%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRP641+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 : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 01:12:46 EDT 2023 % Result : Theorem 13.71s 2.65s % Output : Proof 23.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRP641+1 : TPTP v8.1.2. Released v3.4.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n017.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 : Mon Aug 28 20:56:57 EDT 2023 % 0.14/0.35 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.46/1.23 Prover 4: Preprocessing ... % 3.46/1.23 Prover 1: Preprocessing ... % 3.46/1.27 Prover 5: Preprocessing ... % 3.46/1.27 Prover 3: Preprocessing ... % 3.46/1.27 Prover 2: Preprocessing ... % 3.46/1.28 Prover 0: Preprocessing ... % 3.46/1.28 Prover 6: Preprocessing ... % 7.86/1.84 Prover 1: Warning: ignoring some quantifiers % 8.22/1.88 Prover 5: Proving ... % 8.22/1.92 Prover 3: Warning: ignoring some quantifiers % 8.22/1.94 Prover 1: Constructing countermodel ... % 8.22/1.95 Prover 3: Constructing countermodel ... % 8.22/1.96 Prover 6: Proving ... % 8.22/2.00 Prover 2: Proving ... % 13.25/2.57 Prover 4: Warning: ignoring some quantifiers % 13.71/2.65 Prover 5: proved (2002ms) % 13.71/2.65 % 13.71/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.71/2.65 % 13.71/2.65 Prover 3: stopped % 13.71/2.65 Prover 6: stopped % 13.71/2.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.71/2.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.71/2.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.71/2.66 Prover 2: stopped % 13.71/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.71/2.66 Prover 4: Constructing countermodel ... % 13.71/2.71 Prover 0: Proving ... % 13.71/2.71 Prover 0: stopped % 14.56/2.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.69/2.76 Prover 8: Preprocessing ... % 14.69/2.76 Prover 10: Preprocessing ... % 14.69/2.78 Prover 7: Preprocessing ... % 14.69/2.78 Prover 13: Preprocessing ... % 14.69/2.78 Prover 11: Preprocessing ... % 15.36/2.85 Prover 10: Warning: ignoring some quantifiers % 15.36/2.86 Prover 10: Constructing countermodel ... % 15.90/2.89 Prover 13: Warning: ignoring some quantifiers % 15.90/2.90 Prover 7: Warning: ignoring some quantifiers % 15.90/2.90 Prover 13: Constructing countermodel ... % 15.90/2.91 Prover 7: Constructing countermodel ... % 15.90/2.91 Prover 8: Warning: ignoring some quantifiers % 15.90/2.93 Prover 8: Constructing countermodel ... % 20.67/3.56 Prover 11: Warning: ignoring some quantifiers % 21.14/3.60 Prover 11: Constructing countermodel ... % 22.47/3.79 Prover 7: Found proof (size 59) % 22.47/3.79 Prover 7: proved (1132ms) % 22.47/3.79 Prover 11: stopped % 22.47/3.79 Prover 4: stopped % 22.47/3.79 Prover 8: stopped % 22.47/3.79 Prover 10: stopped % 22.47/3.79 Prover 1: stopped % 22.47/3.79 Prover 13: stopped % 22.47/3.79 % 22.47/3.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.47/3.79 % 22.47/3.80 % SZS output start Proof for theBenchmark % 22.47/3.80 Assumptions after simplification: % 22.47/3.80 --------------------------------- % 22.47/3.80 % 22.47/3.80 (d1_latsubgr) % 22.47/3.84 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.47/3.84 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | % 22.47/3.84 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0) = v2 & % 22.47/3.84 k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & % 22.47/3.84 ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~ % 22.47/3.84 $i(v1) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 22.47/3.84 v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.47/3.84 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 22.47/3.84 