%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : TOP027+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 : n002.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 05:58:51 EDT 2023 % Result : Theorem 17.66s 3.10s % Output : Proof 28.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : TOP027+1 : TPTP v8.1.2. Released v3.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 23:36:03 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.59 ________ _____ % 0.21/0.59 ___ __ \_________(_)________________________________ % 0.21/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.59 % 0.21/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.59 (2023-06-19) % 0.21/0.59 % 0.21/0.59 (c) Philipp Rümmer, 2009-2023 % 0.21/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.59 Amanda Stjerna. % 0.21/0.59 Free software under BSD-3-Clause. % 0.21/0.59 % 0.21/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.59 % 0.21/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.94/1.21 Prover 4: Preprocessing ... % 3.94/1.21 Prover 1: Preprocessing ... % 3.94/1.25 Prover 0: Preprocessing ... % 3.94/1.25 Prover 2: Preprocessing ... % 3.94/1.25 Prover 5: Preprocessing ... % 3.94/1.25 Prover 3: Preprocessing ... % 3.94/1.25 Prover 6: Preprocessing ... % 8.56/2.01 Prover 5: Proving ... % 9.38/2.08 Prover 1: Warning: ignoring some quantifiers % 10.36/2.13 Prover 1: Constructing countermodel ... % 10.36/2.13 Prover 2: Proving ... % 10.36/2.16 Prover 3: Warning: ignoring some quantifiers % 11.06/2.18 Prover 3: Constructing countermodel ... % 11.06/2.18 Prover 6: Proving ... % 14.93/2.69 Prover 4: Warning: ignoring some quantifiers % 15.46/2.76 Prover 4: Constructing countermodel ... % 15.46/2.77 Prover 0: Proving ... % 17.66/3.10 Prover 5: proved (2478ms) % 17.66/3.10 % 17.66/3.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.66/3.10 % 17.66/3.10 Prover 6: stopped % 17.66/3.10 Prover 0: stopped % 17.99/3.12 Prover 2: stopped % 17.99/3.12 Prover 3: stopped % 17.99/3.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.99/3.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.99/3.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.99/3.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.99/3.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.41/3.27 Prover 8: Preprocessing ... % 19.67/3.34 Prover 7: Preprocessing ... % 19.67/3.35 Prover 10: Preprocessing ... % 19.67/3.35 Prover 13: Preprocessing ... % 19.67/3.36 Prover 11: Preprocessing ... % 20.07/3.44 Prover 7: Warning: ignoring some quantifiers % 20.65/3.46 Prover 7: Constructing countermodel ... % 20.78/3.49 Prover 10: Warning: ignoring some quantifiers % 20.78/3.50 Prover 13: Warning: ignoring some quantifiers % 20.78/3.50 Prover 10: Constructing countermodel ... % 21.12/3.53 Prover 13: Constructing countermodel ... % 21.32/3.57 Prover 8: Warning: ignoring some quantifiers % 21.32/3.60 Prover 8: Constructing countermodel ... % 24.50/3.97 Prover 11: Warning: ignoring some quantifiers % 24.50/3.98 Prover 11: Constructing countermodel ... % 28.19/4.44 Prover 10: Found proof (size 146) % 28.19/4.44 Prover 10: proved (1325ms) % 28.19/4.44 Prover 11: stopped % 28.19/4.44 Prover 8: stopped % 28.19/4.44 Prover 7: stopped % 28.19/4.44 Prover 13: stopped % 28.19/4.44 Prover 4: stopped % 28.19/4.44 Prover 1: stopped % 28.19/4.44 % 28.19/4.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 28.19/4.45 % 28.19/4.48 % SZS output start Proof for theBenchmark % 28.19/4.49 Assumptions after simplification: % 28.19/4.49 --------------------------------- % 28.19/4.49 % 28.19/4.49 (cc1_tops_1) % 28.19/4.51 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.19/4.51 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & % 28.19/4.51 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~ % 28.40/4.51 m1_subset_1(v3, v2) | v3_pre_topc(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) | % 28.40/4.51 ~ v1_xboole_0(v3) | ~ m1_subset_1(v3, v2) | v4_pre_topc(v3, v0)))) % 28.40/4.51 % 28.40/4.51 (cc2_tops_1) % 28.40/4.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.52 l1_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] % 28.40/4.52 : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~ m1_subset_1(v3, v2) | v2_tops_1(v3, % 28.40/4.52 v0)))) % 28.40/4.52 % 28.40/4.52 (cc3_tops_1) % 28.40/4.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.52 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & % 28.40/4.52 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v1_xboole_0(v3) | ~ % 28.40/4.52 m1_subset_1(v3, v2) | v3_tops_1(v3, v0)))) % 28.40/4.52 % 28.40/4.52 (cc4_tops_1) % 28.40/4.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.52 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & % 28.40/4.52 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_tops_1(v3, v0) | ~ % 28.40/4.52 m1_subset_1(v3, v2) | v2_tops_1(v3, v0)))) % 28.40/4.52 % 28.40/4.52 (cc5_tops_1) % 28.40/4.