TSTP Solution File: TOP028+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : TOP028+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 : 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 : Fri Sep 1 05:58:52 EDT 2023
% Result : Theorem 18.30s 3.22s
% Output : Proof 26.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : TOP028+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 22:56:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.34/1.26 Prover 4: Preprocessing ...
% 3.34/1.27 Prover 1: Preprocessing ...
% 4.04/1.30 Prover 2: Preprocessing ...
% 4.04/1.30 Prover 3: Preprocessing ...
% 4.04/1.30 Prover 5: Preprocessing ...
% 4.04/1.30 Prover 0: Preprocessing ...
% 4.04/1.31 Prover 6: Preprocessing ...
% 9.15/2.03 Prover 2: Proving ...
% 9.15/2.04 Prover 5: Proving ...
% 9.59/2.11 Prover 1: Warning: ignoring some quantifiers
% 10.34/2.16 Prover 3: Warning: ignoring some quantifiers
% 10.34/2.18 Prover 6: Proving ...
% 10.34/2.18 Prover 1: Constructing countermodel ...
% 10.34/2.19 Prover 3: Constructing countermodel ...
% 14.85/2.76 Prover 4: Warning: ignoring some quantifiers
% 15.45/2.85 Prover 4: Constructing countermodel ...
% 15.45/2.85 Prover 0: Proving ...
% 18.30/3.22 Prover 3: proved (2566ms)
% 18.30/3.22
% 18.30/3.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.30/3.22
% 18.30/3.23 Prover 0: stopped
% 18.30/3.23 Prover 5: stopped
% 18.30/3.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.30/3.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.30/3.24 Prover 6: stopped
% 18.30/3.25 Prover 2: stopped
% 18.30/3.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.30/3.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.30/3.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.83/3.31 Prover 7: Preprocessing ...
% 18.83/3.36 Prover 8: Preprocessing ...
% 19.48/3.37 Prover 13: Preprocessing ...
% 19.60/3.39 Prover 10: Preprocessing ...
% 19.60/3.40 Prover 7: Warning: ignoring some quantifiers
% 19.60/3.41 Prover 11: Preprocessing ...
% 19.85/3.41 Prover 7: Constructing countermodel ...
% 20.62/3.56 Prover 13: Warning: ignoring some quantifiers
% 20.62/3.56 Prover 10: Warning: ignoring some quantifiers
% 21.12/3.60 Prover 8: Warning: ignoring some quantifiers
% 21.12/3.61 Prover 10: Constructing countermodel ...
% 21.12/3.62 Prover 8: Constructing countermodel ...
% 21.12/3.62 Prover 13: Constructing countermodel ...
% 25.79/4.20 Prover 10: Found proof (size 143)
% 25.79/4.20 Prover 10: proved (957ms)
% 25.79/4.20 Prover 7: stopped
% 25.79/4.20 Prover 13: stopped
% 25.79/4.20 Prover 8: stopped
% 25.79/4.20 Prover 1: stopped
% 25.79/4.20 Prover 4: stopped
% 25.79/4.23 Prover 11: Warning: ignoring some quantifiers
% 25.79/4.24 Prover 11: Constructing countermodel ...
% 25.79/4.25 Prover 11: stopped
% 25.79/4.25
% 25.79/4.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.79/4.25
% 26.13/4.29 % SZS output start Proof for theBenchmark
% 26.13/4.30 Assumptions after simplification:
% 26.13/4.30 ---------------------------------
% 26.13/4.30
% 26.13/4.30 (cc1_tops_1)
% 26.13/4.32 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.32 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 26.13/4.32 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~
% 26.13/4.32 m1_subset_1(v3, v2) | v4_pre_topc(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) |
% 26.13/4.32 ~ v1_xboole_0(v3) | ~ m1_subset_1(v3, v2) | v3_pre_topc(v3, v0))))
% 26.13/4.32
% 26.13/4.32 (cc2_tops_1)
% 26.13/4.32 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.32 l1_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i]
% 26.13/4.32 : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~ m1_subset_1(v3, v2) | v2_tops_1(v3,
% 26.13/4.32 v0))))
% 26.13/4.32
% 26.13/4.32 (cc3_tops_1)
% 26.13/4.32 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.32 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 26.13/4.32 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~
% 26.13/4.33 m1_subset_1(v3, v2) | v3_tops_1(v3, v0))))
% 26.13/4.33
% 26.13/4.33 (cc4_tops_1)
% 26.13/4.33 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.33 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 26.13/4.33 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~
% 26.13/4.33 m1_subset_1(v3, v2) | v2_tops_1(v3, v0))))
% 26.13/4.33
% 26.13/4.33 (cc5_tops_1)
% 26.13/4.33 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.33 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 26.13/4.33 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v2_tops_1(v3, v0) | ~
% 26.13/4.33 v4_pre_topc(v3, v0) | ~ m1_subset_1(v3, v2) | v3_tops_1(v3, v0))))
% 26.13/4.33
% 26.13/4.33 (cc6_tops_1)
% 26.13/4.33 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.33 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 26.13/4.33 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~
% 26.13/4.33 v3_pre_topc(v3, v0) | ~ m1_subset_1(v3, v2) | v2_tops_1(v3, v0)) & !
% 26.13/4.33 [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~ v3_pre_topc(v3, v0) | ~
% 26.13/4.33 m1_subset_1(v3, v2) | v4_pre_topc(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) |
% 26.13/4.33 ~ v3_tops_1(v3, v0) | ~ v3_pre_topc(v3, v0) | ~ m1_subset_1(v3, v2) |
% 26.13/4.33 v1_xboole_0(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~
% 26.13/4.33 v3_pre_topc(v3, v0) | ~ m1_subset_1(v3, v2) | v5_membered(v3)) & !
% 26.13/4.33 [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~ v3_pre_topc(v3, v0) | ~
% 26.13/4.33 m1_subset_1(v3, v2) | v4_membered(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 26.13/4.33 v3_tops_1(v3, v0) | ~ v3_pre_topc(v3, v0) | ~ m1_subset_1(v3, v2) |
% 26.13/4.33 v3_membered(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~
% 26.13/4.33 v3_pre_topc(v3, v0) | ~ m1_subset_1(v3, v2) | v2_membered(v3)) & !
