v0) = v3 & k1_zfmisc_1(v3) = v4 & $i(v4) & $i(v3) &
% 27.20/4.54 ( ~ m1_subset_1(v1, v4) | m1_subset_1(v2, v4))))
% 27.20/4.54
% 27.20/4.54 (dt_k5_subset_1)
% 27.20/4.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k5_subset_1(v0,
% 27.20/4.55 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 27.20/4.55 (k1_zfmisc_1(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2, v4) | ~
% 27.20/4.55 m1_subset_1(v1, v4) | m1_subset_1(v3, v4))))
% 27.20/4.55
% 27.20/4.55 (dt_k6_pre_topc)
% 27.20/4.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k6_pre_topc(v0, v1) = v2) | ~
% 27.20/4.55 $i(v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ? [v3: $i] : ? [v4: $i] :
% 27.20/4.55 (u1_struct_0(v0) = v3 & k1_zfmisc_1(v3) = v4 & $i(v4) & $i(v3) & ( ~
% 27.20/4.55 m1_subset_1(v1, v4) | m1_subset_1(v2, v4))))
% 27.20/4.55
% 27.20/4.55 (fc2_tops_1)
% 27.20/4.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k6_pre_topc(v0, v1) = v2) | ~
% 27.20/4.55 $i(v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0) |
% 27.20/4.55 v4_pre_topc(v2, v0) | ? [v3: $i] : ? [v4: $i] : (u1_struct_0(v0) = v3 &
% 27.20/4.55 k1_zfmisc_1(v3) = v4 & $i(v4) & $i(v3) & ~ m1_subset_1(v1, v4)))
% 27.20/4.55
% 27.20/4.55 (rc1_tops_1)
% 27.20/4.55 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.55 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 27.20/4.55 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_pre_topc(v3, v0) &
% 27.20/4.55 m1_subset_1(v3, v2)))
% 27.20/4.55
% 27.20/4.55 (rc2_tops_1)
% 27.20/4.55 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.55 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 27.20/4.55 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_pre_topc(v3, v0) &
% 27.20/4.55 v4_pre_topc(v3, v0) & m1_subset_1(v3, v2)))
% 27.20/4.55
% 27.20/4.55 (rc3_tops_1)
% 27.20/4.55 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.55 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : ?
% 27.20/4.55 [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_pre_topc(v3, v0) &
% 27.20/4.55 v4_pre_topc(v3, v0) & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3)))
% 27.20/4.55
% 27.20/4.55 (rc4_tops_1)
% 27.20/4.55 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.55 l1_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3)
% 27.20/4.55 & $i(v2) & v1_xboole_0(v3) & v2_tops_1(v3, v0) & v5_membered(v3) &
% 27.20/4.55 v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & v1_membered(v3) &
% 27.20/4.56 m1_subset_1(v3, v2)))
% 27.20/4.56
% 27.20/4.56 (rc5_tops_1)
% 27.20/4.56 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.56 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 27.20/4.56 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v1_xboole_0(v3) & v3_pre_topc(v3,
% 27.20/4.56 v0) & v4_pre_topc(v3, v0) & v2_tops_1(v3, v0) & v3_tops_1(v3, v0) &
% 27.20/4.56 v5_membered(v3) & v4_membered(v3) & v3_membered(v3) & v2_membered(v3) &
% 27.20/4.56 v1_membered(v3) & m1_subset_1(v3, v2)))
% 27.20/4.56
% 27.20/4.56 (rc6_pre_topc)
% 27.20/4.56 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.56 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 27.20/4.56 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) &
% 27.20/4.56 m1_subset_1(v3, v2)))
% 27.20/4.56
% 27.20/4.56 (rc7_pre_topc)
% 27.20/4.56 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.56 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : ?
% 27.20/4.56 [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) &
% 27.20/4.56 m1_subset_1(v3, v2) & ~ v1_xboole_0(v3)))
% 27.20/4.56
% 27.20/4.56 (t5_tsp_2)
% 27.20/4.56 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 27.20/4.56 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] :
% 27.20/4.56 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 27.20/4.56 ! [v6: $i] : (v6 = v4 | ~ (k3_tex_4(v0, v5) = v6) | ~ (k5_subset_1(v1,
% 27.20/4.56 v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ v4_pre_topc(v4, v0) | ~
% 27.20/4.56 v1_tsp_2(v3, v0) | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2))))
% 27.20/4.56
% 27.20/4.56 (t7_tsp_2)
% 27.66/4.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 27.66/4.56 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v5) & k6_pre_topc(v0, v4) = v5 &
% 27.66/4.56 k3_tex_4(v0, v6) = v7 & k5_subset_1(v1, v3, v5) = v6 & u1_struct_0(v0) = v1
% 27.66/4.56 & k1_zfmisc_1(v1) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 27.66/4.56 & $i(v1) & $i(v0) & v1_tsp_2(v3, v0) & m1_subset_1(v4, v2) & m1_subset_1(v3,
% 27.66/4.56 v2) & l1_pre_topc(v0) & v2_pre_topc(v0) & ~ v3_struct_0(v0))
% 27.66/4.56
% 27.66/4.56 (function-axioms)
% 27.66/4.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 27.66/4.57 | ~ (k5_subset_1(v4, v3, v2) = v1) | ~ (k5_subset_1(v4, v3, v2) = v0)) &
% 27.66/4.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.66/4.57 (k6_pre_topc(v3, v2) = v1) | ~ (k6_pre_topc(v3, v2) = v0)) & ! [v0: $i] :