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.52 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & % 28.40/4.52 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v4_pre_topc(v3, v0) | ~ % 28.40/4.52 v2_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v3_tops_1(v3, v0)))) % 28.40/4.52 % 28.40/4.52 (cc6_tops_1) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.53 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : (k1_zfmisc_1(v1) = v2 & % 28.40/4.53 $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~ % 28.40/4.53 v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v1_xboole_0(v3)) & ! [v3: % 28.40/4.53 $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~ % 28.40/4.53 m1_subset_1(v3, v2) | v4_pre_topc(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) | % 28.40/4.53 ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | % 28.40/4.53 v2_tops_1(v3, v0)) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | % 28.40/4.53 ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v5_membered(v3)) & ! % 28.40/4.53 [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~ % 28.40/4.53 m1_subset_1(v3, v2) | v4_membered(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 28.40/4.53 v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | % 28.40/4.53 v3_membered(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | % 28.40/4.53 ~ v3_tops_1(v3, v0) | ~ m1_subset_1(v3, v2) | v2_membered(v3)) & ! % 28.40/4.53 [v3: $i] : ( ~ $i(v3) | ~ v3_pre_topc(v3, v0) | ~ v3_tops_1(v3, v0) | ~ % 28.40/4.53 m1_subset_1(v3, v2) | v1_membered(v3)))) % 28.40/4.53 % 28.40/4.53 (dt_k1_tops_1) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_tops_1(v0, v1) = v2) | ~ % 28.40/4.53 $i(v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ? [v3: $i] : ? [v4: $i] : % 28.40/4.53 (u1_struct_0(v0) = v3 & k1_zfmisc_1(v3) = v4 & $i(v4) & $i(v3) & ( ~ % 28.40/4.53 m1_subset_1(v1, v4) | m1_subset_1(v2, v4)))) % 28.40/4.53 % 28.40/4.53 (dt_k3_tex_4) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_tex_4(v0, v1) = v2) | ~ % 28.40/4.53 $i(v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | v3_struct_0(v0) | ? [v3: $i] : ? % 28.40/4.53 [v4: $i] : (u1_struct_0(v0) = v3 & k1_zfmisc_1(v3) = v4 & $i(v4) & $i(v3) & % 28.40/4.53 ( ~ m1_subset_1(v1, v4) | m1_subset_1(v2, v4)))) % 28.40/4.53 % 28.40/4.53 (dt_k5_subset_1) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k5_subset_1(v0, % 28.40/4.53 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 28.40/4.53 (k1_zfmisc_1(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ % 28.40/4.53 m1_subset_1(v1, v4) | m1_subset_1(v3, v4)))) % 28.40/4.53 % 28.40/4.53 (fc6_tops_1) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_tops_1(v0, v1) = v2) | ~ % 28.40/4.53 $i(v1) | ~ $i(v0) | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0) | % 28.40/4.53 v3_pre_topc(v2, v0) | ? [v3: $i] : ? [v4: $i] : (u1_struct_0(v0) = v3 & % 28.40/4.53 k1_zfmisc_1(v3) = v4 & $i(v4) & $i(v3) & ~ m1_subset_1(v1, v4))) % 28.40/4.53 % 28.40/4.53 (rc1_tops_1) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.53 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] : % 28.40/4.53 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_pre_topc(v3, v0) & % 28.40/4.53 m1_subset_1(v3, v2))) % 28.40/4.53 % 28.40/4.53 (rc2_tops_1) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.53 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] : % 28.40/4.53 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_pre_topc(v3, v0) & % 28.40/4.53 v4_pre_topc(v3, v0) & m1_subset_1(v3, v2))) % 28.40/4.53 % 28.40/4.53 (rc3_tops_1) % 28.40/4.53 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.53 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : ? % 28.40/4.53 [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v3_pre_topc(v3, v0) & % 28.40/4.53 v4_pre_topc(v3, v0) & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) % 28.40/4.53 % 28.40/4.53 (rc4_tops_1) % 28.40/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.54 l1_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3) % 28.40/4.54 & $i(v2) & v1_xboole_0(v3) & v2_tops_1(v3, v0) & v5_membered(v3) & % 28.40/4.54 v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & v1_membered(v3) & % 28.40/4.54 m1_subset_1(v3, v2))) % 28.40/4.54 % 28.40/4.54 (rc5_tops_1) % 28.40/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.54 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] : % 28.40/4.54 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v1_xboole_0(v3) & v3_pre_topc(v3, % 28.40/4.54 v0) & v4_pre_topc(v3, v0) & v2_tops_1(v3, v0) & v3_tops_1(v3, v0) & % 28.40/4.54 v5_membered(v3) & v4_membered(v3) & v3_membered(v3) & v2_membered(v3) & % 28.40/4.54 v1_membered(v3) & m1_subset_1(v3, v2))) % 28.40/4.54 % 28.40/4.54 (rc6_pre_topc) % 28.40/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.54 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | ? [v2: $i] : ? [v3: $i] : % 28.40/4.54 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) & % 28.40/4.54 m1_subset_1(v3, v2))) % 28.40/4.54 % 28.40/4.54 (rc7_pre_topc) % 28.40/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.54 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : ? % 28.40/4.54 [v3: $i] : (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v4_pre_topc(v3, v0) & % 28.40/4.54 m1_subset_1(v3, v2) & ~ v1_xboole_0(v3))) % 28.40/4.54 % 28.40/4.54 (t6_tsp_2) % 28.40/4.54 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 28.40/4.54 l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0) | ? [v2: $i] : % 28.40/4.54 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 28.40/4.54 ! [v6: $i] : (v6 = v4 | ~ (k3_tex_4(v0, v5) = v6) | ~ (k5_subset_1(v1, % 28.40/4.54 v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ v3_pre_topc(v4, v0) | ~ % 28.40/4.54 v1_tsp_2(v3, v0) | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2)))) % 28.40/4.54 % 28.40/4.54 (t8_tsp_2) % 28.40/4.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 28.40/4.54 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v5) & k3_tex_4(v0, v6) = v7 & % 28.40/4.54 k5_subset_1(v1, v3, v5) = v6 & k1_tops_1(v0, v4) = v5 & u1_struct_0(v0) = v1 % 28.40/4.54 & k1_zfmisc_1(v1) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 28.40/4.54 & $i(v1) & $i(v0) & v1_tsp_2(v3, v0) & m1_subset_1(v4, v2) & m1_subset_1(v3, % 28.40/4.54 v2) & l1_pre_topc(v0) & v2_pre_topc(v0) & ~ v3_struct_0(v0)) % 28.40/4.54 % 28.40/4.54 (function-axioms) % 28.40/4.