%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRP645+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 : n029.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 01:12:49 EDT 2023 % Result : Theorem 18.85s 3.20s % Output : Proof 22.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP645+1 : TPTP v8.1.2. Released v3.4.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 23:38:41 EDT 2023 % 0.12/0.34 % CPUTime : % 0.51/0.60 ________ _____ % 0.51/0.60 ___ __ \_________(_)________________________________ % 0.51/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.60 % 0.51/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.60 (2023-06-19) % 0.51/0.60 % 0.51/0.60 (c) Philipp Rümmer, 2009-2023 % 0.51/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.60 Amanda Stjerna. % 0.51/0.60 Free software under BSD-3-Clause. % 0.51/0.60 % 0.51/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.60 % 0.51/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.51/0.61 Running up to 7 provers in parallel. % 0.51/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.03/1.13 Prover 4: Preprocessing ... % 3.45/1.13 Prover 1: Preprocessing ... % 3.45/1.16 Prover 6: Preprocessing ... % 3.45/1.16 Prover 3: Preprocessing ... % 3.45/1.16 Prover 2: Preprocessing ... % 3.45/1.16 Prover 5: Preprocessing ... % 3.45/1.16 Prover 0: Preprocessing ... % 8.27/1.82 Prover 1: Warning: ignoring some quantifiers % 9.33/1.92 Prover 1: Constructing countermodel ... % 9.33/1.92 Prover 5: Proving ... % 9.33/1.94 Prover 3: Warning: ignoring some quantifiers % 9.33/1.96 Prover 6: Proving ... % 9.33/1.96 Prover 3: Constructing countermodel ... % 9.63/2.02 Prover 2: Proving ... % 14.92/2.67 Prover 3: gave up % 14.92/2.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.92/2.68 Prover 4: Warning: ignoring some quantifiers % 14.92/2.72 Prover 4: Constructing countermodel ... % 15.41/2.76 Prover 7: Preprocessing ... % 15.72/2.84 Prover 0: Proving ... % 17.07/2.98 Prover 7: Warning: ignoring some quantifiers % 17.07/2.99 Prover 7: Constructing countermodel ... % 18.85/3.20 Prover 5: proved (2578ms) % 18.85/3.20 % 18.85/3.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.85/3.20 % 18.85/3.20 Prover 2: stopped % 18.85/3.20 Prover 6: stopped % 18.85/3.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.85/3.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.85/3.21 Prover 0: stopped % 18.85/3.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.23/3.24 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.23/3.42 Prover 10: Preprocessing ... % 20.23/3.42 Prover 8: Preprocessing ... % 20.23/3.42 Prover 11: Preprocessing ... % 20.77/3.46 Prover 13: Preprocessing ... % 21.34/3.52 Prover 10: Warning: ignoring some quantifiers % 21.34/3.53 Prover 10: Constructing countermodel ... % 21.55/3.55 Prover 1: gave up % 21.55/3.58 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 21.55/3.58 Prover 13: Warning: ignoring some quantifiers % 21.55/3.59 Prover 13: Constructing countermodel ... % 21.55/3.60 Prover 8: Warning: ignoring some quantifiers % 21.55/3.61 Prover 8: Constructing countermodel ... % 22.15/3.63 Prover 7: Found proof (size 47) % 22.15/3.63 Prover 7: proved (952ms) % 22.15/3.63 Prover 8: stopped % 22.15/3.63 Prover 4: stopped % 22.15/3.63 Prover 10: stopped % 22.15/3.64 Prover 11: stopped % 22.15/3.64 Prover 13: stopped % 22.15/3.65 Prover 16: Preprocessing ... % 22.43/3.68 Prover 16: stopped % 22.43/3.68 % 22.43/3.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.43/3.68 % 22.43/3.68 % SZS output start Proof for theBenchmark % 22.43/3.69 Assumptions after simplification: % 22.43/3.69 --------------------------------- % 22.43/3.69 % 22.43/3.69 (d1_latsubgr) % 22.43/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.43/3.72 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | % 22.43/3.72 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0) = v2 & % 22.43/3.72 k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & % 22.43/3.72 ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~ % 22.43/3.72 $i(v1) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 22.43/3.72 v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.43/3.72 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 22.43/3.72 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ m2_relset_1(v1, v2, % 22.43/3.72 v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~ % 22.43/3.72 m1_group_2(v5, v0) | ~ v1_group_1(v5) | (k1_funct_1(v1, v5) = v6 & % 22.43/3.72 $i(v6))) & ! [v5: $i] : (v5 = v1 | ~ $i(v5) | ~ m2_relset_1(v5, v2, % 22.43/3.72 v4) | ~ v1_funct_2(v5, v2, v4) | ~ v1_funct_1(v5) | ? [v6: $i] : ? % 