% 27.66/4.57 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k3_tex_4(v3, v2) = v1)
% 27.66/4.57 | ~ (k3_tex_4(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 27.66/4.57 [v3: $i] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2)
% 27.66/4.57 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 27.66/4.57 (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 27.66/4.57 $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 27.66/4.57 (k1_zfmisc_1(v2) = v0))
% 27.66/4.57
% 27.66/4.57 Further assumptions not needed in the proof:
% 27.66/4.57 --------------------------------------------
% 27.66/4.57 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered,
% 27.66/4.57 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered,
% 27.66/4.57 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered,
% 27.66/4.57 cc3_membered, cc4_membered, commutativity_k3_xboole_0,
% 27.66/4.57 commutativity_k5_subset_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k3_xboole_0,
% 27.66/4.57 dt_l1_pre_topc, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0,
% 27.66/4.57 existence_l1_pre_topc, existence_l1_struct_0, existence_m1_subset_1,
% 27.66/4.57 fc1_struct_0, fc1_subset_1, fc27_membered, fc28_membered, fc29_membered,
% 27.66/4.57 fc30_membered, fc31_membered, fc32_membered, fc33_membered, fc34_membered,
% 27.66/4.57 fc35_membered, fc36_membered, fc6_membered, idempotence_k3_xboole_0,
% 27.66/4.57 idempotence_k5_subset_1, rc1_membered, rc1_subset_1, rc2_subset_1, rc3_struct_0,
% 27.66/4.57 rc5_struct_0, redefinition_k5_subset_1, reflexivity_r1_tarski, t1_subset,
% 27.66/4.57 t2_boole, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 27.66/4.57 t8_boole
% 27.66/4.57
% 27.66/4.57 Those formulas are unsatisfiable:
% 27.66/4.57 ---------------------------------
% 27.66/4.57
% 27.66/4.57 Begin of proof
% 27.66/4.57 |
% 27.66/4.57 | ALPHA: (function-axioms) implies:
% 27.66/4.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 27.66/4.57 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 27.66/4.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 27.66/4.57 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 27.66/4.57 |
% 27.66/4.57 | DELTA: instantiating (t7_tsp_2) with fresh symbols all_79_0, all_79_1,
% 27.66/4.57 | all_79_2, all_79_3, all_79_4, all_79_5, all_79_6, all_79_7 gives:
% 27.66/4.57 | (3) ~ (all_79_0 = all_79_2) & k6_pre_topc(all_79_7, all_79_3) = all_79_2 &
% 27.66/4.57 | k3_tex_4(all_79_7, all_79_1) = all_79_0 & k5_subset_1(all_79_6,
% 27.66/4.57 | all_79_4, all_79_2) = all_79_1 & u1_struct_0(all_79_7) = all_79_6 &
% 27.66/4.57 | k1_zfmisc_1(all_79_6) = all_79_5 & $i(all_79_0) & $i(all_79_1) &
% 27.66/4.57 | $i(all_79_2) & $i(all_79_3) & $i(all_79_4) & $i(all_79_5) &
% 27.66/4.57 | $i(all_79_6) & $i(all_79_7) & v1_tsp_2(all_79_4, all_79_7) &
% 27.66/4.57 | m1_subset_1(all_79_3, all_79_5) & m1_subset_1(all_79_4, all_79_5) &
% 27.66/4.57 | l1_pre_topc(all_79_7) & v2_pre_topc(all_79_7) & ~
% 27.66/4.57 | v3_struct_0(all_79_7)
% 27.66/4.57 |
% 27.66/4.57 | ALPHA: (3) implies:
% 27.66/4.57 | (4) ~ (all_79_0 = all_79_2)
% 27.66/4.57 | (5) ~ v3_struct_0(all_79_7)
% 27.66/4.57 | (6) v2_pre_topc(all_79_7)
% 27.66/4.57 | (7) l1_pre_topc(all_79_7)
% 27.66/4.57 | (8) m1_subset_1(all_79_4, all_79_5)
% 27.66/4.57 | (9) m1_subset_1(all_79_3, all_79_5)
% 27.66/4.57 | (10) v1_tsp_2(all_79_4, all_79_7)
% 27.66/4.57 | (11) $i(all_79_7)
% 27.66/4.57 | (12) $i(all_79_6)
% 27.66/4.57 | (13) $i(all_79_4)
% 27.66/4.57 | (14) $i(all_79_3)
% 27.66/4.57 | (15) $i(all_79_2)
% 27.66/4.57 | (16) $i(all_79_1)
% 27.66/4.57 | (17) k1_zfmisc_1(all_79_6) = all_79_5
% 27.66/4.57 | (18) u1_struct_0(all_79_7) = all_79_6
% 27.66/4.57 | (19) k5_subset_1(all_79_6, all_79_4, all_79_2) = all_79_1
% 27.66/4.58 | (20) k3_tex_4(all_79_7, all_79_1) = all_79_0
% 27.66/4.58 | (21) k6_pre_topc(all_79_7, all_79_3) = all_79_2
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (rc3_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (5), (6), (7), (11), (18) gives:
% 27.66/4.58 | (22) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v1) &
% 27.66/4.58 | $i(v0) & v3_pre_topc(v1, all_79_7) & v4_pre_topc(v1, all_79_7) &
% 27.66/4.58 | m1_subset_1(v1, v0) & ~ v1_xboole_0(v1))
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (rc7_pre_topc) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (5), (6), (7), (11), (18) gives:
% 27.66/4.58 | (23) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v1) &
% 27.66/4.58 | $i(v0) & v4_pre_topc(v1, all_79_7) & m1_subset_1(v1, v0) & ~
% 27.66/4.58 | v1_xboole_0(v1))
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (t5_tsp_2) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (5), (6), (7), (11), (18) gives:
% 27.66/4.58 | (24) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ! [v1: $i] : !