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ m2_relset_1(v1, v2, % 22.47/3.84 v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~ % 22.47/3.84 m1_group_2(v5, v0) | ~ v1_group_1(v5) | (k1_funct_1(v1, v5) = v6 & % 22.47/3.84 $i(v6))) & ! [v5: $i] : (v5 = v1 | ~ $i(v5) | ~ m2_relset_1(v5, v2, % 22.47/3.84 v4) | ~ v1_funct_2(v5, v2, v4) | ~ v1_funct_1(v5) | ? [v6: $i] : ? % 22.47/3.84 [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & % 22.47/3.84 u1_struct_0(v6) = v8 & $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) & % 22.47/3.84 v1_group_1(v6))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_group_3(v0) = % 22.47/3.84 v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ % 22.47/3.84 v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.47/3.84 (k1_latsubgr(v0) = v4 & k1_zfmisc_1(v2) = v3 & u1_struct_0(v0) = v2 & $i(v4) % 22.47/3.84 & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) = % 22.47/3.84 v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1, % 22.47/3.84 v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.47/3.84 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 22.47/3.84 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~ % 22.47/3.84 v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ % 22.47/3.84 v1_group_1(v5) | (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 % 22.47/3.84 = v4 | ~ $i(v5) | ~ m2_relset_1(v5, v1, v3) | ~ v1_funct_2(v5, v1, % 22.47/3.84 v3) | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( % 22.47/3.84 ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8) % 22.47/3.84 & $i(v7) & $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6))))) & ! [v0: % 22.47/3.84 $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 22.47/3.84 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | % 22.47/3.84 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_latsubgr(v0) = v4 & % 22.47/3.84 k1_group_3(v0) = v2 & k1_zfmisc_1(v1) = v3 & $i(v4) & $i(v3) & $i(v2) & ! % 22.47/3.84 [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ $i(v5) | ~ % 22.47/3.84 m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4) % 22.47/3.84 | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | (u1_struct_0(v5) = v6 & % 22.47/3.84 $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ (u1_struct_0(v5) = v6) | ~ % 22.47/3.84 $i(v5) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ % 22.47/3.84 v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.47/3.84 (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v4 | ~ $i(v5) % 22.47/3.84 | ~ m2_relset_1(v5, v2, v3) | ~ v1_funct_2(v5, v2, v3) | ~ % 22.47/3.84 v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) % 22.47/3.84 & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8) & $i(v7) & % 22.47/3.84 $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6))))) % 22.47/3.84 % 22.47/3.84 (dt_k1_latsubgr) % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.47/3.85 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_funct_1(v1) | % 22.47/3.85 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | % 22.47/3.85 ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.47/3.85 v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0) % 22.47/3.85 = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & % 22.47/3.85 $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, v2, v4))) & ! [v0: $i] % 22.47/3.85 : ! [v1: $i] : ( ~ (k1_group_3(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ % 22.47/3.85 v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: % 22.47/3.85 $i] : ? [v4: $i] : (k1_latsubgr(v0) = v2 & k1_zfmisc_1(v3) = v4 & % 22.47/3.85 u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v1, v4) % 22.47/3.85 & v1_funct_2(v2, v1, v4) & v1_funct_1(v2))) & ! [v0: $i] : ! [v1: $i] : % 22.47/3.85 ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) % 22.47/3.85 | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 22.47/3.85 $i] : (k1_latsubgr(v0) = v2 & k1_group_3(v0) = v3 & k1_zfmisc_1(v1) = v4 & % 22.47/3.85 $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v3, v4) & v1_funct_2(v2, v3, % 22.47/3.85 v4) & v1_funct_1(v2))) % 22.47/3.85 % 22.47/3.85 (dt_k2_group_1) % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (k2_group_1(v0) = v1) | ~ $i(v0) | ~ % 22.47/3.85 l1_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & % 22.47/3.85 $i(v2) & m1_subset_1(v1, v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 22.47/3.85 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | v3_struct_0(v0) | % 22.47/3.85 ? [v2: $i] : (k2_group_1(v0) = v2 & $i(v2) & m1_subset_1(v2, v1))) % 22.47/3.85 % 22.47/3.85 (dt_l1_group_1) % 22.47/3.85 ! [v0: $i] : ( ~ $i(v0) | ~ l1_group_1(v0) | l1_struct_0(v0)) % 22.47/3.85 % 22.47/3.85 (dt_m1_group_2) % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) | % 22.47/3.85 ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0)) % 22.47/3.85 & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) | % 22.47/3.85 ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0)) & % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) | ~ % 22.47/3.85 l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0)) % 22.47/3.85 % 22.47/3.85 (fc1_struct_0) % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 22.47/3.85 l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0)) % 22.47/3.85 % 22.47/3.85 (t19_latsubgr) % 22.47/3.85 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.47/3.85 (k2_group_1(v0) = v1 & k1_latsubgr(v0) = v2 & k1_funct_1(v2, v3) = v4 & $i(v4) % 22.47/3.85 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & m1_group_2(v3, v0) & v1_group_1(v3) & % 22.47/3.85 l1_group_1(v0) & v4_group_1(v0) & v3_group_1(v0) & ~ r2_hidden(v1, v4) & ~ % 22.47/3.85 v3_struct_0(v0)) % 22.47/3.85 % 22.47/3.85 (t2_subset) % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v0, v1) | % 22.47/3.85 v1_xboole_0(v1) | r2_hidden(v0, v1)) % 22.47/3.85 % 22.47/3.85 (t53_group_2) % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 22.47/3.85 (k2_group_1(v2) = v3) | ~ (k2_group_1(v0) = v1) | ~ $i(v2) | ~ $i(v0) | % 22.47/3.85 ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ % 22.47/3.85 v3_group_1(v0) | v3_struct_0(v0)) % 22.47/3.85 % 22.47/3.85 (function-axioms) % 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.47/3.85 (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: $i] : ! % 22.47/3.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = % 22.47/3.85 v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.47/3.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ % 22.47/3.85 (g1_group_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 22.47/3.85 v0 | ~ (k2_group_1(v2) = v1) | ~ (k2_group_1(v2) = v0)) & ! [v0: $i] : ! % 22.47/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_latsubgr(v2) = v1) | ~ % 22.47/3.85 (k1_latsubgr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 22.47/3.85 | ~ (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0)) & ! [v0: $i] : ! % 22.47/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ % 22.47/3.85 (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 22.47/3.85 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0)) & ! [v0: $i] : ! % 22.47/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ % 22.47/3.85 (u1_struct_0(v2) = v0)) % 22.47/3.85 % 22.47/3.85 Further assumptions not needed in the proof: % 22.47/3.85 -------------------------------------------- % 22.47/3.85 abstractness_v1_group_1, antisymmetry_r2_hidden, cc1_funct_2, cc1_relset_1, % 