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 28.40/4.54 | ~ (k5_subset_1(v4, v3, v2) = v1) | ~ (k5_subset_1(v4, v3, v2) = v0)) & % 28.40/4.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.40/4.54 (k3_tex_4(v3, v2) = v1) | ~ (k3_tex_4(v3, v2) = v0)) & ! [v0: $i] : ! % 28.40/4.54 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = % 28.40/4.54 v1) | ~ (k3_xboole_0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.40/4.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (k1_tops_1(v3, v2) = v1) | ~ % 28.40/4.54 (k1_tops_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 28.40/4.54 v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : % 28.40/4.54 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ % 28.40/4.54 (k1_zfmisc_1(v2) = v0)) % 28.40/4.54 % 28.40/4.54 Further assumptions not needed in the proof: % 28.40/4.54 -------------------------------------------- % 28.40/4.55 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered, % 28.40/4.55 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered, % 28.40/4.55 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered, % 28.40/4.55 cc3_membered, cc4_membered, commutativity_k3_xboole_0, % 28.40/4.55 commutativity_k5_subset_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k3_xboole_0, % 28.40/4.55 dt_l1_pre_topc, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, % 28.40/4.55 existence_l1_pre_topc, existence_l1_struct_0, existence_m1_subset_1, % 28.40/4.55 fc10_tops_1, fc1_struct_0, fc1_subset_1, fc27_membered, fc28_membered, % 28.40/4.55 fc29_membered, fc30_membered, fc31_membered, fc32_membered, fc33_membered, % 28.40/4.55 fc34_membered, fc35_membered, fc36_membered, fc6_membered, % 28.40/4.55 idempotence_k3_xboole_0, idempotence_k5_subset_1, rc1_membered, rc1_subset_1, % 28.40/4.55 rc2_subset_1, rc3_struct_0, rc5_struct_0, redefinition_k5_subset_1, % 28.40/4.55 reflexivity_r1_tarski, t1_subset, t2_boole, t2_subset, t3_subset, t4_subset, % 28.40/4.55 t5_subset, t6_boole, t7_boole, t8_boole % 28.40/4.55 % 28.40/4.55 Those formulas are unsatisfiable: % 28.40/4.55 --------------------------------- % 28.40/4.55 % 28.40/4.55 Begin of proof % 28.40/4.55 | % 28.40/4.55 | ALPHA: (function-axioms) implies: % 28.40/4.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.40/4.55 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 28.40/4.55 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.40/4.55 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 28.40/4.55 | % 28.40/4.55 | DELTA: instantiating (t8_tsp_2) with fresh symbols all_80_0, all_80_1, % 28.40/4.55 | all_80_2, all_80_3, all_80_4, all_80_5, all_80_6, all_80_7 gives: % 28.40/4.55 | (3) ~ (all_80_0 = all_80_2) & k3_tex_4(all_80_7, all_80_1) = all_80_0 & % 28.40/4.55 | k5_subset_1(all_80_6, all_80_4, all_80_2) = all_80_1 & % 28.40/4.55 | k1_tops_1(all_80_7, all_80_3) = all_80_2 & u1_struct_0(all_80_7) = % 28.40/4.55 | all_80_6 & k1_zfmisc_1(all_80_6) = all_80_5 & $i(all_80_0) & % 28.40/4.55 | $i(all_80_1) & $i(all_80_2) & $i(all_80_3) & $i(all_80_4) & % 28.40/4.55 | $i(all_80_5) & $i(all_80_6) & $i(all_80_7) & v1_tsp_2(all_80_4, % 28.40/4.55 | all_80_7) & m1_subset_1(all_80_3, all_80_5) & m1_subset_1(all_80_4, % 28.40/4.55 | all_80_5) & l1_pre_topc(all_80_7) & v2_pre_topc(all_80_7) & ~ % 28.40/4.55 | v3_struct_0(all_80_7) % 28.40/4.55 | % 28.40/4.55 | ALPHA: (3) implies: % 28.40/4.55 | (4) ~ (all_80_0 = all_80_2) % 28.40/4.55 | (5) ~ v3_struct_0(all_80_7) % 28.40/4.55 | (6) v2_pre_topc(all_80_7) % 28.40/4.55 | (7) l1_pre_topc(all_80_7) % 28.40/4.55 | (8) m1_subset_1(all_80_4, all_80_5) % 28.40/4.55 | (9) m1_subset_1(all_80_3, all_80_5) % 28.40/4.55 | (10) v1_tsp_2(all_80_4, all_80_7) % 28.40/4.55 | (11) $i(all_80_7) % 28.40/4.55 | (12) $i(all_80_6) % 28.40/4.55 | (13) $i(all_80_4) % 28.40/4.55 | (14) $i(all_80_3) % 28.40/4.55 | (15) $i(all_80_2) % 28.40/4.55 | (16) $i(all_80_1) % 28.40/4.55 | (17) k1_zfmisc_1(all_80_6) = all_80_5 % 28.40/4.55 | (18) u1_struct_0(all_80_7) = all_80_6 % 28.40/4.55 | (19) k1_tops_1(all_80_7, all_80_3) = all_80_2 % 28.40/4.55 | (20) k5_subset_1(all_80_6, all_80_4, all_80_2) = all_80_1 % 28.40/4.55 | (21) k3_tex_4(all_80_7, all_80_1) = all_80_0 % 28.40/4.55 | % 28.40/4.56 | GROUND_INST: instantiating (rc3_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (5), (6), (7), (11), (18) gives: % 28.40/4.56 | (22) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v1) & % 28.40/4.56 | $i(v0) & v3_pre_topc(v1, all_80_7) & v4_pre_topc(v1, all_80_7) & % 28.40/4.56 | m1_subset_1(v1, v0) & ~ v1_xboole_0(v1)) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (rc7_pre_topc) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (5), (6), (7), (11), (18) gives: % 28.40/4.56 | (23) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v1) & % 28.40/4.56 | $i(v0) & v4_pre_topc(v1, all_80_7) & m1_subset_1(v1, v0) & ~ % 28.40/4.56 | v1_xboole_0(v1)) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (t6_tsp_2) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (5), (6), (7), (11), (18) gives: % 28.40/4.56 | (24) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ! [v1: $i] : ! % 28.40/4.56 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 28.40/4.56 | (k3_tex_4(all_80_7, v3) = v4) | ~ (k5_subset_1(all_80_6, v1, v2) % 28.40/4.56 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ v3_pre_topc(v2, all_80_7) | % 28.40/4.56 | ~ v1_tsp_2(v1, all_80_7) | ~ m1_subset_1(v2, v0) | ~ % 28.40/4.56 | m1_subset_1(v1, v0))) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (rc5_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (6), (7), (11), (18) gives: % 28.40/4.56 | (25) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v1) & % 28.40/4.56 | $i(v0) & v1_xboole_0(v1) & v3_pre_topc(v1, all_80_7) & % 28.40/4.56 | v4_pre_topc(v1, all_80_7) & v2_tops_1(v1, all_80_7) & v3_tops_1(v1, % 28.40/4.56 | all_80_7) & v5_membered(v1) & v4_membered(v1) & v3_membered(v1) & % 28.40/4.56 | v2_membered(v1) & v1_membered(v1) & m1_subset_1(v1, v0)) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (rc2_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (6), (7), (11), (18) gives: % 28.40/4.56 | (26) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v1) & % 28.40/4.56 | $i(v0) & v3_pre_topc(v1, all_80_7) & v4_pre_topc(v1, all_80_7) & % 28.40/4.56 | m1_subset_1(v1, v0)) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (rc1_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (6), (7), (11), (18) gives: % 28.40/4.56 | (27) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v1) & % 28.40/4.56 | $i(v0) & v3_pre_topc(v1, all_80_7) & m1_subset_1(v1, v0)) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (rc6_pre_topc) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (6), (7), (11), (18) gives: % 28.40/4.56 | (28) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v1) & % 28.40/4.56 | $i(v0) & v4_pre_topc(v1, all_80_7) & m1_subset_1(v1, v0)) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (cc1_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (6), (7), (11), (18) gives: % 28.40/4.56 | (29) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 28.40/4.56 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) | % 28.40/4.56 | v3_pre_topc(v1, all_80_7)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 28.40/4.56 | v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) | v4_pre_topc(v1, % 28.40/4.56 | all_80_7))) % 28.40/4.56 | % 28.40/4.56 | GROUND_INST: instantiating (cc3_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.56 | with (6), (7), (11), (18) gives: % 28.40/4.57 | (30) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 28.40/4.57 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) | % 28.40/4.57 | v3_tops_1(v1, all_80_7))) % 28.40/4.57 | % 28.40/4.57 | GROUND_INST: instantiating (cc6_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.57 | with (6), (7), (11), (18) gives: % 28.40/4.57 | (31) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 28.40/4.57 | $i(v1) | ~ v3_pre_topc(v1, all_80_7) | ~ v3_tops_1(v1, all_80_7) % 28.40/4.57 | | ~ m1_subset_1(v1, v0) | v1_xboole_0(v1)) & ! [v1: $i] : ( ~ % 28.40/4.57 | $i(v1) | ~ v3_pre_topc(v1, all_80_7) | ~ v3_tops_1(v1, all_80_7) % 28.40/4.57 | | ~ m1_subset_1(v1, v0) | v4_pre_topc(v1, all_80_7)) & ! [v1: % 28.40/4.57 | $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, all_80_7) | ~ v3_tops_1(v1, % 28.40/4.57 | all_80_7) | ~ m1_subset_1(v1, v0) | v2_tops_1(v1, all_80_7)) & % 28.40/4.57 | ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, all_80_7) | ~ % 28.40/4.57 | v3_tops_1(v1, all_80_7) | ~ m1_subset_1(v1, v0) | % 28.40/4.57 | v5_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, % 28.40/4.57 | all_80_7) | ~ v3_tops_1(v1, all_80_7) | ~ m1_subset_1(v1, v0) % 28.40/4.57 | | v4_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, % 28.40/4.57 | all_80_7) | ~ v3_tops_1(v1, all_80_7) | ~ m1_subset_1(v1, v0) % 28.40/4.57 | | v3_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, % 28.40/4.57 | all_80_7) | ~ v3_tops_1(v1, all_80_7) | ~ m1_subset_1(v1, v0) % 28.40/4.57 | | v2_membered(v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ v3_pre_topc(v1, % 28.40/4.57 | all_80_7) | ~ v3_tops_1(v1, all_80_7) | ~ m1_subset_1(v1, v0) % 28.40/4.57 | | v1_membered(v1))) % 28.40/4.57 | % 28.40/4.57 | GROUND_INST: instantiating (cc5_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.57 | with (6), (7), (11), (18) gives: % 28.40/4.57 | (32) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 28.40/4.57 | $i(v1) | ~ v4_pre_topc(v1, all_80_7) | ~ v2_tops_1(v1, all_80_7) % 28.40/4.57 | | ~ m1_subset_1(v1, v0) | v3_tops_1(v1, all_80_7))) % 28.40/4.57 | % 28.40/4.57 | GROUND_INST: instantiating (cc4_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.57 | with (6), (7), (11), (18) gives: % 28.40/4.57 | (33) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 28.40/4.57 | $i(v1) | ~ v3_tops_1(v1, all_80_7) | ~ m1_subset_1(v1, v0) | % 28.40/4.57 | v2_tops_1(v1, all_80_7))) % 28.40/4.57 | % 28.40/4.57 | GROUND_INST: instantiating (rc4_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.57 | with (7), (11), (18) gives: % 28.40/4.57 | (34) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v1) & % 28.40/4.57 | $i(v0) & v1_xboole_0(v1) & v2_tops_1(v1, all_80_7) & v5_membered(v1) % 28.40/4.57 | & v4_membered(v1) & v3_membered(v1) & v2_membered(v1) & % 28.40/4.57 | v1_membered(v1) & m1_subset_1(v1, v0)) % 28.40/4.57 | % 28.40/4.57 | GROUND_INST: instantiating (cc2_tops_1) with all_80_7, all_80_6, simplifying % 28.40/4.57 | with (7), (11), (18) gives: % 28.40/4.57 | (35) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 28.40/4.57 | $i(v1) | ~ v1_xboole_0(v1) | ~ m1_subset_1(v1, v0) | % 28.40/4.57 | v2_tops_1(v1, all_80_7))) % 28.40/4.57 | % 28.40/4.57 | GROUND_INST: instantiating (fc6_tops_1) with all_80_7, all_80_3, all_80_2, % 28.40/4.57 | simplifying with (6), (7), (11), (14), (19) gives: % 28.40/4.57 | (36) v3_pre_topc(all_80_2, all_80_7) | ? [v0: $i] : ? [v1: $i] : % 28.40/4.57 | (u1_struct_0(all_80_7) = v0 & k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & % 28.40/4.57 | ~ m1_subset_1(all_80_3, v1)) % 28.40/4.57 | % 28.40/4.58 | GROUND_INST: instantiating (dt_k1_tops_1) with all_80_7, all_80_3, all_80_2, % 28.40/4.58 | simplifying with (7), (11), (14), (19) gives: % 28.40/4.58 | (37) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_80_7) = v0 & % 28.40/4.58 | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ( ~ m1_subset_1(all_80_3, % 28.40/4.58 | v1) | m1_subset_1(all_80_2, v1))) % 