% 27.66/4.58 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 27.66/4.58 | (k3_tex_4(all_79_7, v3) = v4) | ~ (k5_subset_1(all_79_6, v1, v2)
% 27.66/4.58 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ v4_pre_topc(v2, all_79_7) |
% 27.66/4.58 | ~ v1_tsp_2(v1, all_79_7) | ~ m1_subset_1(v2, v0) | ~
% 27.66/4.58 | m1_subset_1(v1, v0)))
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (rc5_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (6), (7), (11), (18) gives:
% 27.66/4.58 | (25) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v1) &
% 27.66/4.58 | $i(v0) & v1_xboole_0(v1) & v3_pre_topc(v1, all_79_7) &
% 27.66/4.58 | v4_pre_topc(v1, all_79_7) & v2_tops_1(v1, all_79_7) & v3_tops_1(v1,
% 27.66/4.58 | all_79_7) & v5_membered(v1) & v4_membered(v1) & v3_membered(v1) &
% 27.66/4.58 | v2_membered(v1) & v1_membered(v1) & m1_subset_1(v1, v0))
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (rc2_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (6), (7), (11), (18) gives:
% 27.66/4.58 | (26) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v1) &
% 27.66/4.58 | $i(v0) & v3_pre_topc(v1, all_79_7) & v4_pre_topc(v1, all_79_7) &
% 27.66/4.58 | m1_subset_1(v1, v0))
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (rc1_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (6), (7), (11), (18) gives:
% 27.66/4.58 | (27) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v1) &
% 27.66/4.58 | $i(v0) & v3_pre_topc(v1, all_79_7) & m1_subset_1(v1, v0))
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (rc6_pre_topc) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (6), (7), (11), (18) gives:
% 27.66/4.58 | (28) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v1) &
% 27.66/4.58 | $i(v0) & v4_pre_topc(v1, all_79_7) & m1_subset_1(v1, v0))
% 27.66/4.58 |
% 27.66/4.58 | GROUND_INST: instantiating (cc1_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.58 | with (6), (7), (11), (18) gives:
% 27.66/4.59 | (29) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 27.66/4.59 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) |
% 27.66/4.59 | v3_pre_topc(v1, all_79_7)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 27.66/4.59 | v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) | v4_pre_topc(v1,
% 27.66/4.59 | all_79_7)))
% 27.66/4.59 |
% 27.66/4.59 | GROUND_INST: instantiating (cc3_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.59 | with (6), (7), (11), (18) gives:
% 27.66/4.59 | (30) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 27.66/4.59 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) |
% 27.66/4.59 | v3_tops_1(v1, all_79_7)))
% 27.66/4.59 |
% 27.66/4.59 | GROUND_INST: instantiating (cc6_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.59 | with (6), (7), (11), (18) gives:
% 27.66/4.59 | (31) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 27.66/4.59 | $i(v1) | ~ v3_pre_topc(v1, all_79_7) | ~ v3_tops_1(v1, all_79_7)
% 27.66/4.59 | | ~ m1_subset_1(v1, v0) | v1_xboole_0(v1)) & ! [v1: $i] : ( ~
% 27.66/4.59 | $i(v1) | ~ v3_pre_topc(v1, all_79_7) | ~ v3_tops_1(v1, all_79_7)
% 27.66/4.59 | | ~ m1_subset_1(v1, v0) | v4_pre_topc(v1, all_79_7)) & ! [v1:
% 27.66/4.59 | $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, all_79_7) | ~ v3_tops_1(v1,
% 27.66/4.59 | all_79_7) | ~ m1_subset_1(v1, v0) | v2_tops_1(v1, all_79_7)) &
% 27.66/4.59 | ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, all_79_7) | ~
% 27.66/4.59 | v3_tops_1(v1, all_79_7) | ~ m1_subset_1(v1, v0) |
% 27.66/4.59 | v5_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1,
% 27.66/4.59 | all_79_7) | ~ v3_tops_1(v1, all_79_7) | ~ m1_subset_1(v1, v0)
% 27.66/4.59 | | v4_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1,
% 27.66/4.59 | all_79_7) | ~ v3_tops_1(v1, all_79_7) | ~ m1_subset_1(v1, v0)
% 27.66/4.59 | | v3_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1,
% 27.66/4.59 | all_79_7) | ~ v3_tops_1(v1, all_79_7) | ~ m1_subset_1(v1, v0)
% 27.66/4.59 | | v2_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1,
% 27.66/4.59 | all_79_7) | ~ v3_tops_1(v1, all_79_7) | ~ m1_subset_1(v1, v0)
% 27.66/4.59 | | v1_membered(v1)))
% 27.66/4.59 |
% 27.66/4.59 | GROUND_INST: instantiating (cc5_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.59 | with (6), (7), (11), (18) gives:
% 27.66/4.59 | (32) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 27.66/4.59 | $i(v1) | ~ v4_pre_topc(v1, all_79_7) | ~ v2_tops_1(v1, all_79_7)
% 27.66/4.59 | | ~ m1_subset_1(v1, v0) | v3_tops_1(v1, all_79_7)))
% 27.66/4.59 |
% 27.66/4.59 | GROUND_INST: instantiating (cc4_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.59 | with (6), (7), (11), (18) gives:
% 27.66/4.59 | (33) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 27.66/4.59 | $i(v1) | ~ v3_tops_1(v1, all_79_7) | ~ m1_subset_1(v1, v0) |
% 27.66/4.59 | v2_tops_1(v1, all_79_7)))
% 27.66/4.59 |
% 27.66/4.59 | GROUND_INST: instantiating (rc4_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.59 | with (7), (11), (18) gives:
% 27.66/4.59 | (34) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v1) &
% 27.66/4.59 | $i(v0) & v1_xboole_0(v1) & v2_tops_1(v1, all_79_7) & v5_membered(v1)
% 27.66/4.59 | & v4_membered(v1) & v3_membered(v1) & v2_membered(v1) &
% 27.66/4.59 | v1_membered(v1) & m1_subset_1(v1, v0))
% 27.66/4.59 |
% 27.66/4.59 | GROUND_INST: instantiating (cc2_tops_1) with all_79_7, all_79_6, simplifying
% 27.66/4.59 | with (7), (11), (18) gives:
% 27.66/4.59 | (35) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 27.66/4.59 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) |
% 27.66/4.59 | v2_tops_1(v1, all_79_7)))
% 27.66/4.59 |
% 27.66/4.59 | GROUND_INST: instantiating (dt_k5_subset_1) with all_79_6, all_79_4, all_79_2,
% 27.66/4.59 | all_79_1, simplifying with (12), (13), (15), (19) gives:
% 27.66/4.60 | (36) ? [v0: $i] : (k1_zfmisc_1(all_79_6) = v0 & $i(v0) & ( ~
% 27.66/4.60 | m1_subset_1(all_79_2, v0) | ~ m1_subset_1(all_79_4, v0) |
% 27.66/4.60 | m1_subset_1(all_79_1, v0)))
% 27.66/4.60 |
% 27.66/4.60 | GROUND_INST: instantiating (dt_k3_tex_4) with all_79_7, all_79_1, all_79_0,
% 27.66/4.60 | simplifying with (5), (7), (11), (16), (20) gives:
% 27.66/4.60 | (37) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_79_7) = v0 &
% 27.66/4.60 | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ( ~ m1_subset_1(all_79_1,
% 27.66/4.60 | v1) | m1_subset_1(all_79_0, v1)))
% 27.66/4.60 |
% 27.83/4.60 | GROUND_INST: instantiating (fc2_tops_1) with all_79_7, all_79_3, all_79_2,
% 27.83/4.60 | simplifying with (6), (7), (11), (14), (21) gives:
% 27.83/4.60 | (38) v4_pre_topc(all_79_2, all_79_7) | ? [v0: $i] : ? [v1: $i] :
% 27.83/4.60 | (u1_struct_0(all_79_7) = v0 & k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) &
% 27.83/4.60 | ~ m1_subset_1(all_79_3, v1))
% 27.83/4.60 |
% 27.83/4.60 | GROUND_INST: instantiating (dt_k6_pre_topc) with all_79_7, all_79_3, all_79_2,
% 27.83/4.60 | simplifying with (7), (11), (14), (21) gives:
% 27.83/4.60 | (39) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_79_7) = v0 &
% 27.83/4.60 | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ( ~ m1_subset_1(all_79_3,
% 27.83/4.60 | v1) | m1_subset_1(all_79_2, v1)))
% 27.83/4.60 |
% 27.83/4.60 | DELTA: instantiating (36) with fresh symbol all_89_0 gives:
% 27.83/4.60 | (40) k1_zfmisc_1(all_79_6) = all_89_0 & $i(all_89_0) & ( ~
% 27.83/4.60 | m1_subset_1(all_79_2, all_89_0) | ~ m1_subset_1(all_79_4, all_89_0)
% 27.83/4.60 | | m1_subset_1(all_79_1, all_89_0))
% 27.83/4.60 |
% 27.83/4.60 | ALPHA: (40) implies:
% 27.83/4.60 | (41) k1_zfmisc_1(all_79_6) = all_89_0
% 27.83/4.60 |
% 27.83/4.60 | DELTA: instantiating (27) with fresh symbols all_91_0, all_91_1 gives:
% 27.83/4.60 | (42) k1_zfmisc_1(all_79_6) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 27.83/4.60 | v3_pre_topc(all_91_0, all_79_7) & m1_subset_1(all_91_0, all_91_1)
% 27.83/4.60 |
% 27.83/4.60 | ALPHA: (42) implies:
% 27.83/4.60 | (43) k1_zfmisc_1(all_79_6) = all_91_1
% 27.83/4.60 |
% 27.83/4.60 | DELTA: instantiating (28) with fresh symbols all_93_0, all_93_1 gives:
% 27.83/4.60 | (44) k1_zfmisc_1(all_79_6) = all_93_1 & $i(all_93_0) & $i(all_93_1) &
% 27.83/4.60 | v4_pre_topc(all_93_0, all_79_7) & m1_subset_1(all_93_0, all_93_1)
% 27.83/4.60 |
% 27.83/4.60 | ALPHA: (44) implies:
% 27.83/4.60 | (45) k1_zfmisc_1(all_79_6) = all_93_1
% 27.83/4.60 |
% 27.83/4.60 | DELTA: instantiating (39) with fresh symbols all_95_0, all_95_1 gives:
% 27.83/4.60 | (46) u1_struct_0(all_79_7) = all_95_1 & k1_zfmisc_1(all_95_1) = all_95_0 &
% 27.83/4.60 | $i(all_95_0) & $i(all_95_1) & ( ~ m1_subset_1(all_79_3, all_95_0) |
% 27.83/4.60 | m1_subset_1(all_79_2, all_95_0))
% 27.83/4.60 |
% 27.83/4.60 | ALPHA: (46) implies:
% 27.83/4.60 | (47) k1_zfmisc_1(all_95_1) = all_95_0
% 27.83/4.60 | (48) u1_struct_0(all_79_7) = all_95_1
% 27.83/4.60 | (49) ~ m1_subset_1(all_79_3, all_95_0) | m1_subset_1(all_79_2, all_95_0)
% 27.83/4.60 |
% 27.83/4.60 | DELTA: instantiating (30) with fresh symbol all_97_0 gives:
% 27.83/4.60 | (50) k1_zfmisc_1(all_79_6) = all_97_0 & $i(all_97_0) & ! [v0: $i] : ( ~
% 27.83/4.60 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_97_0) |
% 27.83/4.60 | v3_tops_1(v0, all_79_7))
% 27.83/4.60 |
% 27.83/4.60 | ALPHA: (50) implies:
% 27.83/4.60 | (51) k1_zfmisc_1(all_79_6) = all_97_0
% 27.83/4.60 |
% 27.83/4.60 | DELTA: instantiating (26) with fresh symbols all_100_0, all_100_1 gives:
% 27.83/4.60 | (52) k1_zfmisc_1(all_79_6) = all_100_1 & $i(all_100_0) & $i(all_100_1) &
% 27.83/4.60 | v3_pre_topc(all_100_0, all_79_7) & v4_pre_topc(all_100_0, all_79_7) &
% 27.83/4.60 | m1_subset_1(all_100_0, all_100_1)
% 27.83/4.60 |
% 27.83/4.60 | ALPHA: (52) implies:
% 27.83/4.60 | (53) k1_zfmisc_1(all_79_6) = all_100_1
% 27.83/4.60 |
% 27.83/4.60 | DELTA: instantiating (37) with fresh symbols all_102_0, all_102_1 gives:
% 27.83/4.61 | (54) u1_struct_0(all_79_7) = all_102_1 & k1_zfmisc_1(all_102_1) = all_102_0
% 27.83/4.61 | & $i(all_102_0) & $i(all_102_1) & ( ~ m1_subset_1(all_79_1, all_102_0)
% 27.83/4.61 | | m1_subset_1(all_79_0, all_102_0))