22.47/3.85 cc5_funct_2, cc6_funct_2, dt_g1_group_1, dt_k1_funct_1, dt_k1_group_3, % 22.47/3.85 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_l1_struct_0, dt_m1_relset_1, % 22.47/3.85 dt_m1_subset_1, dt_m2_relset_1, dt_u1_group_1, dt_u1_struct_0, % 22.47/3.85 existence_l1_group_1, existence_l1_struct_0, existence_m1_group_2, % 22.47/3.85 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1, % 22.47/3.85 fc1_group_3, fc1_subset_1, fc1_xboole_0, fc4_subset_1, free_g1_group_1, % 22.47/3.85 rc1_funct_2, rc1_subset_1, rc1_xboole_0, rc2_partfun1, rc2_subset_1, % 22.47/3.85 rc2_xboole_0, rc3_struct_0, rc5_struct_0, redefinition_m2_relset_1, % 22.47/3.85 reflexivity_r1_tarski, t1_subset, t3_subset, t4_subset, t5_subset, t6_boole, % 22.47/3.85 t7_boole, t8_boole % 22.47/3.85 % 22.47/3.85 Those formulas are unsatisfiable: % 22.47/3.85 --------------------------------- % 22.47/3.85 % 22.47/3.85 Begin of proof % 22.47/3.86 | % 22.47/3.86 | ALPHA: (d1_latsubgr) implies: % 22.47/3.86 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.47/3.86 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.47/3.86 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.47/3.86 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & % 22.47/3.86 | $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ % 22.47/3.86 | (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ % 22.47/3.86 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 22.47/3.86 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.47/3.86 | (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( % 22.47/3.86 | ~ (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ % 22.47/3.86 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 22.47/3.86 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.47/3.86 | (k1_funct_1(v1, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v1 | ~ % 22.47/3.86 | $i(v5) | ~ m2_relset_1(v5, v2, v4) | ~ v1_funct_2(v5, v2, v4) | % 22.47/3.86 | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ % 22.47/3.86 | (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & % 22.47/3.86 | $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) & % 22.47/3.86 | v1_group_1(v6))))) % 22.47/3.86 | % 22.47/3.86 | ALPHA: (dt_k1_latsubgr) implies: % 23.04/3.86 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 23.04/3.86 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 23.04/3.86 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 23.04/3.86 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & % 23.04/3.86 | $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, % 23.04/3.86 | v2, v4))) % 23.04/3.86 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 23.04/3.86 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 23.04/3.86 | v1_funct_1(v1) | v3_struct_0(v0)) % 23.04/3.86 | % 23.04/3.86 | ALPHA: (dt_k2_group_1) implies: % 23.04/3.86 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 23.04/3.86 | l1_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (k2_group_1(v0) = v2 % 23.04/3.86 | & $i(v2) & m1_subset_1(v2, v1))) % 23.04/3.86 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_group_1(v0) = v1) | ~ $i(v0) | ~ % 23.04/3.86 | l1_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = % 23.04/3.86 | v2 & $i(v2) & m1_subset_1(v1, v2))) % 23.04/3.86 | % 23.04/3.86 | ALPHA: (dt_m1_group_2) implies: % 23.04/3.86 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, % 23.04/3.86 | v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | % 23.04/3.86 | v3_struct_0(v0)) % 23.04/3.86 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, % 23.04/3.86 | v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | % 23.04/3.86 | v3_struct_0(v0)) % 23.04/3.86 | % 23.04/3.86 | ALPHA: (function-axioms) implies: % 23.04/3.