22.43/3.72 [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & % 22.43/3.72 u1_struct_0(v6) = v8 & $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) & % 22.43/3.72 v1_group_1(v6))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_group_3(v0) = % 22.43/3.72 v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ % 22.43/3.72 v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.43/3.72 (k1_latsubgr(v0) = v4 & k1_zfmisc_1(v2) = v3 & u1_struct_0(v0) = v2 & $i(v4) % 22.43/3.72 & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) = % 22.43/3.72 v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1, % 22.43/3.72 v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.43/3.72 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 22.43/3.72 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~ % 22.43/3.72 v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ % 22.43/3.72 v1_group_1(v5) | (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 % 22.43/3.72 = v4 | ~ $i(v5) | ~ m2_relset_1(v5, v1, v3) | ~ v1_funct_2(v5, v1, % 22.43/3.72 v3) | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( % 22.43/3.72 ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8) % 22.43/3.72 & $i(v7) & $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6))))) & ! [v0: % 22.43/3.72 $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 22.43/3.72 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | % 22.43/3.72 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_latsubgr(v0) = v4 & % 22.43/3.72 k1_group_3(v0) = v2 & k1_zfmisc_1(v1) = v3 & $i(v4) & $i(v3) & $i(v2) & ! % 22.43/3.72 [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ $i(v5) | ~ % 22.43/3.72 m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4) % 22.43/3.72 | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | (u1_struct_0(v5) = v6 & % 22.43/3.72 $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ (u1_struct_0(v5) = v6) | ~ % 22.43/3.72 $i(v5) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ % 22.43/3.72 v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.43/3.72 (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v4 | ~ $i(v5) % 22.43/3.72 | ~ m2_relset_1(v5, v2, v3) | ~ v1_funct_2(v5, v2, v3) | ~ % 22.43/3.72 v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) % 22.43/3.72 & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8) & $i(v7) & % 22.43/3.72 $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6))))) % 22.43/3.72 % 22.43/3.72 (dt_k1_latsubgr) % 22.43/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.43/3.72 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_funct_1(v1) | % 22.43/3.72 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | % 22.43/3.72 ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.43/3.72 v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0) % 22.43/3.72 = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & % 22.43/3.72 $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, v2, v4))) & ! [v0: $i] % 22.43/3.72 : ! [v1: $i] : ( ~ (k1_group_3(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ % 22.43/3.72 v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: % 22.43/3.72 $i] : ? [v4: $i] : (k1_latsubgr(v0) = v2 & k1_zfmisc_1(v3) = v4 & % 22.43/3.72 u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v1, v4) % 22.43/3.72 & v1_funct_2(v2, v1, v4) & v1_funct_1(v2))) & ! [v0: $i] : ! [v1: $i] : % 22.43/3.72 ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) % 22.43/3.72 | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 22.43/3.72 $i] : (k1_latsubgr(v0) = v2 & k1_group_3(v0) = v3 & k1_zfmisc_1(v1) = v4 & % 22.43/3.72 $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v3, v4) & v1_funct_2(v2, v3, % 22.43/3.72 v4) & v1_funct_1(v2))) % 22.43/3.72 % 22.43/3.72 (dt_k9_group_2) % 22.43/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k9_group_2(v0, % 22.43/3.72 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v2, % 22.43/3.72 v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ % 22.43/3.72 v3_group_1(v0) | m1_group_2(v3, v0) | v3_struct_0(v0)) & ! [v0: $i] : ! % 22.43/3.72 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k9_group_2(v0, v1, v2) = v3) | ~ % 22.43/3.72 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, % 22.43/3.72 v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.43/3.72 v1_group_1(v3) | v3_struct_0(v0)) % 22.43/3.72 % 22.43/3.72 (t23_latsubgr) % 22.43/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.43/3.73 $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ (k1_funct_1(v1, v4) = v5) | ~ % 22.43/3.73 (k1_funct_1(v1, v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ % 22.43/3.73 m1_group_2(v4, v0) | ~ m1_group_2(v2, v0) | ~ v1_group_1(v4) | ~ % 22.43/3.73 v1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.43/3.73 v3_struct_0(v0) | ? [v6: $i] : ? [v7: $i] : (k9_group_2(v0, v2, v4) = v6 & % 22.43/3.73 k3_xboole_0(v3, v5) = v7 & u1_struct_0(v6) = v7 & $i(v7) & $i(v6))) & ! % 22.43/3.