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (54) implies:
% 27.83/4.61 | (55) k1_zfmisc_1(all_102_1) = all_102_0
% 27.83/4.61 | (56) u1_struct_0(all_79_7) = all_102_1
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (35) with fresh symbol all_104_0 gives:
% 27.83/4.61 | (57) k1_zfmisc_1(all_79_6) = all_104_0 & $i(all_104_0) & ! [v0: $i] : ( ~
% 27.83/4.61 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_104_0) |
% 27.83/4.61 | v2_tops_1(v0, all_79_7))
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (57) implies:
% 27.83/4.61 | (58) k1_zfmisc_1(all_79_6) = all_104_0
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (33) with fresh symbol all_107_0 gives:
% 27.83/4.61 | (59) k1_zfmisc_1(all_79_6) = all_107_0 & $i(all_107_0) & ! [v0: $i] : ( ~
% 27.83/4.61 | $i(v0) | ~ v3_tops_1(v0, all_79_7) | ~ m1_subset_1(v0, all_107_0)
% 27.83/4.61 | | v2_tops_1(v0, all_79_7))
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (59) implies:
% 27.83/4.61 | (60) k1_zfmisc_1(all_79_6) = all_107_0
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (23) with fresh symbols all_110_0, all_110_1 gives:
% 27.83/4.61 | (61) k1_zfmisc_1(all_79_6) = all_110_1 & $i(all_110_0) & $i(all_110_1) &
% 27.83/4.61 | v4_pre_topc(all_110_0, all_79_7) & m1_subset_1(all_110_0, all_110_1) &
% 27.83/4.61 | ~ v1_xboole_0(all_110_0)
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (61) implies:
% 27.83/4.61 | (62) k1_zfmisc_1(all_79_6) = all_110_1
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (32) with fresh symbol all_112_0 gives:
% 27.83/4.61 | (63) k1_zfmisc_1(all_79_6) = all_112_0 & $i(all_112_0) & ! [v0: $i] : ( ~
% 27.83/4.61 | $i(v0) | ~ v4_pre_topc(v0, all_79_7) | ~ v2_tops_1(v0, all_79_7) |
% 27.83/4.61 | ~ m1_subset_1(v0, all_112_0) | v3_tops_1(v0, all_79_7))
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (63) implies:
% 27.83/4.61 | (64) k1_zfmisc_1(all_79_6) = all_112_0
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (22) with fresh symbols all_117_0, all_117_1 gives:
% 27.83/4.61 | (65) k1_zfmisc_1(all_79_6) = all_117_1 & $i(all_117_0) & $i(all_117_1) &
% 27.83/4.61 | v3_pre_topc(all_117_0, all_79_7) & v4_pre_topc(all_117_0, all_79_7) &
% 27.83/4.61 | m1_subset_1(all_117_0, all_117_1) & ~ v1_xboole_0(all_117_0)
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (65) implies:
% 27.83/4.61 | (66) k1_zfmisc_1(all_79_6) = all_117_1
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (29) with fresh symbol all_119_0 gives:
% 27.83/4.61 | (67) k1_zfmisc_1(all_79_6) = all_119_0 & $i(all_119_0) & ! [v0: $i] : ( ~
% 27.83/4.61 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_119_0) |
% 27.83/4.61 | v3_pre_topc(v0, all_79_7)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 27.83/4.61 | v1_xboole_0(v0) | ~ m1_subset_1(v0, all_119_0) | v4_pre_topc(v0,
% 27.83/4.61 | all_79_7))
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (67) implies:
% 27.83/4.61 | (68) k1_zfmisc_1(all_79_6) = all_119_0
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (34) with fresh symbols all_122_0, all_122_1 gives:
% 27.83/4.61 | (69) k1_zfmisc_1(all_79_6) = all_122_1 & $i(all_122_0) & $i(all_122_1) &
% 27.83/4.61 | v1_xboole_0(all_122_0) & v2_tops_1(all_122_0, all_79_7) &
% 27.83/4.61 | v5_membered(all_122_0) & v4_membered(all_122_0) &
% 27.83/4.61 | v3_membered(all_122_0) & v2_membered(all_122_0) &
% 27.83/4.61 | v1_membered(all_122_0) & m1_subset_1(all_122_0, all_122_1)
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (69) implies:
% 27.83/4.61 | (70) k1_zfmisc_1(all_79_6) = all_122_1
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (24) with fresh symbol all_124_0 gives:
% 27.83/4.61 | (71) k1_zfmisc_1(all_79_6) = all_124_0 & $i(all_124_0) & ! [v0: $i] : !
% 27.83/4.61 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 27.83/4.61 | (k3_tex_4(all_79_7, v2) = v3) | ~ (k5_subset_1(all_79_6, v0, v1) =
% 27.83/4.61 | v2) | ~ $i(v1) | ~ $i(v0) | ~ v4_pre_topc(v1, all_79_7) | ~
% 27.83/4.61 | v1_tsp_2(v0, all_79_7) | ~ m1_subset_1(v1, all_124_0) | ~
% 27.83/4.61 | m1_subset_1(v0, all_124_0))
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (71) implies:
% 27.83/4.61 | (72) k1_zfmisc_1(all_79_6) = all_124_0
% 27.83/4.61 | (73) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 27.83/4.61 | (k3_tex_4(all_79_7, v2) = v3) | ~ (k5_subset_1(all_79_6, v0, v1) =
% 27.83/4.61 | v2) | ~ $i(v1) | ~ $i(v0) | ~ v4_pre_topc(v1, all_79_7) | ~
% 27.83/4.61 | v1_tsp_2(v0, all_79_7) | ~ m1_subset_1(v1, all_124_0) | ~
% 27.83/4.61 | m1_subset_1(v0, all_124_0))
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (25) with fresh symbols all_127_0, all_127_1 gives:
% 27.83/4.61 | (74) k1_zfmisc_1(all_79_6) = all_127_1 & $i(all_127_0) & $i(all_127_1) &
% 27.83/4.61 | v1_xboole_0(all_127_0) & v3_pre_topc(all_127_0, all_79_7) &
% 27.83/4.61 | v4_pre_topc(all_127_0, all_79_7) & v2_tops_1(all_127_0, all_79_7) &
% 27.83/4.61 | v3_tops_1(all_127_0, all_79_7) & v5_membered(all_127_0) &
% 27.83/4.61 | v4_membered(all_127_0) & v3_membered(all_127_0) &