% 26.13/4.33 [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~ v3_pre_topc(v3, v0) | ~
% 26.13/4.33 m1_subset_1(v3, v2) | v1_membered(v3))))
% 26.13/4.33
% 26.13/4.33 (dt_k1_pre_topc)
% 26.13/4.33 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.33 l1_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : (k1_pre_topc(v0) = v2 &
% 26.13/4.33 k1_zfmisc_1(v1) = v3 & $i(v3) & $i(v2) & m1_subset_1(v2, v3)))
% 26.13/4.33
% 26.13/4.33 (dt_l1_pre_topc)
% 26.13/4.33 ! [v0: $i] : ( ~ $i(v0) | ~ l1_pre_topc(v0) | l1_struct_0(v0))
% 26.13/4.33
% 26.13/4.33 (fc7_tops_1)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_pre_topc(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v4_pre_topc(v1, v0)) & ! [v0: $i] :
% 26.13/4.34 ! [v1: $i] : ( ~ (k1_pre_topc(v0) = v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ~
% 26.13/4.34 v2_pre_topc(v0) | v3_pre_topc(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 26.13/4.34 (k1_pre_topc(v0) = v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0)
% 26.13/4.34 | v1_xboole_0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_pre_topc(v0) = v1)
% 26.13/4.34 | ~ $i(v0) | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v5_membered(v1)) &
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_pre_topc(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v4_membered(v1)) & ! [v0: $i] : !
% 26.13/4.34 [v1: $i] : ( ~ (k1_pre_topc(v0) = v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ~
% 26.13/4.34 v2_pre_topc(v0) | v3_membered(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 26.13/4.34 (k1_pre_topc(v0) = v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0)
% 26.13/4.34 | v2_membered(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_pre_topc(v0) = v1)
% 26.13/4.34 | ~ $i(v0) | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v1_membered(v1))
% 26.13/4.34
% 26.13/4.34 (rc1_tops_1)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.13/4.34 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_pre_topc(v3, v0) &
% 26.13/4.34 m1_subset_1(v3, v2)))
% 26.13/4.34
% 26.13/4.34 (rc2_tops_1)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.13/4.34 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) &
% 26.13/4.34 v3_pre_topc(v3, v0) & m1_subset_1(v3, v2)))
% 26.13/4.34
% 26.13/4.34 (rc3_tops_1)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : ?
% 26.13/4.34 [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) &
% 26.13/4.34 v3_pre_topc(v3, v0) & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3)))
% 26.13/4.34
% 26.13/4.34 (rc4_tops_1)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3)
% 26.13/4.34 & $i(v2) & v2_tops_1(v3, v0) & v1_xboole_0(v3) & v5_membered(v3) &
% 26.13/4.34 v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & v1_membered(v3) &
% 26.13/4.34 m1_subset_1(v3, v2)))
% 26.13/4.34
% 26.13/4.34 (rc5_struct_0)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_struct_0(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.13/4.34 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & m1_subset_1(v3, v2) & ~
% 26.13/4.34 v1_xboole_0(v3)))
% 26.13/4.34
% 26.13/4.34 (rc5_tops_1)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.13/4.34 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_tops_1(v3, v0) & v2_tops_1(v3,
% 26.13/4.34 v0) & v4_pre_topc(v3, v0) & v3_pre_topc(v3, v0) & v1_xboole_0(v3) &
% 26.13/4.34 v5_membered(v3) & v4_membered(v3) & v3_membered(v3) & v2_membered(v3) &
% 26.13/4.34 v1_membered(v3) & m1_subset_1(v3, v2)))
% 26.13/4.34
% 26.13/4.34 (rc6_pre_topc)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] :
% 26.13/4.34 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) &
% 26.13/4.34 m1_subset_1(v3, v2)))
% 26.13/4.34
% 26.13/4.34 (rc7_pre_topc)
% 26.13/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.34 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : ?
% 26.13/4.34 [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) &
% 26.13/4.34 m1_subset_1(v3, v2) & ~ v1_xboole_0(v3)))
% 26.13/4.34
% 26.13/4.34 (t10_tsp_2)
% 26.13/4.34 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (u1_struct_0(v0) = v1 &
% 26.13/4.34 k1_zfmisc_1(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & l1_pre_topc(v0) &
% 26.13/4.34 v2_pre_topc(v0) & ~ v3_struct_0(v0) & ! [v3: $i] : ( ~ $i(v3) | ~
% 26.13/4.34 v1_tsp_2(v3, v0) | ~ m1_subset_1(v3, v2)))
% 26.13/4.34
% 26.13/4.34 (t11_tsp_1)
% 26.13/4.35 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.35 l1_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 26.13/4.35 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_tex_2(v3, v0) | ~
% 26.13/4.35 m1_subset_1(v3, v2) | v1_tsp_1(v3, v0))))
% 26.13/4.35
% 26.13/4.35 (t35_tex_2)
% 26.13/4.35 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.35 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] :
% 26.13/4.35 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~
% 26.13/4.35 v1_xboole_0(v3) | ~ m1_subset_1(v3, v2) | v3_tex_2(v3, v0))))
% 26.13/4.35
% 26.13/4.35 (t6_boole)
% 26.13/4.35 $i(k1_xboole_0) & ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~
% 26.13/4.35 v1_xboole_0(v0))
% 26.13/4.35
% 26.13/4.35 (t9_tsp_2)
% 26.13/4.35 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.35 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] :
% 26.13/4.35 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v1_tsp_1(v3,
% 26.13/4.35 v0) | ~ m1_subset_1(v3, v2) | ? [v4: $i] : ($i(v4) & r1_tarski(v3,
% 26.13/4.35 v4) & v1_tsp_2(v4, v0) & m1_subset_1(v4, v2)))))
% 26.13/4.35
% 26.13/4.35 (function-axioms)
% 26.13/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_pre_topc(v2) = v1)
% 26.13/4.35 | ~ (k1_pre_topc(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 26.13/4.35 = v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i]