28.40/4.58 | % 28.40/4.58 | GROUND_INST: instantiating (dt_k5_subset_1) with all_80_6, all_80_4, all_80_2, % 28.40/4.58 | all_80_1, simplifying with (12), (13), (15), (20) gives: % 28.40/4.58 | (38) ? [v0: $i] : (k1_zfmisc_1(all_80_6) = v0 & $i(v0) & ( ~ % 28.40/4.58 | m1_subset_1(all_80_2, v0) | ~ m1_subset_1(all_80_4, v0) | % 28.40/4.58 | m1_subset_1(all_80_1, v0))) % 28.40/4.58 | % 28.40/4.58 | GROUND_INST: instantiating (dt_k3_tex_4) with all_80_7, all_80_1, all_80_0, % 28.40/4.58 | simplifying with (5), (7), (11), (16), (21) gives: % 28.40/4.58 | (39) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_80_7) = v0 & % 28.40/4.58 | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ( ~ m1_subset_1(all_80_1, % 28.40/4.58 | v1) | m1_subset_1(all_80_0, v1))) % 28.40/4.58 | % 28.40/4.58 | DELTA: instantiating (38) with fresh symbol all_90_0 gives: % 28.40/4.58 | (40) k1_zfmisc_1(all_80_6) = all_90_0 & $i(all_90_0) & ( ~ % 28.40/4.58 | m1_subset_1(all_80_2, all_90_0) | ~ m1_subset_1(all_80_4, all_90_0) % 28.40/4.58 | | m1_subset_1(all_80_1, all_90_0)) % 28.40/4.58 | % 28.40/4.58 | ALPHA: (40) implies: % 28.40/4.58 | (41) k1_zfmisc_1(all_80_6) = all_90_0 % 28.40/4.58 | % 28.40/4.58 | DELTA: instantiating (28) with fresh symbols all_92_0, all_92_1 gives: % 28.40/4.58 | (42) k1_zfmisc_1(all_80_6) = all_92_1 & $i(all_92_0) & $i(all_92_1) & % 28.40/4.58 | v4_pre_topc(all_92_0, all_80_7) & m1_subset_1(all_92_0, all_92_1) % 28.40/4.58 | % 28.40/4.58 | ALPHA: (42) implies: % 28.92/4.58 | (43) k1_zfmisc_1(all_80_6) = all_92_1 % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (27) with fresh symbols all_94_0, all_94_1 gives: % 28.92/4.58 | (44) k1_zfmisc_1(all_80_6) = all_94_1 & $i(all_94_0) & $i(all_94_1) & % 28.92/4.58 | v3_pre_topc(all_94_0, all_80_7) & m1_subset_1(all_94_0, all_94_1) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (44) implies: % 28.92/4.58 | (45) k1_zfmisc_1(all_80_6) = all_94_1 % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (39) with fresh symbols all_96_0, all_96_1 gives: % 28.92/4.58 | (46) u1_struct_0(all_80_7) = all_96_1 & k1_zfmisc_1(all_96_1) = all_96_0 & % 28.92/4.58 | $i(all_96_0) & $i(all_96_1) & ( ~ m1_subset_1(all_80_1, all_96_0) | % 28.92/4.58 | m1_subset_1(all_80_0, all_96_0)) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (46) implies: % 28.92/4.58 | (47) k1_zfmisc_1(all_96_1) = all_96_0 % 28.92/4.58 | (48) u1_struct_0(all_80_7) = all_96_1 % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (26) with fresh symbols all_98_0, all_98_1 gives: % 28.92/4.58 | (49) k1_zfmisc_1(all_80_6) = all_98_1 & $i(all_98_0) & $i(all_98_1) & % 28.92/4.58 | v3_pre_topc(all_98_0, all_80_7) & v4_pre_topc(all_98_0, all_80_7) & % 28.92/4.58 | m1_subset_1(all_98_0, all_98_1) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (49) implies: % 28.92/4.58 | (50) k1_zfmisc_1(all_80_6) = all_98_1 % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (30) with fresh symbol all_100_0 gives: % 28.92/4.58 | (51) k1_zfmisc_1(all_80_6) = all_100_0 & $i(all_100_0) & ! [v0: $i] : ( ~ % 28.92/4.58 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_100_0) | % 28.92/4.58 | v3_tops_1(v0, all_80_7)) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (51) implies: % 28.92/4.58 | (52) k1_zfmisc_1(all_80_6) = all_100_0 % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (37) with fresh symbols all_103_0, all_103_1 gives: % 28.92/4.58 | (53) u1_struct_0(all_80_7) = all_103_1 & k1_zfmisc_1(all_103_1) = all_103_0 % 28.92/4.58 | & $i(all_103_0) & $i(all_103_1) & ( ~ m1_subset_1(all_80_3, all_103_0) % 28.92/4.58 | | m1_subset_1(all_80_2, all_103_0)) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (53) implies: % 28.92/4.58 | (54) k1_zfmisc_1(all_103_1) = all_103_0 % 28.92/4.58 | (55) u1_struct_0(all_80_7) = all_103_1 % 28.92/4.58 | (56) ~ m1_subset_1(all_80_3, all_103_0) | m1_subset_1(all_80_2, all_103_0) % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (23) with fresh symbols all_105_0, all_105_1 gives: % 28.92/4.58 | (57) k1_zfmisc_1(all_80_6) = all_105_1 & $i(all_105_0) & $i(all_105_1) & % 28.92/4.58 | v4_pre_topc(all_105_0, all_80_7) & m1_subset_1(all_105_0, all_105_1) & % 28.92/4.58 | ~ v1_xboole_0(all_105_0) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (57) implies: % 28.92/4.58 | (58) k1_zfmisc_1(all_80_6) = all_105_1 % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (35) with fresh symbol all_107_0 gives: % 28.92/4.58 | (59) k1_zfmisc_1(all_80_6) = all_107_0 & $i(all_107_0) & ! [v0: $i] : ( ~ % 28.92/4.58 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_107_0) | % 28.92/4.58 | v2_tops_1(v0, all_80_7)) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (59) implies: % 28.92/4.58 | (60) k1_zfmisc_1(all_80_6) = all_107_0 % 28.92/4.58 | % 28.92/4.58 | DELTA: instantiating (33) with fresh symbol all_110_0 gives: % 28.92/4.58 | (61) k1_zfmisc_1(all_80_6) = all_110_0 & $i(all_110_0) & ! [v0: $i] : ( ~ % 28.92/4.58 | $i(v0) | ~ v3_tops_1(v0, all_80_7) | ~ m1_subset_1(v0, all_110_0) % 28.92/4.58 | | v2_tops_1(v0, all_80_7)) % 28.92/4.58 | % 28.92/4.58 | ALPHA: (61) implies: % 28.92/4.59 | (62) k1_zfmisc_1(all_80_6) = all_110_0 % 28.92/4.59 | % 28.92/4.59 | DELTA: instantiating (32) with fresh symbol all_113_0 gives: % 28.92/4.59 | (63) k1_zfmisc_1(all_80_6) = all_113_0 & $i(all_113_0) & ! [v0: $i] : ( ~ % 28.92/4.59 | $i(v0) | ~ v4_pre_topc(v0, all_80_7) | ~ v2_tops_1(v0, all_80_7) | % 28.92/4.59 | ~ m1_subset_1(v0, all_113_0) | v3_tops_1(v0, all_80_7)) % 28.92/4.59 | % 28.92/4.59 | ALPHA: (63) implies: % 28.92/4.59 | (64) k1_zfmisc_1(all_80_6) = all_113_0 % 28.92/4.59 | % 28.92/4.59 | DELTA: instantiating (22) with fresh symbols all_116_0, all_116_1 gives: % 28.92/4.59 | (65) k1_zfmisc_1(all_80_6) = all_116_1 & $i(all_116_0) & $i(all_116_1) & % 28.92/4.59 | v3_pre_topc(all_116_0, all_80_7) & v4_pre_topc(all_116_0, all_80_7) & % 28.92/4.59 | m1_subset_1(all_116_0, all_116_1) & ~ v1_xboole_0(all_116_0) % 28.92/4.59 | % 28.92/4.59 | ALPHA: (65) implies: % 28.92/4.59 | (66) k1_zfmisc_1(all_80_6) = all_116_1 % 28.92/4.59 | % 28.92/4.59 | DELTA: instantiating (29) with fresh symbol all_120_0 gives: % 28.92/4.59 | (67) k1_zfmisc_1(all_80_6) = all_120_0 & $i(all_120_0) & ! [v0: $i] : ( ~ % 28.92/4.59 | $i(v0) | ~ v1_xboole_0(v0) | ~ m1_subset_1(v0, all_120_0) | % 28.92/4.59 | v3_pre_topc(v0, all_80_7)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 28.92/4.59 | v1_xboole_0(v0) | ~ m1_subset_1(v0, all_120_0) | v4_pre_topc(v0, % 28.92/4.59 | all_80_7)) % 28.92/4.59 | % 28.92/4.59 | ALPHA: (67) implies: % 28.92/4.59 | (68) k1_zfmisc_1(all_80_6) = all_120_0 % 28.92/4.59 | % 28.92/4.59 | DELTA: instantiating (24) with fresh symbol all_123_0 gives: % 28.92/4.59 | (69) k1_zfmisc_1(all_80_6) = all_123_0 & $i(all_123_0) & ! [v0: $i] : ! % 28.92/4.59 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 28.92/4.59 | (k3_tex_4(all_80_7, v2) = v3) | ~ (k5_subset_1(all_80_6, v0, v1) = % 28.92/4.59 | v2) | ~ $i(v1) | ~ $i(v0) | ~ v3_pre_topc(v1, all_80_7) | ~ % 28.92/4.59 | v1_tsp_2(v0, all_80_7) | ~ m1_subset_1(v1, all_123_0) | ~ % 28.92/4.59 | m1_subset_1(v0, all_123_0)) % 28.92/4.59 | % 28.92/4.59 | ALPHA: (69) implies: % 28.92/4.59 | (70) k1_zfmisc_1(all_80_6) = all_123_0 % 28.92/4.59 | (71) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 28.92/4.59 | (k3_tex_4(all_80_7, v2) = v3) | ~ (k5_subset_1(all_80_6, v0, v1) = % 28.92/4.59 | v2) | ~ $i(v1) | ~ $i(v0) | ~ v3_pre_topc(v1, all_80_7) | ~ % 28.92/4.59 | v1_tsp_2(v0, all_80_7) | ~ m1_subset_1(v1, all_123_0) | ~ % 28.92/4.59 | m1_subset_1(v0, all_123_0)) % 28.92/4.59 | % 28.92/4.59 | DELTA: instantiating (34) with fresh symbols all_126_0, all_126_1 gives: % 28.92/4.59 | (72) k1_zfmisc_1(all_80_6) = all_126_1 & $i(all_126_0) & $i(all_126_1) & % 28.92/4.59 | v1_xboole_0(all_126_0) & v2_tops_1(all_126_0, all_80_7) & % 28.92/4.59 | v5_membered(all_126_0) & v4_membered(all_126_0) & % 28.92/4.59 | v3_membered(all_126_0) & v2_membered(all_126_0) & % 28.92/4.59 | v1_membered(all_126_0) & m1_subset_1(all_126_0, all_126_1) % 28.92/4.59 | % 28.92/4.59 | ALPHA: (72) implies: % 28.92/4.59 | (73) k1_zfmisc_1(all_80_6) = all_126_1 % 28.92/4.59 | % 28.92/4.59 | DELTA: instantiating (25) with fresh symbols all_128_0, all_128_1 gives: % 28.92/4.59 | (74) k1_zfmisc_1(all_80_6) = all_128_1 & $i(all_128_0) & $i(all_128_1) & % 28.92/4.59 | v1_xboole_0(all_128_0) & v3_pre_topc(all_128_0, all_80_7) & % 28.92/4.59 | v4_pre_topc(all_128_0, all_80_7) & v2_tops_1(all_128_0, all_80_7) & % 28.92/4.59 | v3_tops_1(all_128_0, all_80_7) & v5_membered(all_128_0) & % 28.92/4.59 | v4_membered(all_128_0) & v3_membered(all_128_0) & % 28.92/4.59 | v2_membered(all_128_0) & v1_membered(all_128_0) & % 28.92/4.59 | m1_subset_1(all_128_0, all_128_1) % 28.92/4.59 | % 28.92/4.59 | ALPHA: (74) implies: % 28.92/4.59 | (75) k1_zfmisc_1(all_80_6) = all_128_1 % 28.92/4.59 | % 28.92/4.59 | DELTA: instantiating (31) with fresh symbol all_130_0 gives: % 28.92/4.59 | (76) k1_zfmisc_1(all_80_6) = all_130_0 & $i(all_130_0) & ! [v0: $i] : ( ~ % 28.92/4.59 | $i(v0) | ~ v3_pre_topc(v0, all_80_7) | ~ v3_tops_1(v0, all_80_7) | % 28.92/4.59 | ~ m1_subset_1(v0, all_130_0) | v1_xboole_0(v0)) & ! [v0: $i] : ( ~ % 28.92/4.59 | $i(v0) | ~ v3_pre_topc(v0, all_80_7) | ~ v3_tops_1(v0, all_80_7) | % 28.92/4.59 | ~ m1_subset_1(v0, all_130_0) | v4_pre_topc(v0, all_80_7)) & ! [v0: % 28.92/4.59 | $i] : ( ~ $i(v0) | ~ v3_pre_topc(v0, all_80_7) | ~ v3_tops_1(v0, % 28.92/4.59 | all_80_7) | ~ m1_subset_1(v0, all_130_0) | v2_tops_1(v0, % 28.92/4.59 | all_80_7)) & ! [v0: $i] : ( ~ $i(v0) | ~ v3_pre_topc(v0, % 28.92/4.59 | all_80_7) | ~ v3_tops_1(v0, all_80_7) | ~ m1_subset_1(v0, % 28.92/4.59 | all_130_0) | v5_membered(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 28.92/4.59 | v3_pre_topc(v0, all_80_7) | ~ v3_tops_1(v0, all_80_7) | ~ % 28.92/4.59 | m1_subset_1(v0, all_130_0) | v4_membered(v0)) & ! [v0: $i] : ( ~ % 28.92/4.59 | $i(v0) | ~ v3_pre_topc(v0, all_80_7) | ~ v3_tops_1(v0, all_80_7) | % 28.92/4.59 | ~ m1_subset_1(v0, all_130_0) | v3_membered(v0)) & ! [v0: $i] : ( ~ % 28.92/4.59 | $i(v0) | ~ v3_pre_topc(v0, all_80_7) | ~ v3_tops_1(v0, all_80_7) | % 28.92/4.59 | ~ m1_subset_1(v0, all_130_0) | v2_membered(v0)) & ! [v0: $i] : ( ~ % 28.92/4.59 | $i(v0) | ~ v3_pre_topc(v0, all_80_7) | ~ v3_tops_1(v0, all_80_7) | % 28.92/4.59 | ~ m1_subset_1(v0, all_130_0) | v1_membered(v0)) % 28.92/4.59 | % 28.92/4.59 | ALPHA: (76) implies: % 28.92/4.59 | (77) k1_zfmisc_1(all_80_6) = all_130_0 % 28.92/4.59 | % 28.92/4.59 | GROUND_INST: instantiating (1) with all_80_5, all_94_1, all_80_6, simplifying % 28.92/4.59 | with (17), (45) gives: % 28.92/4.59 | (78) all_94_1 = all_80_5 % 28.92/4.59 | % 28.92/4.59 | GROUND_INST: instantiating (1) with all_90_0, all_94_1, all_80_6, simplifying % 28.92/4.59 | with (41), (45) gives: % 28.92/4.59 | (79) all_94_1 = all_90_0 % 28.92/4.59 | % 28.92/4.59 | GROUND_INST: instantiating (1) with all_94_1, all_98_1, all_80_6, simplifying % 28.92/4.59 | with (45), (50) gives: % 28.92/4.59 | (80) all_98_1 = all_94_1 % 28.92/4.59 | % 28.92/4.59 | GROUND_INST: instantiating (1) with all_105_1, all_110_0, all_80_6, % 28.92/4.59 | simplifying with (58), (62) gives: % 28.92/4.59 | (81) all_110_0 = all_105_1 % 28.92/4.59 | % 28.92/4.59 | GROUND_INST: instantiating (1) with all_100_0, all_110_0, all_80_6, % 28.92/4.59 | simplifying with (52), (62) gives: % 28.92/4.59 | (82) all_110_0 = all_100_0 % 28.92/4.59 | % 28.92/4.59 | GROUND_INST: instantiating (1) with all_98_1, all_110_0, all_80_6, simplifying % 28.92/4.59 | with (50), (62) gives: % 28.92/4.59 | (83) all_110_0 = all_98_1 % 28.92/4.59 | % 28.92/4.59 | GROUND_INST: instantiating (1) with all_110_0, all_116_1, all_80_6, % 28.92/4.59 | simplifying with (62), (66) gives: % 28.92/4.59 | (84) all_116_1 = all_110_0 % 28.92/4.59 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_92_1, all_116_1, all_80_6, simplifying % 28.92/4.60 | with (43), (66) gives: % 28.92/4.60 | (85) all_116_1 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_116_1, all_120_0, all_80_6, % 28.92/4.60 | simplifying with (66), (68) gives: % 28.92/4.60 | (86) all_120_0 = all_116_1 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_126_1, all_128_1, all_80_6, % 28.92/4.60 | simplifying with (73), (75) gives: % 28.92/4.60 | (87) all_128_1 = all_126_1 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_123_0, all_128_1, all_80_6, % 28.92/4.60 | simplifying with (70), (75) gives: % 28.92/4.60 | (88) all_128_1 = all_123_0 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_120_0, all_128_1, all_80_6, % 28.92/4.60 | simplifying with (68), (75) gives: % 28.92/4.60 | (89) all_128_1 = all_120_0 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_107_0, all_128_1, all_80_6, % 28.92/4.60 | simplifying with (60), (75) gives: % 28.92/4.60 | (90) all_128_1 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_116_1, all_130_0, all_80_6, % 28.92/4.60 | simplifying with (66), (77) gives: % 28.92/4.60 | (91) all_130_0 = all_116_1 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_113_0, all_130_0, all_80_6, % 28.92/4.60 | simplifying with (64), (77) gives: % 28.92/4.60 | (92) all_130_0 = all_113_0 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (2) with all_80_6, all_103_1, all_80_7, simplifying % 28.92/4.60 | with (18), (55) gives: % 28.92/4.60 | (93) all_103_1 = all_80_6 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (2) with all_96_1, all_103_1, all_80_7, simplifying % 28.92/4.60 | with (48), (55) gives: % 28.92/4.60 | (94) all_103_1 = all_96_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (91), (92) imply: % 28.92/4.60 | (95) all_116_1 = all_113_0 % 28.92/4.60 | % 28.92/4.60 | SIMP: (95) implies: % 28.92/4.60 | (96) all_116_1 = all_113_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (87), (88) imply: % 28.92/4.60 | (97) all_126_1 = all_123_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (87), (90) imply: % 28.92/4.60 | (98) all_126_1 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (87), (89) imply: % 28.92/4.60 | (99) all_126_1 = all_120_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (97), (98) imply: % 28.92/4.60 | (100) all_123_0 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (97), (99) imply: % 28.92/4.60 | (101) all_123_0 = all_120_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (100), (101) imply: % 28.92/4.60 | (102) all_120_0 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | SIMP: (102) implies: % 28.92/4.60 | (103) all_120_0 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (86), (103) imply: % 28.92/4.60 | (104) all_116_1 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | SIMP: (104) implies: % 28.92/4.60 | (105) all_116_1 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (84), (96) imply: % 28.92/4.60 | (106) all_113_0 = all_110_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (96), (105) imply: % 28.92/4.60 | (107) all_113_0 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (85), (96) imply: % 28.92/4.60 | (108) all_113_0 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (106), (107) imply: % 28.92/4.60 | (109) all_110_0 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | SIMP: (109) implies: % 28.92/4.60 | (110) all_110_0 = all_107_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (107), (108) imply: % 28.92/4.60 | (111) all_107_0 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (81), (83) imply: % 28.92/4.60 | (112) all_105_1 = all_98_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (81), (82) imply: % 28.92/4.60 | (113) all_105_1 = all_100_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (81), (110) imply: % 28.92/4.60 | (114) all_107_0 = all_105_1 % 28.92/4.60 | % 28.92/4.60 | SIMP: (114) implies: % 28.92/4.60 | (115) all_107_0 = all_105_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (111), (115) imply: % 28.92/4.60 | (116) all_105_1 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | SIMP: (116) implies: % 28.92/4.60 | (117) all_105_1 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (112), (113) imply: % 28.92/4.60 | (118) all_100_0 = all_98_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (113), (117) imply: % 28.92/4.60 | (119) all_100_0 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (93), (94) imply: % 28.92/4.60 | (120) all_96_1 = all_80_6 % 28.92/4.60 | % 28.92/4.60 | SIMP: (120) implies: % 28.92/4.60 | (121) all_96_1 = all_80_6 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (118), (119) imply: % 28.92/4.60 | (122) all_98_1 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | SIMP: (122) implies: % 28.92/4.60 | (123) all_98_1 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (80), (123) imply: % 28.92/4.60 | (124) all_94_1 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | SIMP: (124) implies: % 28.92/4.60 | (125) all_94_1 = all_92_1 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (78), (125) imply: % 28.92/4.60 | (126) all_92_1 = all_80_5 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (79), (125) imply: % 28.92/4.60 | (127) all_92_1 = all_90_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (126), (127) imply: % 28.92/4.60 | (128) all_90_0 = all_80_5 