% 27.83/4.61 | v2_membered(all_127_0) & v1_membered(all_127_0) &
% 27.83/4.61 | m1_subset_1(all_127_0, all_127_1)
% 27.83/4.61 |
% 27.83/4.61 | ALPHA: (74) implies:
% 27.83/4.61 | (75) k1_zfmisc_1(all_79_6) = all_127_1
% 27.83/4.61 |
% 27.83/4.61 | DELTA: instantiating (31) with fresh symbol all_129_0 gives:
% 27.83/4.62 | (76) k1_zfmisc_1(all_79_6) = all_129_0 & $i(all_129_0) & ! [v0: $i] : ( ~
% 27.83/4.62 | $i(v0) | ~ v3_pre_topc(v0, all_79_7) | ~ v3_tops_1(v0, all_79_7) |
% 27.83/4.62 | ~ m1_subset_1(v0, all_129_0) | v1_xboole_0(v0)) & ! [v0: $i] : ( ~
% 27.83/4.62 | $i(v0) | ~ v3_pre_topc(v0, all_79_7) | ~ v3_tops_1(v0, all_79_7) |
% 27.83/4.62 | ~ m1_subset_1(v0, all_129_0) | v4_pre_topc(v0, all_79_7)) & ! [v0:
% 27.83/4.62 | $i] : ( ~ $i(v0) | ~ v3_pre_topc(v0, all_79_7) | ~ v3_tops_1(v0,
% 27.83/4.62 | all_79_7) | ~ m1_subset_1(v0, all_129_0) | v2_tops_1(v0,
% 27.83/4.62 | all_79_7)) & ! [v0: $i] : ( ~ $i(v0) | ~ v3_pre_topc(v0,
% 27.83/4.62 | all_79_7) | ~ v3_tops_1(v0, all_79_7) | ~ m1_subset_1(v0,
% 27.83/4.62 | all_129_0) | v5_membered(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 27.83/4.62 | v3_pre_topc(v0, all_79_7) | ~ v3_tops_1(v0, all_79_7) | ~
% 27.83/4.62 | m1_subset_1(v0, all_129_0) | v4_membered(v0)) & ! [v0: $i] : ( ~
% 27.83/4.62 | $i(v0) | ~ v3_pre_topc(v0, all_79_7) | ~ v3_tops_1(v0, all_79_7) |
% 27.83/4.62 | ~ m1_subset_1(v0, all_129_0) | v3_membered(v0)) & ! [v0: $i] : ( ~
% 27.83/4.62 | $i(v0) | ~ v3_pre_topc(v0, all_79_7) | ~ v3_tops_1(v0, all_79_7) |
% 27.83/4.62 | ~ m1_subset_1(v0, all_129_0) | v2_membered(v0)) & ! [v0: $i] : ( ~
% 27.83/4.62 | $i(v0) | ~ v3_pre_topc(v0, all_79_7) | ~ v3_tops_1(v0, all_79_7) |
% 27.83/4.62 | ~ m1_subset_1(v0, all_129_0) | v1_membered(v0))
% 27.83/4.62 |
% 27.83/4.62 | ALPHA: (76) implies:
% 27.83/4.62 | (77) k1_zfmisc_1(all_79_6) = all_129_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_79_5, all_93_1, all_79_6, simplifying
% 27.83/4.62 | with (17), (45) gives:
% 27.83/4.62 | (78) all_93_1 = all_79_5
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_89_0, all_93_1, all_79_6, simplifying
% 27.83/4.62 | with (41), (45) gives:
% 27.83/4.62 | (79) all_93_1 = all_89_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_93_1, all_97_0, all_79_6, simplifying
% 27.83/4.62 | with (45), (51) gives:
% 27.83/4.62 | (80) all_97_0 = all_93_1
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_104_0, all_110_1, all_79_6,
% 27.83/4.62 | simplifying with (58), (62) gives:
% 27.83/4.62 | (81) all_110_1 = all_104_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_100_1, all_110_1, all_79_6,
% 27.83/4.62 | simplifying with (53), (62) gives:
% 27.83/4.62 | (82) all_110_1 = all_100_1
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_97_0, all_110_1, all_79_6, simplifying
% 27.83/4.62 | with (51), (62) gives:
% 27.83/4.62 | (83) all_110_1 = all_97_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_110_1, all_117_1, all_79_6,
% 27.83/4.62 | simplifying with (62), (66) gives:
% 27.83/4.62 | (84) all_117_1 = all_110_1
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_91_1, all_117_1, all_79_6, simplifying
% 27.83/4.62 | with (43), (66) gives:
% 27.83/4.62 | (85) all_117_1 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_117_1, all_119_0, all_79_6,
% 27.83/4.62 | simplifying with (66), (68) gives:
% 27.83/4.62 | (86) all_119_0 = all_117_1
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_124_0, all_127_1, all_79_6,
% 27.83/4.62 | simplifying with (72), (75) gives:
% 27.83/4.62 | (87) all_127_1 = all_124_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_122_1, all_127_1, all_79_6,
% 27.83/4.62 | simplifying with (70), (75) gives:
% 27.83/4.62 | (88) all_127_1 = all_122_1
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_119_0, all_127_1, all_79_6,
% 27.83/4.62 | simplifying with (68), (75) gives:
% 27.83/4.62 | (89) all_127_1 = all_119_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_107_0, all_127_1, all_79_6,
% 27.83/4.62 | simplifying with (60), (75) gives:
% 27.83/4.62 | (90) all_127_1 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_117_1, all_129_0, all_79_6,
% 27.83/4.62 | simplifying with (66), (77) gives:
% 27.83/4.62 | (91) all_129_0 = all_117_1
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (1) with all_112_0, all_129_0, all_79_6,
% 27.83/4.62 | simplifying with (64), (77) gives:
% 27.83/4.62 | (92) all_129_0 = all_112_0
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (2) with all_79_6, all_102_1, all_79_7, simplifying
% 27.83/4.62 | with (18), (56) gives:
% 27.83/4.62 | (93) all_102_1 = all_79_6
% 27.83/4.62 |
% 27.83/4.62 | GROUND_INST: instantiating (2) with all_95_1, all_102_1, all_79_7, simplifying
% 27.83/4.62 | with (48), (56) gives:
% 27.83/4.62 | (94) all_102_1 = all_95_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (91), (92) imply:
% 27.83/4.62 | (95) all_117_1 = all_112_0
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (95) implies:
% 27.83/4.62 | (96) all_117_1 = all_112_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (87), (88) imply:
% 27.83/4.62 | (97) all_124_0 = all_122_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (87), (90) imply:
% 27.83/4.62 | (98) all_124_0 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (87), (89) imply:
% 27.83/4.62 | (99) all_124_0 = all_119_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (97), (98) imply:
% 27.83/4.62 | (100) all_122_1 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (97), (99) imply:
% 27.83/4.62 | (101) all_122_1 = all_119_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (100), (101) imply:
% 27.83/4.62 | (102) all_119_0 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (102) implies:
% 27.83/4.62 | (103) all_119_0 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (86), (103) imply:
% 27.83/4.62 | (104) all_117_1 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (104) implies:
% 27.83/4.62 | (105) all_117_1 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (84), (96) imply:
% 27.83/4.62 | (106) all_112_0 = all_110_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (96), (105) imply:
% 27.83/4.62 | (107) all_112_0 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (85), (96) imply:
% 27.83/4.62 | (108) all_112_0 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (106), (107) imply:
% 27.83/4.62 | (109) all_110_1 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (109) implies:
% 27.83/4.62 | (110) all_110_1 = all_107_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (107), (108) imply:
% 27.83/4.62 | (111) all_107_0 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (81), (83) imply:
% 27.83/4.62 | (112) all_104_0 = all_97_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (81), (82) imply:
% 27.83/4.62 | (113) all_104_0 = all_100_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (81), (110) imply:
% 27.83/4.62 | (114) all_107_0 = all_104_0
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (114) implies:
% 27.83/4.62 | (115) all_107_0 = all_104_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (111), (115) imply:
% 27.83/4.62 | (116) all_104_0 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (116) implies:
% 27.83/4.62 | (117) all_104_0 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (112), (113) imply:
% 27.83/4.62 | (118) all_100_1 = all_97_0
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (113), (117) imply:
% 27.83/4.62 | (119) all_100_1 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (93), (94) imply:
% 27.83/4.62 | (120) all_95_1 = all_79_6
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (120) implies:
% 27.83/4.62 | (121) all_95_1 = all_79_6
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (118), (119) imply:
% 27.83/4.62 | (122) all_97_0 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (122) implies:
% 27.83/4.62 | (123) all_97_0 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | COMBINE_EQS: (80), (123) imply:
% 27.83/4.62 | (124) all_93_1 = all_91_1
% 27.83/4.62 |
% 27.83/4.62 | SIMP: (124) implies:
% 27.83/4.63 | (125) all_93_1 = all_91_1
% 27.83/4.63 |
% 27.83/4.63 | COMBINE_EQS: (78), (125) imply:
% 27.83/4.63 | (126) all_91_1 = all_79_5
% 27.83/4.63 |
% 27.83/4.63 | COMBINE_EQS: (79), (125) imply:
% 27.83/4.63 | (127) all_91_1 = all_89_0
% 27.83/4.63 |
% 27.83/4.63 | COMBINE_EQS: (126), (127) imply:
% 27.83/4.63 | (128) all_89_0 = all_79_5
% 27.83/4.63 |
% 27.83/4.63 | COMBINE_EQS: (111), (126) imply:
% 27.83/4.63 | (129) all_107_0 = all_79_5
% 27.83/4.63 |
% 27.83/4.63 | COMBINE_EQS: (100), (129) imply:
% 27.83/4.63 | (130) all_122_1 = all_79_5
% 27.83/4.63 |
% 27.83/4.63 | COMBINE_EQS: (97), (130) imply:
% 27.83/4.63 | (131) all_124_0 = all_79_5
% 27.83/4.63 |
% 27.83/4.63 | REDUCE: (55), (93) imply:
% 27.83/4.63 | (132) k1_zfmisc_1(all_79_6) = all_102_0
% 27.83/4.63 |
% 27.83/4.63 | REDUCE: (47), (121) imply:
% 27.83/4.63 | (133) k1_zfmisc_1(all_79_6) = all_95_0
% 27.83/4.63 |
% 27.83/4.63 | GROUND_INST: instantiating (1) with all_79_5, all_102_0, all_79_6, simplifying
% 27.83/4.63 | with (17), (132) gives:
% 27.83/4.63 | (134) all_102_0 = all_79_5
% 27.83/4.63 |
% 27.83/4.63 | GROUND_INST: instantiating (1) with all_95_0, all_102_0, all_79_6, simplifying
% 27.83/4.63 | with (132), (133) gives:
% 27.83/4.63 | (135) all_102_0 = all_95_0
% 27.83/4.63 |
% 27.83/4.63 | COMBINE_EQS: (134), (135) imply:
% 27.83/4.63 | (136) all_95_0 = all_79_5
% 27.83/4.63 |
% 27.83/4.63 | BETA: splitting (38) gives:
% 27.83/4.63 |
% 27.83/4.63 | Case 1:
% 27.83/4.63 | |
% 27.83/4.63 | | (137) v4_pre_topc(all_79_2, all_79_7)
% 27.83/4.63 | |
% 27.83/4.63 | | BETA: splitting (49) gives:
% 27.83/4.63 | |
% 27.83/4.63 | | Case 1:
% 27.83/4.63 | | |
% 27.83/4.63 | | | (138) ~ m1_subset_1(all_79_3, all_95_0)
% 27.83/4.63 | | |
% 27.83/4.63 | | | REDUCE: (136), (138) imply:
% 27.83/4.63 | | | (139) ~ m1_subset_1(all_79_3, all_79_5)
% 27.83/4.63 | | |
% 27.83/4.63 | | | PRED_UNIFY: (9), (139) imply:
% 27.83/4.63 | | | (140) $false
% 27.83/4.63 | | |
% 27.83/4.63 | | | CLOSE: (140) is inconsistent.