% 26.13/4.35 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 26.13/4.35 (k1_zfmisc_1(v2) = v0))
% 26.13/4.35
% 26.13/4.35 Further assumptions not needed in the proof:
% 26.13/4.35 --------------------------------------------
% 26.13/4.35 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered,
% 26.13/4.35 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered,
% 26.13/4.35 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered,
% 26.13/4.35 cc3_membered, cc4_membered, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_l1_struct_0,
% 26.13/4.35 dt_m1_subset_1, dt_u1_struct_0, existence_l1_pre_topc, existence_l1_struct_0,
% 26.13/4.35 existence_m1_subset_1, fc1_pre_topc, fc1_struct_0, fc1_subset_1, fc1_tops_1,
% 26.13/4.35 fc6_membered, rc1_membered, rc1_subset_1, rc2_subset_1, rc3_struct_0,
% 26.13/4.35 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 26.13/4.35 t7_boole, t8_boole
% 26.13/4.35
% 26.13/4.35 Those formulas are unsatisfiable:
% 26.13/4.35 ---------------------------------
% 26.13/4.35
% 26.13/4.35 Begin of proof
% 26.13/4.35 |
% 26.13/4.35 | ALPHA: (fc7_tops_1) implies:
% 26.13/4.35 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_pre_topc(v0) = v1) | ~ $i(v0) | ~
% 26.13/4.35 | l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v1_xboole_0(v1))
% 26.13/4.35 |
% 26.13/4.35 | ALPHA: (t6_boole) implies:
% 26.13/4.35 | (2) ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~ v1_xboole_0(v0))
% 26.13/4.35 |
% 26.13/4.35 | ALPHA: (function-axioms) implies:
% 26.13/4.35 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.13/4.35 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 26.13/4.35 |
% 26.13/4.35 | DELTA: instantiating (t10_tsp_2) with fresh symbols all_64_0, all_64_1,
% 26.13/4.35 | all_64_2 gives:
% 26.13/4.35 | (4) u1_struct_0(all_64_2) = all_64_1 & k1_zfmisc_1(all_64_1) = all_64_0 &
% 26.13/4.35 | $i(all_64_0) & $i(all_64_1) & $i(all_64_2) & l1_pre_topc(all_64_2) &
% 26.13/4.35 | v2_pre_topc(all_64_2) & ~ v3_struct_0(all_64_2) & ! [v0: $i] : ( ~
% 26.13/4.35 | $i(v0) | ~ v1_tsp_2(v0, all_64_2) | ~ m1_subset_1(v0, all_64_0))
% 26.13/4.35 |
% 26.13/4.35 | ALPHA: (4) implies:
% 26.13/4.36 | (5) ~ v3_struct_0(all_64_2)
% 26.13/4.36 | (6) v2_pre_topc(all_64_2)
% 26.13/4.36 | (7) l1_pre_topc(all_64_2)
% 26.13/4.36 | (8) $i(all_64_2)
% 26.13/4.36 | (9) k1_zfmisc_1(all_64_1) = all_64_0
% 26.13/4.36 | (10) u1_struct_0(all_64_2) = all_64_1
% 26.13/4.36 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ v1_tsp_2(v0, all_64_2) | ~
% 26.13/4.36 | m1_subset_1(v0, all_64_0))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (dt_l1_pre_topc) with all_64_2, simplifying with
% 26.13/4.36 | (7), (8) gives:
% 26.13/4.36 | (12) l1_struct_0(all_64_2)
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (rc3_tops_1) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (5), (6), (7), (8), (10) gives:
% 26.13/4.36 | (13) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.13/4.36 | $i(v0) & v4_pre_topc(v1, all_64_2) & v3_pre_topc(v1, all_64_2) &
% 26.13/4.36 | m1_subset_1(v1, v0) & ~ v1_xboole_0(v1))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (rc7_pre_topc) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (5), (6), (7), (8), (10) gives:
% 26.13/4.36 | (14) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.13/4.36 | $i(v0) & v4_pre_topc(v1, all_64_2) & m1_subset_1(v1, v0) & ~
% 26.13/4.36 | v1_xboole_0(v1))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (t9_tsp_2) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (5), (6), (7), (8), (10) gives:
% 26.13/4.36 | (15) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.13/4.36 | $i(v1) | ~ v1_tsp_1(v1, all_64_2) | ~ m1_subset_1(v1, v0) | ?
% 26.13/4.36 | [v2: $i] : ($i(v2) & r1_tarski(v1, v2) & v1_tsp_2(v2, all_64_2) &
% 26.13/4.36 | m1_subset_1(v2, v0))))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (t35_tex_2) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (5), (6), (7), (8), (10) gives:
% 26.13/4.36 | (16) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.13/4.36 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) |
% 26.13/4.36 | v3_tex_2(v1, all_64_2)))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (rc5_tops_1) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (6), (7), (8), (10) gives:
% 26.13/4.36 | (17) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.13/4.36 | $i(v0) & v3_tops_1(v1, all_64_2) & v2_tops_1(v1, all_64_2) &
% 26.13/4.36 | v4_pre_topc(v1, all_64_2) & v3_pre_topc(v1, all_64_2) &
% 26.13/4.36 | v1_xboole_0(v1) & v5_membered(v1) & v4_membered(v1) &
% 26.13/4.36 | v3_membered(v1) & v2_membered(v1) & v1_membered(v1) &
% 26.13/4.36 | m1_subset_1(v1, v0))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (rc2_tops_1) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (6), (7), (8), (10) gives:
% 26.13/4.36 | (18) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.13/4.36 | $i(v0) & v4_pre_topc(v1, all_64_2) & v3_pre_topc(v1, all_64_2) &
% 26.13/4.36 | m1_subset_1(v1, v0))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (rc6_pre_topc) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (6), (7), (8), (10) gives:
% 26.13/4.36 | (19) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.13/4.36 | $i(v0) & v4_pre_topc(v1, all_64_2) & m1_subset_1(v1, v0))
% 26.13/4.36 |
% 26.13/4.36 | GROUND_INST: instantiating (rc1_tops_1) with all_64_2, all_64_1, simplifying
% 26.13/4.36 | with (6), (7), (8), (10) gives:
% 26.13/4.37 | (20) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.13/4.37 | $i(v0) & v3_pre_topc(v1, all_64_2) & m1_subset_1(v1, v0))
% 26.13/4.37 |