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.04/3.86 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 23.04/3.86 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.04/3.86 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 23.04/3.86 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.04/3.86 | (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0)) % 23.04/3.86 | % 23.04/3.87 | DELTA: instantiating (t19_latsubgr) with fresh symbols all_53_0, all_53_1, % 23.04/3.87 | all_53_2, all_53_3, all_53_4 gives: % 23.04/3.87 | (11) k2_group_1(all_53_4) = all_53_3 & k1_latsubgr(all_53_4) = all_53_2 & % 23.04/3.87 | k1_funct_1(all_53_2, all_53_1) = all_53_0 & $i(all_53_0) & % 23.04/3.87 | $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & $i(all_53_4) & % 23.04/3.87 | m1_group_2(all_53_1, all_53_4) & v1_group_1(all_53_1) & % 23.04/3.87 | l1_group_1(all_53_4) & v4_group_1(all_53_4) & v3_group_1(all_53_4) & % 23.04/3.87 | ~ r2_hidden(all_53_3, all_53_0) & ~ v3_struct_0(all_53_4) % 23.04/3.87 | % 23.04/3.87 | ALPHA: (11) implies: % 23.04/3.87 | (12) ~ v3_struct_0(all_53_4) % 23.04/3.87 | (13) ~ r2_hidden(all_53_3, all_53_0) % 23.04/3.87 | (14) v3_group_1(all_53_4) % 23.04/3.87 | (15) v4_group_1(all_53_4) % 23.04/3.87 | (16) l1_group_1(all_53_4) % 23.04/3.87 | (17) v1_group_1(all_53_1) % 23.04/3.87 | (18) m1_group_2(all_53_1, all_53_4) % 23.04/3.87 | (19) $i(all_53_4) % 23.04/3.87 | (20) $i(all_53_2) % 23.04/3.87 | (21) $i(all_53_1) % 23.04/3.87 | (22) k1_funct_1(all_53_2, all_53_1) = all_53_0 % 23.04/3.87 | (23) k1_latsubgr(all_53_4) = all_53_2 % 23.04/3.87 | (24) k2_group_1(all_53_4) = all_53_3 % 23.04/3.87 | % 23.04/3.87 | GROUND_INST: instantiating (6) with all_53_4, all_53_1, simplifying with (12), % 23.04/3.87 | (14), (16), (18), (19), (21) gives: % 23.04/3.87 | (25) l1_group_1(all_53_1) % 23.04/3.87 | % 23.04/3.87 | GROUND_INST: instantiating (3) with all_53_4, all_53_2, simplifying with (12), % 23.04/3.87 | (14), (15), (16), (19), (23) gives: % 23.04/3.87 | (26) v1_funct_1(all_53_2) % 23.04/3.87 | % 23.04/3.87 | GROUND_INST: instantiating (2) with all_53_4, all_53_2, simplifying with (12), % 23.04/3.87 | (14), (15), (16), (19), (23) gives: % 23.04/3.87 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_53_4) = v0 & % 23.04/3.87 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_53_4) = v1 & $i(v2) & $i(v1) % 23.04/3.87 | & $i(v0) & m2_relset_1(all_53_2, v0, v2) & v1_funct_2(all_53_2, v0, % 23.04/3.87 | v2)) % 23.04/3.87 | % 23.04/3.87 | GROUND_INST: instantiating (1) with all_53_4, all_53_2, simplifying with (12), % 23.04/3.87 | (14), (15), (16), (19), (23) gives: % 23.04/3.87 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_53_4) = v0 & % 23.04/3.87 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_53_4) = v1 & $i(v2) & $i(v1) % 23.04/3.87 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (k1_funct_1(all_53_2, v3) % 23.04/3.87 | = v4) | ~ $i(v3) | ~ $i(all_53_2) | ~ m2_relset_1(all_53_2, % 23.04/3.87 | v0, v2) | ~ v1_funct_2(all_53_2, v0, v2) | ~ % 23.04/3.87 | v1_funct_1(all_53_2) | ~ m1_group_2(v3, all_53_4) | ~ % 23.04/3.87 | v1_group_1(v3) | (u1_struct_0(v3) = v4 & $i(v4))) & ! [v3: $i] : % 23.04/3.87 | ! [v4: $i] : ( ~ (u1_struct_0(v3) = v4) | ~ $i(v3) | ~ % 23.04/3.87 | $i(all_53_2) | ~ m2_relset_1(all_53_2, v0, v2) | ~ % 23.04/3.87 | v1_funct_2(all_53_2, v0, v2) | ~ v1_funct_1(all_53_2) | ~ % 23.04/3.87 | m1_group_2(v3, all_53_4) | ~ v1_group_1(v3) | % 23.04/3.87 | (k1_funct_1(all_53_2, v3) = v4 & $i(v4))) & ! [v3: any] : (v3 = % 23.04/3.87 | all_53_2 | ~ $i(v3) | ~ m2_relset_1(v3, v0, v2) | ~ % 23.04/3.87 | v1_funct_2(v3, v0, v2) | ~ v1_funct_1(v3) | ? [v4: $i] : ? [v5: % 23.04/3.87 | $i] : ? [v6: $i] : ( ~ (v6 = v5) & k1_funct_1(v3, v4) = v5 & % 23.04/3.87 | u1_struct_0(v4) = v6 & $i(v6) & $i(v5) & $i(v4) & m1_group_2(v4, % 23.04/3.87 | all_53_4) & v1_group_1(v4)))) % 23.04/3.87 | % 23.04/3.87 | GROUND_INST: instantiating (5) with all_53_4, all_53_3, simplifying with (12), % 23.04/3.87 | (16), (19), (24) gives: % 23.04/3.87 | (29) ? [v0: $i] : (u1_struct_0(all_53_4) = v0 & $i(v0) & % 23.04/3.87 | m1_subset_1(all_53_3, v0)) % 23.04/3.87 | % 23.04/3.87 | DELTA: instantiating (29) with fresh symbol all_67_0 gives: % 23.04/3.87 | (30) u1_struct_0(all_53_4) = all_67_0 & $i(all_67_0) & % 23.04/3.87 | m1_subset_1(all_53_3, all_67_0) % 23.04/3.87 | % 23.04/3.87 | ALPHA: (30) implies: % 23.04/3.88 | (31) u1_struct_0(all_53_4) = all_67_0 % 23.04/3.88 | % 23.04/3.88 | DELTA: instantiating (27) with fresh symbols all_69_0, all_69_1, all_69_2 % 23.04/3.88 | gives: % 23.04/3.88 | (32) k1_group_3(all_53_4) = all_69_2 & k1_zfmisc_1(all_69_1) = all_69_0 & % 23.04/3.88 | u1_struct_0(all_53_4) = all_69_1 & $i(all_69_0) & $i(all_69_1) & % 23.04/3.88 | $i(all_69_2) & m2_relset_1(all_53_2, all_69_2, all_69_0) & % 23.04/3.88 | v1_funct_2(all_53_2, all_69_2, all_69_0) % 23.04/3.88 | % 23.04/3.88 | ALPHA: (32) implies: % 23.04/3.88 | (33) v1_funct_2(all_53_2, all_69_2, all_69_0) % 23.04/3.88 | (34) m2_relset_1(all_53_2, all_69_2, all_69_0) % 23.04/3.88 | (35) u1_struct_0(all_53_4) = all_69_1 % 23.04/3.88 | (36) k1_zfmisc_1(all_69_1) = all_69_0 % 23.04/3.88 | (37) k1_group_3(all_53_4) = all_69_2 % 23.04/3.88 | % 23.04/3.88 | DELTA: instantiating (28) with fresh symbols all_71_0, all_71_1, all_71_2 % 23.04/3.88 | gives: % 23.04/3.88 | (38) k1_group_3(all_53_4) = all_71_2 & k1_zfmisc_1(all_71_1) = all_71_0 & % 23.04/3.88 | u1_struct_0(all_53_4) = all_71_1 & $i(all_71_0) & $i(all_71_1) & % 23.04/3.88 | $i(all_71_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_funct_1(all_53_2, % 23.04/3.88 | v0) = v1) | ~ $i(v0) | ~ $i(all_53_2) | ~ % 23.04/3.88 | m2_relset_1(all_53_2, all_71_2, all_71_0) | ~ v1_funct_2(all_53_2, % 23.04/3.88 | all_71_2, all_71_0) | ~ v1_funct_1(all_53_2) | ~ m1_group_2(v0, % 23.04/3.88 | all_53_4) | ~ v1_group_1(v0) | (u1_struct_0(v0) = v1 & $i(v1))) & % 23.04/3.88 | ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | % 23.04/3.88 | ~ $i(all_53_2) | ~ m2_relset_1(all_53_2, all_71_2, all_71_0) | ~ % 23.04/3.88 | v1_funct_2(all_53_2, all_71_2, all_71_0) | ~ v1_funct_1(all_53_2) | % 23.04/3.88 | ~ m1_group_2(v0, all_53_4) | ~ v1_group_1(v0) | % 23.04/3.88 | (k1_funct_1(all_53_2, v0) = v1 & $i(v1))) & ! [v0: any] : (v0 = % 23.04/3.88 | all_53_2 | ~ $i(v0) | ~ m2_relset_1(v0, all_71_2, all_71_0) | ~ % 23.04/3.88 | v1_funct_2(v0, all_71_2, all_71_0) | ~ v1_funct_1(v0) | ? [v1: $i] % 23.04/3.88 | : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & k1_funct_1(v0, v1) = % 23.04/3.88 | v2 & u1_struct_0(v1) = v3 & $i(v3) & $i(v2) & $i(v1) & % 23.04/3.88 | m1_group_2(v1, all_53_4) & v1_group_1(v1))) % 23.04/3.88 | % 23.04/3.88 | ALPHA: (38) implies: % 23.04/3.88 | (39) u1_struct_0(all_53_4) = all_71_1 % 23.04/3.88 | (40) k1_zfmisc_1(all_71_1) = all_71_0 % 23.04/3.88 | (41) k1_group_3(all_53_4) = all_71_2 % 23.04/3.88 | (42) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_funct_1(all_53_2, v0) = v1) | ~ % 23.04/3.88 | $i(v0) | ~ $i(all_53_2) | ~ m2_relset_1(all_53_2, all_71_2, % 23.04/3.88 | all_71_0) | ~ v1_funct_2(all_53_2, all_71_2, all_71_0) | ~ % 23.04/3.88 | v1_funct_1(all_53_2) | ~ m1_group_2(v0, all_53_4) | ~ % 23.04/3.88 | v1_group_1(v0) | (u1_struct_0(v0) = v1 & $i(v1))) % 23.04/3.88 | % 23.04/3.88 | GROUND_INST: instantiating (8) with all_69_1, all_71_1, all_53_4, simplifying % 23.04/3.88 | with (35), (39) gives: % 23.04/3.88 | (43) all_71_1 = all_69_1 % 23.04/3.88 | % 23.04/3.88 | GROUND_INST: instantiating (8) with all_67_0, all_71_1, all_53_4, simplifying % 23.04/3.88 | with (31), (39) gives: % 23.04/3.88 | (44) all_71_1 = all_67_0 % 23.04/3.88 | % 23.04/3.88 | GROUND_INST: instantiating (9) with all_69_0, all_71_0, all_69_1, simplifying % 23.04/3.88 | with (36) gives: % 23.04/3.88 | (45) all_71_0 = all_69_0 | ~ (k1_zfmisc_1(all_69_1) = all_71_0) % 23.04/3.88 | % 23.04/3.88 | GROUND_INST: instantiating (10) with all_69_2, all_71_2, all_53_4, simplifying % 23.04/3.88 | with (37), (41) gives: % 23.04/3.88 | (46) all_71_2 = all_69_2 % 23.04/3.88 | % 23.04/3.88 | COMBINE_EQS: (43), (44) imply: % 23.04/3.88 | (47) all_69_1 = all_67_0 % 23.04/3.88 | % 23.04/3.88 | SIMP: (47) implies: % 23.04/3.88 | (48) all_69_1 = all_67_0 % 23.04/3.88 | % 23.04/3.88 | REDUCE: (40), (44) imply: % 23.04/3.88 | (49) k1_zfmisc_1(all_67_0) = all_71_0 % 23.04/3.88 | % 23.04/3.88 | BETA: splitting (45) gives: % 23.04/3.88 | % 23.04/3.88 | Case 1: % 23.04/3.88 | | % 23.04/3.88 | | (50) ~ (k1_zfmisc_1(all_69_1) = all_71_0) % 23.04/3.88 | | % 23.04/3.88 | | REDUCE: (48), (50) imply: % 23.04/3.88 | | (51) ~ (k1_zfmisc_1(all_67_0) = all_71_0) % 23.04/3.88 | | % 23.04/3.88 | | PRED_UNIFY: (49), (51) imply: % 23.04/3.88 | | (52) $false % 23.04/3.88 | | % 23.04/3.88 | | CLOSE: (52) is inconsistent. % 23.04/3.88 | | % 23.04/3.88 | Case 2: % 23.04/3.88 | | % 23.04/3.89 | | (53) all_71_0 = all_69_0 % 23.04/3.89 | | % 23.04/3.89 | | GROUND_INST: instantiating (dt_l1_group_1) with all_53_1, simplifying with % 23.04/3.89 | | (21), (25) gives: % 23.04/3.89 | | (54) l1_struct_0(all_53_1) % 23.04/3.89 | | % 23.04/3.89 | | GROUND_INST: instantiating (42) with all_53_1, all_53_0, simplifying with % 23.04/3.89 | | (17), (18), (20), (21), (22), (26) gives: % 23.04/3.89 | | (55) ~ m2_relset_1(all_53_2, all_71_2, all_71_0) | ~ % 23.04/3.89 | | v1_funct_2(all_53_2, all_71_2, all_71_0) | (u1_struct_0(all_53_1) = % 23.04/3.89 | | all_53_0 & $i(all_53_0)) % 23.04/3.89 | | % 23.04/3.89 | | BETA: splitting (55) gives: % 23.04/3.89 | | % 23.04/3.89 | | Case 1: % 23.04/3.89 | | | % 23.04/3.89 | | | (56) ~ m2_relset_1(all_53_2, all_71_2, all_71_0) % 23.04/3.89 | | | % 23.04/3.89 | | | REDUCE: (46), (53), (56) imply: % 23.04/3.89 | | | (57) ~ m2_relset_1(all_53_2, all_69_2, all_69_0) % 23.04/3.89 | | | % 23.04/3.89 | | | PRED_UNIFY: (34), (57) imply: % 23.04/3.89 | | | (58) $false % 23.04/3.89 | | | % 23.04/3.89 | | | CLOSE: (58) is inconsistent. % 23.04/3.89 | | | % 23.04/3.89 | | Case 2: % 23.04/3.89 | | | % 23.04/3.89 | | | (59) ~ v1_funct_2(all_53_2, all_71_2, all_71_0) | % 23.04/3.89 | | | (u1_struct_0(all_53_1) = all_53_0 & $i(all_53_0)) % 23.04/3.89 | | | % 23.04/3.89 | | | BETA: splitting (59) gives: % 23.04/3.89 | | | % 23.04/3.89 | | | Case 1: % 23.04/3.89 | | | | % 23.04/3.89 | | | | (60) ~ v1_funct_2(all_53_2, all_71_2, all_71_0) % 23.04/3.89 | | | | % 23.04/3.89 | | | | REDUCE: (46), (53), (60) imply: % 23.04/3.89 | | | | (61) ~ v1_funct_2(all_53_2, all_69_2, all_69_0) % 23.04/3.89 | | | | % 23.04/3.89 | | | | PRED_UNIFY: (33), (61) imply: % 23.04/3.89 | | | | (62) $false % 23.04/3.89 | | | | % 23.04/3.89 | | | | CLOSE: (62) is inconsistent. % 23.04/3.89 | | | | % 23.04/3.89 | | | Case 2: % 23.04/3.89 | | | | % 23.04/3.89 | | | | (63) u1_struct_0(all_53_1) = all_53_0 & $i(all_53_0) % 23.04/3.89 | | | | % 23.04/3.89 | | | | ALPHA: (63) implies: % 23.04/3.89 | | | | (64) $i(all_53_0) % 23.04/3.89 | | | | (65) u1_struct_0(all_53_1) = all_53_0 % 23.04/3.89 | | | | % 23.04/3.89 | | | | GROUND_INST: instantiating (fc1_struct_0) with all_53_1, all_53_0, % 23.04/3.89 | | | | simplifying with (21), (54), (65) gives: % 23.04/3.89 | | | | (66) ~ v1_xboole_0(all_53_0) | v3_struct_0(all_53_1) % 23.04/3.89 | | | | % 23.04/3.89 | | | | GROUND_INST: instantiating (4) with all_53_1, all_53_0, simplifying with % 23.04/3.89 | | | | (21), (25), (65) gives: % 23.04/3.89 | | | | (67) v3_struct_0(all_53_1) | ? [v0: $i] : (k2_group_1(all_53_1) = v0 % 23.04/3.89 | | | | & $i(v0) & m1_subset_1(v0, all_53_0)) % 23.04/3.89 | | | | % 23.04/3.89 | | | | BETA: splitting (66) gives: % 23.04/3.89 | | | | % 23.04/3.89 | | | | Case 1: % 23.04/3.89 | | | | | % 23.04/3.89 | | | | | (68) ~ v1_xboole_0(all_53_0) % 23.04/3.89 | | | | | % 23.04/3.89 | | | | | BETA: splitting (67) gives: % 23.04/3.89 | | | | | % 23.04/3.89 | | | | | Case 1: % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | (69) v3_struct_0(all_53_1) % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | GROUND_INST: instantiating (7) with all_53_4, all_53_1, simplifying % 23.04/3.89 | | | | | | with (12), (14), (16), (18), (19), (21), (69) gives: % 23.04/3.89 | | | | | | (70) $false % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | CLOSE: (70) is inconsistent. % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | Case 2: % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | (71) ? [v0: $i] : (k2_group_1(all_53_1) = v0 & $i(v0) & % 23.04/3.89 | | | | | | m1_subset_1(v0, all_53_0)) % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | DELTA: instantiating (71) with fresh symbol all_275_0 gives: % 23.04/3.89 | | | | | | (72) k2_group_1(all_53_1) = all_275_0 & $i(all_275_0) & % 23.04/3.89 | | | | | | m1_subset_1(all_275_0, all_53_0) % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | ALPHA: (72) implies: % 23.04/3.89 | | | | | | (73) m1_subset_1(all_275_0, all_53_0) % 23.04/3.89 | | | | | | (74) $i(all_275_0) % 23.04/3.89 | | | | | | (75) k2_group_1(all_53_1) = all_275_0 % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | GROUND_INST: instantiating (t2_subset) with all_275_0, all_53_0, % 23.04/3.89 | | | | | | simplifying with (64), (68), (73), (74) gives: % 23.04/3.89 | | | | | | (76) r2_hidden(all_275_0, all_53_0) % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | GROUND_INST: instantiating (t53_group_2) with all_53_4, all_53_3, % 23.04/3.89 | | | | | | all_53_1, all_275_0, simplifying with (12), (14), (15), % 23.04/3.89 | | | | | | (16), (18), (19), (21), (24), (75) gives: % 23.04/3.89 | | | | | | (77) all_275_0 = all_53_3 % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | REDUCE: (76), (77) imply: % 23.04/3.89 | | | | | | (78) r2_hidden(all_53_3, all_53_0) % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | PRED_UNIFY: (13), (78) imply: % 23.04/3.89 | | | | | | (79) $false % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | | CLOSE: (79) is inconsistent. % 23.04/3.89 | | | | | | % 23.04/3.89 | | | | | End of split % 23.04/3.89 | | | | | % 23.04/3.89 | | | | Case 2: % 23.04/3.89 | | | | | % 23.04/3.89 | | | | | (80) v3_struct_0(all_53_1) % 23.04/3.89 | | | | | % 23.04/3.89 | | | | | GROUND_INST: instantiating (7) with all_53_4, all_53_1, simplifying % 23.04/3.89 | | | | | with (12), (14), (16), (18), (19), (21), (80) gives: % 23.04/3.89 | | | | | (81) $false % 23.04/3.89 | | | | | % 23.04/3.89 | | | | | CLOSE: (81) is inconsistent. % 23.04/3.89 | | | | | % 23.04/3.89 | | | | End of split % 23.04/3.89 | | | | % 23.04/3.89 | | | End of split % 23.04/3.89 | | | % 23.04/3.89 | | End of split % 23.04/3.89 | | % 23.04/3.89 | End of split % 23.04/3.89 | % 23.04/3.89 End of proof % 23.04/3.89 % SZS output end Proof for theBenchmark % 23.04/3.89 % 23.04/3.89 3266ms %------------------------------------------------------------------------------