% 27.83/4.63 | | |
% 27.83/4.63 | | Case 2:
% 27.83/4.63 | | |
% 27.83/4.63 | | | (141) m1_subset_1(all_79_2, all_95_0)
% 27.83/4.63 | | |
% 27.83/4.63 | | | REDUCE: (136), (141) imply:
% 27.83/4.63 | | | (142) m1_subset_1(all_79_2, all_79_5)
% 27.83/4.63 | | |
% 27.83/4.63 | | | GROUND_INST: instantiating (73) with all_79_4, all_79_2, all_79_1,
% 27.83/4.63 | | | all_79_0, simplifying with (10), (13), (15), (19), (20),
% 27.83/4.63 | | | (137) gives:
% 27.83/4.63 | | | (143) all_79_0 = all_79_2 | ~ m1_subset_1(all_79_2, all_124_0) | ~
% 27.83/4.63 | | | m1_subset_1(all_79_4, all_124_0)
% 27.83/4.63 | | |
% 27.83/4.63 | | | BETA: splitting (143) gives:
% 27.83/4.63 | | |
% 27.83/4.63 | | | Case 1:
% 27.83/4.63 | | | |
% 27.83/4.63 | | | | (144) ~ m1_subset_1(all_79_2, all_124_0)
% 27.83/4.63 | | | |
% 27.83/4.63 | | | | REDUCE: (131), (144) imply:
% 27.83/4.63 | | | | (145) ~ m1_subset_1(all_79_2, all_79_5)
% 27.83/4.63 | | | |
% 27.83/4.63 | | | | PRED_UNIFY: (142), (145) imply:
% 27.83/4.63 | | | | (146) $false
% 27.83/4.63 | | | |
% 27.83/4.63 | | | | CLOSE: (146) is inconsistent.
% 27.83/4.63 | | | |
% 27.83/4.63 | | | Case 2:
% 27.83/4.63 | | | |
% 27.83/4.63 | | | | (147) all_79_0 = all_79_2 | ~ m1_subset_1(all_79_4, all_124_0)
% 27.83/4.63 | | | |
% 27.83/4.63 | | | | BETA: splitting (147) gives:
% 27.83/4.63 | | | |
% 27.83/4.63 | | | | Case 1:
% 27.83/4.63 | | | | |
% 27.83/4.63 | | | | | (148) ~ m1_subset_1(all_79_4, all_124_0)
% 27.83/4.63 | | | | |
% 27.83/4.63 | | | | | REDUCE: (131), (148) imply:
% 27.83/4.63 | | | | | (149) ~ m1_subset_1(all_79_4, all_79_5)
% 27.83/4.63 | | | | |
% 28.00/4.63 | | | | | PRED_UNIFY: (8), (149) imply:
% 28.00/4.63 | | | | | (150) $false
% 28.00/4.63 | | | | |
% 28.00/4.63 | | | | | CLOSE: (150) is inconsistent.
% 28.00/4.63 | | | | |
% 28.00/4.63 | | | | Case 2:
% 28.00/4.63 | | | | |
% 28.00/4.63 | | | | | (151) all_79_0 = all_79_2
% 28.00/4.63 | | | | |
% 28.00/4.63 | | | | | REDUCE: (4), (151) imply:
% 28.00/4.63 | | | | | (152) $false
% 28.00/4.63 | | | | |
% 28.00/4.63 | | | | | CLOSE: (152) is inconsistent.
% 28.00/4.63 | | | | |
% 28.00/4.63 | | | | End of split
% 28.00/4.63 | | | |
% 28.00/4.63 | | | End of split
% 28.00/4.63 | | |
% 28.00/4.63 | | End of split
% 28.00/4.63 | |
% 28.00/4.63 | Case 2:
% 28.00/4.63 | |
% 28.00/4.63 | | (153) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_79_7) = v0 &
% 28.00/4.63 | | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ~ m1_subset_1(all_79_3,
% 28.00/4.63 | | v1))
% 28.00/4.63 | |
% 28.00/4.63 | | DELTA: instantiating (153) with fresh symbols all_144_0, all_144_1 gives:
% 28.00/4.63 | | (154) u1_struct_0(all_79_7) = all_144_1 & k1_zfmisc_1(all_144_1) =
% 28.00/4.63 | | all_144_0 & $i(all_144_0) & $i(all_144_1) & ~
% 28.00/4.63 | | m1_subset_1(all_79_3, all_144_0)
% 28.00/4.63 | |
% 28.00/4.63 | | ALPHA: (154) implies:
% 28.00/4.63 | | (155) ~ m1_subset_1(all_79_3, all_144_0)
% 28.00/4.63 | | (156) k1_zfmisc_1(all_144_1) = all_144_0
% 28.00/4.63 | | (157) u1_struct_0(all_79_7) = all_144_1
% 28.00/4.63 | |
% 28.00/4.63 | | GROUND_INST: instantiating (2) with all_79_6, all_144_1, all_79_7,
% 28.00/4.63 | | simplifying with (18), (157) gives:
% 28.00/4.63 | | (158) all_144_1 = all_79_6
% 28.00/4.63 | |
% 28.00/4.63 | | REDUCE: (156), (158) imply:
% 28.00/4.63 | | (159) k1_zfmisc_1(all_79_6) = all_144_0
% 28.00/4.63 | |
% 28.00/4.63 | | GROUND_INST: instantiating (1) with all_79_5, all_144_0, all_79_6,
% 28.00/4.63 | | simplifying with (17), (159) gives:
% 28.00/4.63 | | (160) all_144_0 = all_79_5
% 28.00/4.63 | |
% 28.00/4.63 | | REDUCE: (155), (160) imply:
% 28.00/4.63 | | (161) ~ m1_subset_1(all_79_3, all_79_5)
% 28.00/4.63 | |
% 28.00/4.63 | | PRED_UNIFY: (9), (161) imply:
% 28.00/4.63 | | (162) $false
% 28.00/4.63 | |
% 28.00/4.63 | | CLOSE: (162) is inconsistent.
% 28.00/4.63 | |
% 28.00/4.63 | End of split
% 28.00/4.63 |
% 28.00/4.63 End of proof
% 28.00/4.63 % SZS output end Proof for theBenchmark
% 28.00/4.63
% 28.00/4.63 4025ms
%------------------------------------------------------------------------------