% 26.13/4.37 | GROUND_INST: instantiating (cc6_tops_1) with all_64_2, all_64_1, simplifying
% 26.13/4.37 | with (6), (7), (8), (10) gives:
% 26.13/4.37 | (21) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.13/4.37 | $i(v1) | ~ v3_tops_1(v1, all_64_2) | ~ v3_pre_topc(v1, all_64_2)
% 26.13/4.37 | | ~ m1_subset_1(v1, v0) | v2_tops_1(v1, all_64_2)) & ! [v1: $i]
% 26.13/4.37 | : ( ~ $i(v1) | ~ v3_tops_1(v1, all_64_2) | ~ v3_pre_topc(v1,
% 26.13/4.37 | all_64_2) | ~ m1_subset_1(v1, v0) | v4_pre_topc(v1, all_64_2))
% 26.13/4.37 | & ! [v1: $i] : ( ~ $i(v1) | ~ v3_tops_1(v1, all_64_2) | ~
% 26.13/4.37 | v3_pre_topc(v1, all_64_2) | ~ m1_subset_1(v1, v0) |
% 26.13/4.37 | v1_xboole_0(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_tops_1(v1,
% 26.13/4.37 | all_64_2) | ~ v3_pre_topc(v1, all_64_2) | ~ m1_subset_1(v1,
% 26.13/4.37 | v0) | v5_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 26.13/4.37 | v3_tops_1(v1, all_64_2) | ~ v3_pre_topc(v1, all_64_2) | ~
% 26.13/4.37 | m1_subset_1(v1, v0) | v4_membered(v1)) & ! [v1: $i] : ( ~ $i(v1)
% 26.13/4.37 | | ~ v3_tops_1(v1, all_64_2) | ~ v3_pre_topc(v1, all_64_2) | ~
% 26.13/4.37 | m1_subset_1(v1, v0) | v3_membered(v1)) & ! [v1: $i] : ( ~ $i(v1)
% 26.13/4.37 | | ~ v3_tops_1(v1, all_64_2) | ~ v3_pre_topc(v1, all_64_2) | ~
% 26.13/4.37 | m1_subset_1(v1, v0) | v2_membered(v1)) & ! [v1: $i] : ( ~ $i(v1)
% 26.13/4.37 | | ~ v3_tops_1(v1, all_64_2) | ~ v3_pre_topc(v1, all_64_2) | ~
% 26.13/4.37 | m1_subset_1(v1, v0) | v1_membered(v1)))
% 26.13/4.37 |
% 26.13/4.37 | GROUND_INST: instantiating (cc4_tops_1) with all_64_2, all_64_1, simplifying
% 26.13/4.37 | with (6), (7), (8), (10) gives:
% 26.13/4.37 | (22) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.13/4.37 | $i(v1) | ~ v3_tops_1(v1, all_64_2) | ~ m1_subset_1(v1, v0) |
% 26.13/4.37 | v2_tops_1(v1, all_64_2)))
% 26.13/4.37 |
% 26.13/4.37 | GROUND_INST: instantiating (cc5_tops_1) with all_64_2, all_64_1, simplifying
% 26.13/4.37 | with (6), (7), (8), (10) gives:
% 26.13/4.37 | (23) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.13/4.37 | $i(v1) | ~ v2_tops_1(v1, all_64_2) | ~ v4_pre_topc(v1, all_64_2)
% 26.13/4.37 | | ~ m1_subset_1(v1, v0) | v3_tops_1(v1, all_64_2)))
% 26.13/4.37 |
% 26.13/4.37 | GROUND_INST: instantiating (cc3_tops_1) with all_64_2, all_64_1, simplifying
% 26.59/4.37 | with (6), (7), (8), (10) gives:
% 26.59/4.37 | (24) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.59/4.37 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) |
% 26.59/4.37 | v3_tops_1(v1, all_64_2)))
% 26.59/4.37 |
% 26.59/4.37 | GROUND_INST: instantiating (cc1_tops_1) with all_64_2, all_64_1, simplifying
% 26.59/4.37 | with (6), (7), (8), (10) gives:
% 26.59/4.37 | (25) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.59/4.37 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) |
% 26.59/4.37 | v4_pre_topc(v1, all_64_2)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 26.59/4.37 | v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) | v3_pre_topc(v1,
% 26.59/4.37 | all_64_2)))
% 26.59/4.37 |
% 26.59/4.37 | GROUND_INST: instantiating (t11_tsp_1) with all_64_2, all_64_1, simplifying
% 26.59/4.37 | with (5), (7), (8), (10) gives:
% 26.59/4.37 | (26) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.59/4.37 | $i(v1) | ~ v3_tex_2(v1, all_64_2) | ~ m1_subset_1(v1, v0) |
% 26.59/4.37 | v1_tsp_1(v1, all_64_2)))
% 26.59/4.37 |
% 26.59/4.37 | GROUND_INST: instantiating (rc4_tops_1) with all_64_2, all_64_1, simplifying
% 26.59/4.37 | with (7), (8), (10) gives:
% 26.59/4.38 | (27) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.59/4.38 | $i(v0) & v2_tops_1(v1, all_64_2) & v1_xboole_0(v1) & v5_membered(v1)
% 26.59/4.38 | & v4_membered(v1) & v3_membered(v1) & v2_membered(v1) &
% 26.59/4.38 | v1_membered(v1) & m1_subset_1(v1, v0))
% 26.59/4.38 |
% 26.59/4.38 | GROUND_INST: instantiating (cc2_tops_1) with all_64_2, all_64_1, simplifying
% 26.59/4.38 | with (7), (8), (10) gives:
% 26.59/4.38 | (28) ? [v0: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.59/4.38 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) |
% 26.59/4.38 | v2_tops_1(v1, all_64_2)))
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (20) with fresh symbols all_75_0, all_75_1 gives:
% 26.59/4.38 | (29) k1_zfmisc_1(all_64_1) = all_75_1 & $i(all_75_0) & $i(all_75_1) &
% 26.59/4.38 | v3_pre_topc(all_75_0, all_64_2) & m1_subset_1(all_75_0, all_75_1)
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (29) implies:
% 26.59/4.38 | (30) k1_zfmisc_1(all_64_1) = all_75_1
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (19) with fresh symbols all_77_0, all_77_1 gives:
% 26.59/4.38 | (31) k1_zfmisc_1(all_64_1) = all_77_1 & $i(all_77_0) & $i(all_77_1) &
% 26.59/4.38 | v4_pre_topc(all_77_0, all_64_2) & m1_subset_1(all_77_0, all_77_1)
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (31) implies:
% 26.59/4.38 | (32) k1_zfmisc_1(all_64_1) = all_77_1
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (22) with fresh symbol all_79_0 gives:
% 26.59/4.38 | (33) k1_zfmisc_1(all_64_1) = all_79_0 & $i(all_79_0) & ! [v0: $i] : ( ~
% 26.59/4.38 | $i(v0) | ~ v3_tops_1(v0, all_64_2) | ~ m1_subset_1(v0, all_79_0) |
% 26.59/4.38 | v2_tops_1(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (33) implies:
% 26.59/4.38 | (34) k1_zfmisc_1(all_64_1) = all_79_0
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (14) with fresh symbols all_82_0, all_82_1 gives:
% 26.59/4.38 | (35) k1_zfmisc_1(all_64_1) = all_82_1 & $i(all_82_0) & $i(all_82_1) &
% 26.59/4.38 | v4_pre_topc(all_82_0, all_64_2) & m1_subset_1(all_82_0, all_82_1) & ~
% 26.59/4.38 | v1_xboole_0(all_82_0)
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (35) implies:
% 26.59/4.38 | (36) k1_zfmisc_1(all_64_1) = all_82_1