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (111), (126) imply: % 28.92/4.60 | (129) all_107_0 = all_80_5 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (100), (129) imply: % 28.92/4.60 | (130) all_123_0 = all_80_5 % 28.92/4.60 | % 28.92/4.60 | REDUCE: (54), (93) imply: % 28.92/4.60 | (131) k1_zfmisc_1(all_80_6) = all_103_0 % 28.92/4.60 | % 28.92/4.60 | REDUCE: (47), (121) imply: % 28.92/4.60 | (132) k1_zfmisc_1(all_80_6) = all_96_0 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_80_5, all_103_0, all_80_6, simplifying % 28.92/4.60 | with (17), (131) gives: % 28.92/4.60 | (133) all_103_0 = all_80_5 % 28.92/4.60 | % 28.92/4.60 | GROUND_INST: instantiating (1) with all_96_0, all_103_0, all_80_6, simplifying % 28.92/4.60 | with (131), (132) gives: % 28.92/4.60 | (134) all_103_0 = all_96_0 % 28.92/4.60 | % 28.92/4.60 | COMBINE_EQS: (133), (134) imply: % 28.92/4.60 | (135) all_96_0 = all_80_5 % 28.92/4.60 | % 28.92/4.60 | BETA: splitting (56) gives: % 28.92/4.60 | % 28.92/4.60 | Case 1: % 28.92/4.60 | | % 28.92/4.60 | | (136) ~ m1_subset_1(all_80_3, all_103_0) % 28.92/4.60 | | % 28.92/4.60 | | REDUCE: (133), (136) imply: % 28.92/4.60 | | (137) ~ m1_subset_1(all_80_3, all_80_5) % 28.92/4.60 | | % 28.92/4.60 | | PRED_UNIFY: (9), (137) imply: % 28.92/4.60 | | (138) $false % 28.92/4.61 | | % 28.92/4.61 | | CLOSE: (138) is inconsistent. % 28.92/4.61 | | % 28.92/4.61 | Case 2: % 28.92/4.61 | | % 28.92/4.61 | | (139) m1_subset_1(all_80_3, all_103_0) % 28.92/4.61 | | (140) m1_subset_1(all_80_2, all_103_0) % 28.92/4.61 | | % 28.92/4.61 | | REDUCE: (133), (140) imply: % 28.92/4.61 | | (141) m1_subset_1(all_80_2, all_80_5) % 28.92/4.61 | | % 28.92/4.61 | | BETA: splitting (36) gives: % 28.92/4.61 | | % 28.92/4.61 | | Case 1: % 28.92/4.61 | | | % 28.92/4.61 | | | (142) v3_pre_topc(all_80_2, all_80_7) % 28.92/4.61 | | | % 28.92/4.61 | | | GROUND_INST: instantiating (71) with all_80_4, all_80_2, all_80_1, % 28.92/4.61 | | | all_80_0, simplifying with (10), (13), (15), (20), (21), % 28.92/4.61 | | | (142) gives: % 28.92/4.61 | | | (143) all_80_0 = all_80_2 | ~ m1_subset_1(all_80_2, all_123_0) | ~ % 28.92/4.61 | | | m1_subset_1(all_80_4, all_123_0) % 28.92/4.61 | | | % 28.92/4.61 | | | BETA: splitting (143) gives: % 28.92/4.61 | | | % 28.92/4.61 | | | Case 1: % 28.92/4.61 | | | | % 28.92/4.61 | | | | (144) ~ m1_subset_1(all_80_2, all_123_0) % 28.92/4.61 | | | | % 28.92/4.61 | | | | REDUCE: (130), (144) imply: % 28.92/4.61 | | | | (145) ~ m1_subset_1(all_80_2, all_80_5) % 28.92/4.61 | | | | % 28.92/4.61 | | | | PRED_UNIFY: (141), (145) imply: % 28.92/4.61 | | | | (146) $false % 28.92/4.61 | | | | % 28.92/4.61 | | | | CLOSE: (146) is inconsistent. % 28.92/4.61 | | | | % 28.92/4.61 | | | Case 2: % 28.92/4.61 | | | | % 28.92/4.61 | | | | (147) all_80_0 = all_80_2 | ~ m1_subset_1(all_80_4, all_123_0) % 28.92/4.61 | | | | % 28.92/4.61 | | | | BETA: splitting (147) gives: % 28.92/4.61 | | | | % 28.92/4.61 | | | | Case 1: % 28.92/4.61 | | | | | % 28.92/4.61 | | | | | (148) ~ m1_subset_1(all_80_4, all_123_0) % 28.92/4.61 | | | | | % 28.92/4.61 | | | | | REDUCE: (130), (148) imply: % 28.92/4.61 | | | | | (149) ~ m1_subset_1(all_80_4, all_80_5) % 28.92/4.61 | | | | | % 28.92/4.61 | | | | | PRED_UNIFY: (8), (149) imply: % 28.92/4.61 | | | | | (150) $false % 28.92/4.61 | | | | | % 28.92/4.61 | | | | | CLOSE: (150) is inconsistent. % 28.92/4.61 | | | | | % 28.92/4.61 | | | | Case 2: % 28.92/4.61 | | | | | % 28.92/4.61 | | | | | (151) all_80_0 = all_80_2 % 28.92/4.61 | | | | | % 28.92/4.61 | | | | | REDUCE: (4), (151) imply: % 28.92/4.61 | | | | | (152) $false % 28.92/4.61 | | | | | % 28.92/4.61 | | | | | CLOSE: (152) is inconsistent. % 28.92/4.61 | | | | | % 28.92/4.61 | | | | End of split % 28.92/4.61 | | | | % 28.92/4.61 | | | End of split % 28.92/4.61 | | | % 28.92/4.61 | | Case 2: % 28.92/4.61 | | | % 28.92/4.61 | | | (153) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_80_7) = v0 & % 28.92/4.61 | | | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ~ % 28.92/4.61 | | | m1_subset_1(all_80_3, v1)) % 28.92/4.61 | | | % 28.92/4.61 | | | DELTA: instantiating (153) with fresh symbols all_149_0, all_149_1 gives: % 28.92/4.61 | | | (154) u1_struct_0(all_80_7) = all_149_1 & k1_zfmisc_1(all_149_1) = % 28.92/4.61 | | | all_149_0 & $i(all_149_0) & $i(all_149_1) & ~ % 28.92/4.61 | | | m1_subset_1(all_80_3, all_149_0) % 28.92/4.61 | | | % 28.92/4.61 | | | ALPHA: (154) implies: % 28.92/4.61 | | | (155) ~ m1_subset_1(all_80_3, all_149_0) % 28.92/4.61 | | | (156) k1_zfmisc_1(all_149_1) = all_149_0 % 28.92/4.61 | | | (157) u1_struct_0(all_80_7) = all_149_1 % 28.92/4.61 | | | % 28.92/4.61 | | | GROUND_INST: instantiating (2) with all_80_6, all_149_1, all_80_7, % 28.92/4.61 | | | simplifying with (18), (157) gives: % 28.92/4.61 | | | (158) all_149_1 = all_80_6 % 28.92/4.61 | | | % 28.92/4.61 | | | REDUCE: (156), (158) imply: % 28.92/4.61 | | | (159) k1_zfmisc_1(all_80_6) = all_149_0 % 28.92/4.61 | | | % 28.92/4.61 | | | GROUND_INST: instantiating (1) with all_80_5, all_149_0, all_80_6, % 28.92/4.61 | | | simplifying with (17), (159) gives: % 28.92/4.61 | | | (160) all_149_0 = all_80_5 % 28.92/4.61 | | | % 28.92/4.61 | | | REDUCE: (155), (160) imply: % 28.92/4.61 | | | (161) ~ m1_subset_1(all_80_3, all_80_5) % 28.92/4.61 | | | % 28.92/4.61 | | | PRED_UNIFY: (9), (161) imply: % 28.92/4.61 | | | (162) $false % 28.92/4.61 | | | % 28.92/4.61 | | | CLOSE: (162) is inconsistent. % 28.92/4.61 | | | % 28.92/4.61 | | End of split % 28.92/4.61 | | % 28.92/4.61 | End of split % 28.92/4.61 | % 28.92/4.61 End of proof % 28.92/4.61 % SZS output end Proof for theBenchmark % 28.92/4.61 % 28.92/4.61 4017ms %------------------------------------------------------------------------------