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (28) with fresh symbol all_84_0 gives:
% 26.59/4.38 | (37) k1_zfmisc_1(all_64_1) = all_84_0 & $i(all_84_0) & ! [v0: $i] : ( ~
% 26.59/4.38 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_84_0) |
% 26.59/4.38 | v2_tops_1(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (37) implies:
% 26.59/4.38 | (38) k1_zfmisc_1(all_64_1) = all_84_0
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (26) with fresh symbol all_87_0 gives:
% 26.59/4.38 | (39) k1_zfmisc_1(all_64_1) = all_87_0 & $i(all_87_0) & ! [v0: $i] : ( ~
% 26.59/4.38 | $i(v0) | ~ v3_tex_2(v0, all_64_2) | ~ m1_subset_1(v0, all_87_0) |
% 26.59/4.38 | v1_tsp_1(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (39) implies:
% 26.59/4.38 | (40) k1_zfmisc_1(all_64_1) = all_87_0
% 26.59/4.38 | (41) ! [v0: $i] : ( ~ $i(v0) | ~ v3_tex_2(v0, all_64_2) | ~
% 26.59/4.38 | m1_subset_1(v0, all_87_0) | v1_tsp_1(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (24) with fresh symbol all_90_0 gives:
% 26.59/4.38 | (42) k1_zfmisc_1(all_64_1) = all_90_0 & $i(all_90_0) & ! [v0: $i] : ( ~
% 26.59/4.38 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_90_0) |
% 26.59/4.38 | v3_tops_1(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (42) implies:
% 26.59/4.38 | (43) k1_zfmisc_1(all_64_1) = all_90_0
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (18) with fresh symbols all_93_0, all_93_1 gives:
% 26.59/4.38 | (44) k1_zfmisc_1(all_64_1) = all_93_1 & $i(all_93_0) & $i(all_93_1) &
% 26.59/4.38 | v4_pre_topc(all_93_0, all_64_2) & v3_pre_topc(all_93_0, all_64_2) &
% 26.59/4.38 | m1_subset_1(all_93_0, all_93_1)
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (44) implies:
% 26.59/4.38 | (45) k1_zfmisc_1(all_64_1) = all_93_1
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (16) with fresh symbol all_95_0 gives:
% 26.59/4.38 | (46) k1_zfmisc_1(all_64_1) = all_95_0 & $i(all_95_0) & ! [v0: $i] : ( ~
% 26.59/4.38 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_95_0) |
% 26.59/4.38 | v3_tex_2(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (46) implies:
% 26.59/4.38 | (47) k1_zfmisc_1(all_64_1) = all_95_0
% 26.59/4.38 | (48) ! [v0: $i] : ( ~ $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0,
% 26.59/4.38 | all_95_0) | v3_tex_2(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (23) with fresh symbol all_98_0 gives:
% 26.59/4.38 | (49) k1_zfmisc_1(all_64_1) = all_98_0 & $i(all_98_0) & ! [v0: $i] : ( ~
% 26.59/4.38 | $i(v0) | ~ v2_tops_1(v0, all_64_2) | ~ v4_pre_topc(v0, all_64_2) |
% 26.59/4.38 | ~ m1_subset_1(v0, all_98_0) | v3_tops_1(v0, all_64_2))
% 26.59/4.38 |
% 26.59/4.38 | ALPHA: (49) implies:
% 26.59/4.38 | (50) k1_zfmisc_1(all_64_1) = all_98_0
% 26.59/4.38 |
% 26.59/4.38 | DELTA: instantiating (13) with fresh symbols all_101_0, all_101_1 gives:
% 26.59/4.39 | (51) k1_zfmisc_1(all_64_1) = all_101_1 & $i(all_101_0) & $i(all_101_1) &
% 26.59/4.39 | v4_pre_topc(all_101_0, all_64_2) & v3_pre_topc(all_101_0, all_64_2) &
% 26.59/4.39 | m1_subset_1(all_101_0, all_101_1) & ~ v1_xboole_0(all_101_0)
% 26.59/4.39 |
% 26.59/4.39 | ALPHA: (51) implies:
% 26.59/4.39 | (52) k1_zfmisc_1(all_64_1) = all_101_1
% 26.59/4.39 |
% 26.59/4.39 | DELTA: instantiating (15) with fresh symbol all_103_0 gives:
% 26.59/4.39 | (53) k1_zfmisc_1(all_64_1) = all_103_0 & $i(all_103_0) & ! [v0: $i] : ( ~
% 26.59/4.39 | $i(v0) | ~ v1_tsp_1(v0, all_64_2) | ~ m1_subset_1(v0, all_103_0) |
% 26.59/4.39 | ? [v1: $i] : ($i(v1) & r1_tarski(v0, v1) & v1_tsp_2(v1, all_64_2) &
% 26.59/4.39 | m1_subset_1(v1, all_103_0)))
% 26.59/4.39 |
% 26.59/4.39 | ALPHA: (53) implies:
% 26.59/4.39 | (54) k1_zfmisc_1(all_64_1) = all_103_0
% 26.59/4.39 | (55) ! [v0: $i] : ( ~ $i(v0) | ~ v1_tsp_1(v0, all_64_2) | ~
% 26.59/4.39 | m1_subset_1(v0, all_103_0) | ? [v1: $i] : ($i(v1) & r1_tarski(v0,
% 26.59/4.39 | v1) & v1_tsp_2(v1, all_64_2) & m1_subset_1(v1, all_103_0)))
% 26.59/4.39 |
% 26.59/4.39 | DELTA: instantiating (25) with fresh symbol all_106_0 gives:
% 26.59/4.39 | (56) k1_zfmisc_1(all_64_1) = all_106_0 & $i(all_106_0) & ! [v0: $i] : ( ~
% 26.59/4.39 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_106_0) |
% 26.59/4.39 | v4_pre_topc(v0, all_64_2)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 26.59/4.39 | v1_xboole_0(v0) | ~ m1_subset_1(v0, all_106_0) | v3_pre_topc(v0,
% 26.59/4.39 | all_64_2))
% 26.59/4.39 |
% 26.59/4.39 | ALPHA: (56) implies:
% 26.59/4.39 | (57) k1_zfmisc_1(all_64_1) = all_106_0
% 26.59/4.39 |
% 26.59/4.39 | DELTA: instantiating (27) with fresh symbols all_109_0, all_109_1 gives:
% 26.59/4.39 | (58) k1_zfmisc_1(all_64_1) = all_109_1 & $i(all_109_0) & $i(all_109_1) &
% 26.59/4.39 | v2_tops_1(all_109_0, all_64_2) & v1_xboole_0(all_109_0) &
% 26.59/4.39 | v5_membered(all_109_0) & v4_membered(all_109_0) &
% 26.59/4.39 | v3_membered(all_109_0) & v2_membered(all_109_0) &
% 26.59/4.39 | v1_membered(all_109_0) & m1_subset_1(all_109_0, all_109_1)
% 26.59/4.39 |
% 26.59/4.39 | ALPHA: (58) implies:
% 26.59/4.39 | (59) k1_zfmisc_1(all_64_1) = all_109_1
% 26.59/4.39 |
% 26.59/4.39 | DELTA: instantiating (17) with fresh symbols all_111_0, all_111_1 gives:
% 26.59/4.39 | (60) k1_zfmisc_1(all_64_1) = all_111_1 & $i(all_111_0) & $i(all_111_1) &
% 26.59/4.39 | v3_tops_1(all_111_0, all_64_2) & v2_tops_1(all_111_0, all_64_2) &
% 26.59/4.39 | v4_pre_topc(all_111_0, all_64_2) & v3_pre_topc(all_111_0, all_64_2) &
% 26.59/4.39 | v1_xboole_0(all_111_0) & v5_membered(all_111_0) &
% 26.59/4.39 | v4_membered(all_111_0) & v3_membered(all_111_0) &
% 26.59/4.39 | v2_membered(all_111_0) & v1_membered(all_111_0) &
% 26.59/4.39 | m1_subset_1(all_111_0, all_111_1)
% 26.59/4.39 |
% 26.59/4.39 | ALPHA: (60) implies:
% 26.59/4.39 | (61) k1_zfmisc_1(all_64_1) = all_111_1
% 26.59/4.39 |
% 26.59/4.39 | DELTA: instantiating (21) with fresh symbol all_113_0 gives:
% 26.59/4.39 | (62) k1_zfmisc_1(all_64_1) = all_113_0 & $i(all_113_0) & ! [v0: $i] : ( ~
% 26.59/4.39 | $i(v0) | ~ v3_tops_1(v0, all_64_2) | ~ v3_pre_topc(v0, all_64_2) |
% 26.59/4.39 | ~ m1_subset_1(v0, all_113_0) | v2_tops_1(v0, all_64_2)) & ! [v0:
% 26.59/4.39 | $i] : ( ~ $i(v0) | ~ v3_tops_1(v0, all_64_2) | ~ v3_pre_topc(v0,
% 26.59/4.39 | all_64_2) | ~ m1_subset_1(v0, all_113_0) | v4_pre_topc(v0,
% 26.59/4.39 | all_64_2)) & ! [v0: $i] : ( ~ $i(v0) | ~ v3_tops_1(v0, all_64_2)
% 26.59/4.39 | | ~ v3_pre_topc(v0, all_64_2) | ~ m1_subset_1(v0, all_113_0) |
% 26.59/4.39 | v1_xboole_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ v3_tops_1(v0,
% 26.59/4.39 | all_64_2) | ~ v3_pre_topc(v0, all_64_2) | ~ m1_subset_1(v0,
% 26.59/4.39 | all_113_0) | v5_membered(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 26.59/4.39 | v3_tops_1(v0, all_64_2) | ~ v3_pre_topc(v0, all_64_2) | ~
% 26.59/4.39 | m1_subset_1(v0, all_113_0) | v4_membered(v0)) & ! [v0: $i] : ( ~
% 26.59/4.39 | $i(v0) | ~ v3_tops_1(v0, all_64_2) | ~ v3_pre_topc(v0, all_64_2) |
% 26.59/4.39 | ~ m1_subset_1(v0, all_113_0) | v3_membered(v0)) & ! [v0: $i] : ( ~
% 26.59/4.39 | $i(v0) | ~ v3_tops_1(v0, all_64_2) | ~ v3_pre_topc(v0, all_64_2) |
% 26.59/4.39 | ~ m1_subset_1(v0, all_113_0) | v2_membered(v0)) & ! [v0: $i] : ( ~
% 26.59/4.39 | $i(v0) | ~ v3_tops_1(v0, all_64_2) | ~ v3_pre_topc(v0, all_64_2) |
% 26.59/4.39 | ~ m1_subset_1(v0, all_113_0) | v1_membered(v0))
% 26.59/4.39 |
% 26.59/4.39 | ALPHA: (62) implies:
% 26.59/4.39 | (63) k1_zfmisc_1(all_64_1) = all_113_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_77_1, all_79_0, all_64_1, simplifying
% 26.59/4.39 | with (32), (34) gives:
% 26.59/4.39 | (64) all_79_0 = all_77_1
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_77_1, all_82_1, all_64_1, simplifying
% 26.59/4.39 | with (32), (36) gives:
% 26.59/4.39 | (65) all_82_1 = all_77_1
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_79_0, all_84_0, all_64_1, simplifying
% 26.59/4.39 | with (34), (38) gives:
% 26.59/4.39 | (66) all_84_0 = all_79_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_90_0, all_98_0, all_64_1, simplifying
% 26.59/4.39 | with (43), (50) gives:
% 26.59/4.39 | (67) all_98_0 = all_90_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_90_0, all_101_1, all_64_1, simplifying
% 26.59/4.39 | with (43), (52) gives:
% 26.59/4.39 | (68) all_101_1 = all_90_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_87_0, all_101_1, all_64_1, simplifying
% 26.59/4.39 | with (40), (52) gives:
% 26.59/4.39 | (69) all_101_1 = all_87_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_84_0, all_101_1, all_64_1, simplifying
% 26.59/4.39 | with (38), (52) gives:
% 26.59/4.39 | (70) all_101_1 = all_84_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_98_0, all_103_0, all_64_1, simplifying
% 26.59/4.39 | with (50), (54) gives:
% 26.59/4.39 | (71) all_103_0 = all_98_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_95_0, all_106_0, all_64_1, simplifying
% 26.59/4.39 | with (47), (57) gives:
% 26.59/4.39 | (72) all_106_0 = all_95_0
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_93_1, all_106_0, all_64_1, simplifying
% 26.59/4.39 | with (45), (57) gives:
% 26.59/4.39 | (73) all_106_0 = all_93_1
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_82_1, all_106_0, all_64_1, simplifying
% 26.59/4.39 | with (36), (57) gives:
% 26.59/4.39 | (74) all_106_0 = all_82_1
% 26.59/4.39 |
% 26.59/4.39 | GROUND_INST: instantiating (3) with all_103_0, all_109_1, all_64_1,
% 26.59/4.39 | simplifying with (54), (59) gives:
% 26.59/4.40 | (75) all_109_1 = all_103_0
% 26.59/4.40 |
% 26.59/4.40 | GROUND_INST: instantiating (3) with all_64_0, all_111_1, all_64_1, simplifying
% 26.59/4.40 | with (9), (61) gives:
% 26.59/4.40 | (76) all_111_1 = all_64_0
% 26.59/4.40 |
% 26.59/4.40 | GROUND_INST: instantiating (3) with all_95_0, all_111_1, all_64_1, simplifying
% 26.59/4.40 | with (47), (61) gives:
% 26.59/4.40 | (77) all_111_1 = all_95_0
% 26.59/4.40 |
% 26.71/4.40 | GROUND_INST: instantiating (3) with all_109_1, all_113_0, all_64_1,
% 26.71/4.40 | simplifying with (59), (63) gives:
% 26.71/4.40 | (78) all_113_0 = all_109_1
% 26.71/4.40 |
% 26.71/4.40 | GROUND_INST: instantiating (3) with all_75_1, all_113_0, all_64_1, simplifying
% 26.71/4.40 | with (30), (63) gives:
% 26.71/4.40 | (79) all_113_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (78), (79) imply:
% 26.71/4.40 | (80) all_109_1 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (80) implies:
% 26.71/4.40 | (81) all_109_1 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (76), (77) imply:
% 26.71/4.40 | (82) all_95_0 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (82) implies:
% 26.71/4.40 | (83) all_95_0 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (75), (81) imply:
% 26.71/4.40 | (84) all_103_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (84) implies:
% 26.71/4.40 | (85) all_103_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (72), (73) imply:
% 26.71/4.40 | (86) all_95_0 = all_93_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (86) implies:
% 26.71/4.40 | (87) all_95_0 = all_93_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (73), (74) imply:
% 26.71/4.40 | (88) all_93_1 = all_82_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (71), (85) imply:
% 26.71/4.40 | (89) all_98_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (89) implies:
% 26.71/4.40 | (90) all_98_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (68), (69) imply:
% 26.71/4.40 | (91) all_90_0 = all_87_0
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (91) implies:
% 26.71/4.40 | (92) all_90_0 = all_87_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (69), (70) imply:
% 26.71/4.40 | (93) all_87_0 = all_84_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (67), (90) imply:
% 26.71/4.40 | (94) all_90_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (94) implies:
% 26.71/4.40 | (95) all_90_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (83), (87) imply:
% 26.71/4.40 | (96) all_93_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (96) implies:
% 26.71/4.40 | (97) all_93_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (88), (97) imply:
% 26.71/4.40 | (98) all_82_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (98) implies:
% 26.71/4.40 | (99) all_82_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (92), (95) imply:
% 26.71/4.40 | (100) all_87_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (100) implies:
% 26.71/4.40 | (101) all_87_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (93), (101) imply:
% 26.71/4.40 | (102) all_84_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (102) implies:
% 26.71/4.40 | (103) all_84_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (66), (103) imply:
% 26.71/4.40 | (104) all_79_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (104) implies:
% 26.71/4.40 | (105) all_79_0 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (65), (99) imply:
% 26.71/4.40 | (106) all_77_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (106) implies:
% 26.71/4.40 | (107) all_77_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (64), (105) imply:
% 26.71/4.40 | (108) all_77_1 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (108) implies:
% 26.71/4.40 | (109) all_77_1 = all_75_1
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (107), (109) imply:
% 26.71/4.40 | (110) all_75_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | SIMP: (110) implies:
% 26.71/4.40 | (111) all_75_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (101), (111) imply:
% 26.71/4.40 | (112) all_87_0 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (85), (111) imply:
% 26.71/4.40 | (113) all_103_0 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | GROUND_INST: instantiating (rc5_struct_0) with all_64_2, all_64_1, simplifying
% 26.71/4.40 | with (5), (8), (10), (12) gives:
% 26.71/4.40 | (114) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_64_1) = v0 & $i(v1) &
% 26.71/4.40 | $i(v0) & m1_subset_1(v1, v0) & ~ v1_xboole_0(v1))
% 26.71/4.40 |
% 26.71/4.40 | GROUND_INST: instantiating (dt_k1_pre_topc) with all_64_2, all_64_1,
% 26.71/4.40 | simplifying with (8), (10), (12) gives:
% 26.71/4.40 | (115) ? [v0: $i] : ? [v1: $i] : (k1_pre_topc(all_64_2) = v0 &
% 26.71/4.40 | k1_zfmisc_1(all_64_1) = v1 & $i(v1) & $i(v0) & m1_subset_1(v0, v1))
% 26.71/4.40 |
% 26.71/4.40 | DELTA: instantiating (115) with fresh symbols all_126_0, all_126_1 gives:
% 26.71/4.40 | (116) k1_pre_topc(all_64_2) = all_126_1 & k1_zfmisc_1(all_64_1) = all_126_0
% 26.71/4.40 | & $i(all_126_0) & $i(all_126_1) & m1_subset_1(all_126_1, all_126_0)
% 26.71/4.40 |
% 26.71/4.40 | ALPHA: (116) implies:
% 26.71/4.40 | (117) m1_subset_1(all_126_1, all_126_0)
% 26.71/4.40 | (118) $i(all_126_1)
% 26.71/4.40 | (119) k1_zfmisc_1(all_64_1) = all_126_0
% 26.71/4.40 | (120) k1_pre_topc(all_64_2) = all_126_1
% 26.71/4.40 |
% 26.71/4.40 | DELTA: instantiating (114) with fresh symbols all_128_0, all_128_1 gives:
% 26.71/4.40 | (121) k1_zfmisc_1(all_64_1) = all_128_1 & $i(all_128_0) & $i(all_128_1) &
% 26.71/4.40 | m1_subset_1(all_128_0, all_128_1) & ~ v1_xboole_0(all_128_0)
% 26.71/4.40 |
% 26.71/4.40 | ALPHA: (121) implies:
% 26.71/4.40 | (122) k1_zfmisc_1(all_64_1) = all_128_1
% 26.71/4.40 |
% 26.71/4.40 | GROUND_INST: instantiating (3) with all_64_0, all_128_1, all_64_1, simplifying
% 26.71/4.40 | with (9), (122) gives:
% 26.71/4.40 | (123) all_128_1 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | GROUND_INST: instantiating (3) with all_126_0, all_128_1, all_64_1,
% 26.71/4.40 | simplifying with (119), (122) gives:
% 26.71/4.40 | (124) all_128_1 = all_126_0
% 26.71/4.40 |
% 26.71/4.40 | COMBINE_EQS: (123), (124) imply:
% 26.71/4.40 | (125) all_126_0 = all_64_0
% 26.71/4.40 |
% 26.71/4.40 | REDUCE: (117), (125) imply:
% 26.71/4.40 | (126) m1_subset_1(all_126_1, all_64_0)
% 26.71/4.40 |
% 26.71/4.40 | GROUND_INST: instantiating (1) with all_64_2, all_126_1, simplifying with (6),
% 26.71/4.40 | (7), (8), (120) gives:
% 26.71/4.40 | (127) v1_xboole_0(all_126_1)
% 26.71/4.40 |
% 26.71/4.41 | GROUND_INST: instantiating (2) with all_126_1, simplifying with (118), (127)
% 26.71/4.41 | gives:
% 26.71/4.41 | (128) all_126_1 = k1_xboole_0
% 26.71/4.41 |
% 26.71/4.41 | REDUCE: (118), (128) imply:
% 26.71/4.41 | (129) $i(k1_xboole_0)
% 26.71/4.41 |
% 26.71/4.41 | REDUCE: (127), (128) imply:
% 26.71/4.41 | (130) v1_xboole_0(k1_xboole_0)
% 26.71/4.41 |
% 26.71/4.41 | REDUCE: (126), (128) imply:
% 26.71/4.41 | (131) m1_subset_1(k1_xboole_0, all_64_0)
% 26.71/4.41 |
% 26.71/4.41 | GROUND_INST: instantiating (48) with k1_xboole_0, simplifying with (129),
% 26.71/4.41 | (130) gives:
% 26.71/4.41 | (132) ~ m1_subset_1(k1_xboole_0, all_95_0) | v3_tex_2(k1_xboole_0,
% 26.71/4.41 | all_64_2)
% 26.71/4.41 |
% 26.71/4.41 | BETA: splitting (132) gives:
% 26.71/4.41 |
% 26.71/4.41 | Case 1:
% 26.71/4.41 | |
% 26.71/4.41 | | (133) ~ m1_subset_1(k1_xboole_0, all_95_0)
% 26.71/4.41 | |
% 26.71/4.41 | | REDUCE: (83), (133) imply:
% 26.71/4.41 | | (134) ~ m1_subset_1(k1_xboole_0, all_64_0)
% 26.71/4.41 | |
% 26.71/4.41 | | PRED_UNIFY: (131), (134) imply:
% 26.71/4.41 | | (135) $false
% 26.71/4.41 | |
% 26.71/4.41 | | CLOSE: (135) is inconsistent.
% 26.71/4.41 | |
% 26.71/4.41 | Case 2:
% 26.71/4.41 | |
% 26.71/4.41 | | (136) m1_subset_1(k1_xboole_0, all_95_0)
% 26.71/4.41 | | (137) v3_tex_2(k1_xboole_0, all_64_2)
% 26.71/4.41 | |
% 26.71/4.41 | | GROUND_INST: instantiating (41) with k1_xboole_0, simplifying with (129),
% 26.71/4.41 | | (137) gives:
% 26.71/4.41 | | (138) ~ m1_subset_1(k1_xboole_0, all_87_0) | v1_tsp_1(k1_xboole_0,
% 26.71/4.41 | | all_64_2)
% 26.71/4.41 | |
% 26.71/4.41 | | BETA: splitting (138) gives:
% 26.71/4.41 | |
% 26.71/4.41 | | Case 1:
% 26.71/4.41 | | |
% 26.71/4.41 | | | (139) ~ m1_subset_1(k1_xboole_0, all_87_0)
% 26.71/4.41 | | |
% 26.71/4.41 | | | REDUCE: (112), (139) imply:
% 26.71/4.41 | | | (140) ~ m1_subset_1(k1_xboole_0, all_64_0)
% 26.71/4.41 | | |
% 26.71/4.41 | | | PRED_UNIFY: (131), (140) imply:
% 26.71/4.41 | | | (141) $false
% 26.71/4.41 | | |
% 26.71/4.41 | | | CLOSE: (141) is inconsistent.
% 26.71/4.41 | | |
% 26.71/4.41 | | Case 2:
% 26.71/4.41 | | |
% 26.71/4.41 | | | (142) m1_subset_1(k1_xboole_0, all_87_0)
% 26.71/4.41 | | | (143) v1_tsp_1(k1_xboole_0, all_64_2)
% 26.71/4.41 | | |
% 26.71/4.41 | | | GROUND_INST: instantiating (55) with k1_xboole_0, simplifying with (129),
% 26.71/4.41 | | | (143) gives:
% 26.71/4.41 | | | (144) ~ m1_subset_1(k1_xboole_0, all_103_0) | ? [v0: $i] : ($i(v0) &
% 26.71/4.41 | | | r1_tarski(k1_xboole_0, v0) & v1_tsp_2(v0, all_64_2) &
% 26.71/4.41 | | | m1_subset_1(v0, all_103_0))
% 26.71/4.41 | | |
% 26.71/4.41 | | | BETA: splitting (144) gives:
% 26.71/4.41 | | |
% 26.71/4.41 | | | Case 1:
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | (145) ~ m1_subset_1(k1_xboole_0, all_103_0)
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | REDUCE: (113), (145) imply:
% 26.71/4.41 | | | | (146) ~ m1_subset_1(k1_xboole_0, all_64_0)
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | PRED_UNIFY: (131), (146) imply:
% 26.71/4.41 | | | | (147) $false
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | CLOSE: (147) is inconsistent.
% 26.71/4.41 | | | |
% 26.71/4.41 | | | Case 2:
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | (148) ? [v0: $i] : ($i(v0) & r1_tarski(k1_xboole_0, v0) &
% 26.71/4.41 | | | | v1_tsp_2(v0, all_64_2) & m1_subset_1(v0, all_103_0))
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | DELTA: instantiating (148) with fresh symbol all_256_0 gives:
% 26.71/4.41 | | | | (149) $i(all_256_0) & r1_tarski(k1_xboole_0, all_256_0) &
% 26.71/4.41 | | | | v1_tsp_2(all_256_0, all_64_2) & m1_subset_1(all_256_0,
% 26.71/4.41 | | | | all_103_0)
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | ALPHA: (149) implies:
% 26.71/4.41 | | | | (150) m1_subset_1(all_256_0, all_103_0)
% 26.71/4.41 | | | | (151) v1_tsp_2(all_256_0, all_64_2)
% 26.71/4.41 | | | | (152) $i(all_256_0)
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | REDUCE: (113), (150) imply:
% 26.71/4.41 | | | | (153) m1_subset_1(all_256_0, all_64_0)
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | GROUND_INST: instantiating (11) with all_256_0, simplifying with (151),
% 26.71/4.41 | | | | (152), (153) gives:
% 26.71/4.41 | | | | (154) $false
% 26.71/4.41 | | | |
% 26.71/4.41 | | | | CLOSE: (154) is inconsistent.
% 26.71/4.41 | | | |
% 26.71/4.41 | | | End of split
% 26.71/4.41 | | |
% 26.71/4.41 | | End of split
% 26.71/4.41 | |
% 26.71/4.41 | End of split
% 26.71/4.41 |
% 26.71/4.41 End of proof
% 26.71/4.41 % SZS output end Proof for theBenchmark
% 26.71/4.41
% 26.71/4.41 3795ms
%------------------------------------------------------------------------------