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 22.43/3.73 : ( ~ (k1_latsubgr(v0) = v1) | ~ (k1_funct_1(v1, v2) = v3) | ~ % 22.43/3.73 (k9_group_2(v0, v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ % 22.43/3.73 m1_group_2(v4, v0) | ~ m1_group_2(v2, v0) | ~ v1_group_1(v4) | ~ % 22.43/3.73 v1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.43/3.73 v3_struct_0(v0) | ? [v6: $i] : ? [v7: $i] : (k1_funct_1(v1, v4) = v7 & % 22.43/3.73 k3_xboole_0(v3, v7) = v6 & u1_struct_0(v5) = v6 & $i(v7) & $i(v6))) % 22.43/3.73 % 22.43/3.73 (t24_latsubgr) % 22.43/3.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 22.43/3.73 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v6) & % 22.43/3.73 k1_latsubgr(v0) = v1 & k1_funct_1(v1, v5) = v6 & k1_funct_1(v1, v4) = v7 & % 22.43/3.73 k1_funct_1(v1, v2) = v3 & k9_group_2(v0, v2, v4) = v5 & k3_xboole_0(v3, v7) % 22.43/3.73 = v8 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 22.43/3.73 & $i(v0) & m1_group_2(v4, v0) & m1_group_2(v2, v0) & v1_group_1(v4) & % 22.43/3.73 v1_group_1(v2) & l1_group_1(v0) & v4_group_1(v0) & v3_group_1(v0) & ~ % 22.43/3.73 v3_struct_0(v0)) % 22.43/3.73 % 22.43/3.73 (function-axioms) % 22.43/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 22.43/3.73 | ~ (k8_group_2(v4, v3, v2) = v1) | ~ (k8_group_2(v4, v3, v2) = v0)) & ! % 22.43/3.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 22.43/3.73 ~ (k9_group_2(v4, v3, v2) = v1) | ~ (k9_group_2(v4, v3, v2) = v0)) & ! % 22.43/3.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.43/3.73 (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: $i] : ! % 22.43/3.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k3_xboole_0(v3, v2) = % 22.43/3.73 v1) | ~ (k3_xboole_0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 22.43/3.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ % 22.43/3.73 (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 22.43/3.73 [v3: $i] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ (g1_group_1(v3, v2) = % 22.43/3.73 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.43/3.73 (k1_latsubgr(v2) = v1) | ~ (k1_latsubgr(v2) = v0)) & ! [v0: $i] : ! [v1: % 22.43/3.73 $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) % 22.43/3.73 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.43/3.73 (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! [v1: % 22.43/3.73 $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) % 22.43/3.73 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.43/3.73 (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 22.43/3.73 % 22.43/3.73 Further assumptions not needed in the proof: % 22.43/3.73 -------------------------------------------- % 22.43/3.73 abstractness_v1_group_1, antisymmetry_r2_hidden, cc1_funct_2, cc1_relset_1, % 22.43/3.73 cc5_funct_2, cc6_funct_2, commutativity_k3_xboole_0, commutativity_k9_group_2, % 22.43/3.73 dt_g1_group_1, dt_k1_funct_1, dt_k1_group_3, dt_k1_xboole_0, dt_k1_zfmisc_1, % 22.43/3.73 dt_k2_zfmisc_1, dt_k3_xboole_0, dt_k8_group_2, dt_l1_group_1, dt_l1_struct_0, % 22.43/3.73 dt_m1_group_2, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_group_1, % 22.43/3.73 dt_u1_struct_0, existence_l1_group_1, existence_l1_struct_0, % 22.43/3.73 existence_m1_group_2, existence_m1_relset_1, existence_m1_subset_1, % 22.43/3.73 existence_m2_relset_1, fc1_group_3, fc1_struct_0, fc1_subset_1, fc1_xboole_0, % 22.43/3.73 fc4_subset_1, free_g1_group_1, idempotence_k3_xboole_0, rc1_funct_2, % 22.43/3.73 rc1_subset_1, rc1_xboole_0, rc2_partfun1, rc2_subset_1, rc2_xboole_0, % 22.43/3.73 rc3_struct_0, rc5_struct_0, redefinition_k9_group_2, redefinition_m2_relset_1, % 22.43/3.73 reflexivity_r1_tarski, t1_subset, t2_boole, t2_subset, t3_subset, t4_subset, % 22.43/3.73 t5_subset, t6_boole, t7_boole, t8_boole % 22.43/3.73 % 22.43/3.73 Those formulas are unsatisfiable: % 22.43/3.73 --------------------------------- % 22.43/3.73 % 22.43/3.73 Begin of proof % 22.43/3.73 | % 22.43/3.73 | ALPHA: (d1_latsubgr) implies: % 22.43/3.73 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.43/3.73 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.43/3.73 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.43/3.73 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & % 22.43/3.73 | $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ % 22.43/3.74 | (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ % 22.43/3.74 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 22.43/3.74 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.43/3.74 | (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( % 22.43/3.74 | ~ (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ % 22.43/3.74 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 22.43/3.74 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 22.43/3.74 | (k1_funct_1(v1, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v1 | ~ % 22.43/3.74 | $i(v5) | ~ m2_relset_1(v5, v2, v4) | ~ v1_funct_2(v5, v2, v4) | % 22.43/3.74 | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ % 22.43/3.74 | (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & % 22.43/3.74 | $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) & % 22.43/3.74 | v1_group_1(v6))))) % 22.43/3.74 | % 22.43/3.74 | ALPHA: (dt_k1_latsubgr) implies: % 22.43/3.74 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.43/3.74 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.43/3.74 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.43/3.74 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & % 22.43/3.74 | $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, % 22.43/3.74 | v2, v4))) % 22.43/3.74 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 22.43/3.74 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 22.43/3.74 | v1_funct_1(v1) | v3_struct_0(v0)) % 22.43/3.74 | % 22.43/3.74 | ALPHA: (dt_k9_group_2) implies: % 22.43/3.74 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 22.43/3.74 | (k9_group_2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 22.43/3.74 | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ % 22.43/3.74 | v4_group_1(v0) | ~ v3_group_1(v0) | v1_group_1(v3) | % 22.43/3.74 | v3_struct_0(v0)) % 22.43/3.74 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 22.43/3.74 | (k9_group_2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 22.43/3.74 | ~ m1_group_2(v2, v0) | ~ m1_group_2(v1, v0) | ~ l1_group_1(v0) | ~ % 22.43/3.74 | v4_group_1(v0) | ~ v3_group_1(v0) | m1_group_2(v3, v0) | % 22.43/3.74 | v3_struct_0(v0)) % 22.43/3.74 | % 22.43/3.74 | ALPHA: (t23_latsubgr) implies: % 22.43/3.74 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.43/3.74 | ! [v5: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ (k1_funct_1(v1, v4) = v5) % 22.43/3.74 | | ~ (k1_funct_1(v1, v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | % 22.43/3.74 | ~ m1_group_2(v4, v0) | ~ m1_group_2(v2, v0) | ~ v1_group_1(v4) | ~ % 22.43/3.74 | v1_group_1(v2) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ % 22.43/3.74 | v3_group_1(v0) | v3_struct_0(v0) | ? [v6: $i] : ? [v7: $i] : % 22.43/3.74 | (k9_group_2(v0, v2, v4) = v6 & k3_xboole_0(v3, v5) = v7 & % 22.43/3.74 | u1_struct_0(v6) = v7 & $i(v7) & $i(v6))) % 22.43/3.74 | % 22.43/3.74 | ALPHA: (function-axioms) implies: % 22.43/3.74 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.43/3.74 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 22.43/3.74 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.43/3.74 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 22.43/3.74 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_group_3(v2) % 22.43/3.74 | = v1) | ~ (k1_group_3(v2) = v0)) % 22.43/3.74 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.43/3.74 | (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0)) % 22.43/3.74 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.43/3.74 | (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) % 22.43/3.74 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.43/3.74 | (v1 = v0 | ~ (k9_group_2(v4, v3, v2) = v1) | ~ (k9_group_2(v4, v3, % 22.43/3.74 | v2) = v0)) % 22.43/3.74 | % 22.43/3.74 | DELTA: instantiating (t24_latsubgr) with fresh symbols all_59_0, all_59_1, % 22.43/3.74 | all_59_2, all_59_3, all_59_4, all_59_5, all_59_6, all_59_7, all_59_8 % 22.43/3.74 | gives: % 22.43/3.74 | (13) ~ (all_59_0 = all_59_2) & k1_latsubgr(all_59_8) = all_59_7 & % 22.43/3.74 | k1_funct_1(all_59_7, all_59_3) = all_59_2 & k1_funct_1(all_59_7, % 22.43/3.74 | all_59_4) = all_59_1 & k1_funct_1(all_59_7, all_59_6) = all_59_5 & % 22.43/3.74 | k9_group_2(all_59_8, all_59_6, all_59_4) = all_59_3 & % 22.43/3.74 | k3_xboole_0(all_59_5, all_59_1) = all_59_0 & $i(all_59_0) & % 22.43/3.74 | $i(all_59_1) & $i(all_59_2) & $i(all_59_3) & $i(all_59_4) & % 22.43/3.74 | $i(all_59_5) & $i(all_59_6) & $i(all_59_7) & $i(all_59_8) & % 22.43/3.74 | m1_group_2(all_59_4, all_59_8) & m1_group_2(all_59_6, all_59_8) & % 22.43/3.74 | v1_group_1(all_59_4) & v1_group_1(all_59_6) & l1_group_1(all_59_8) & % 22.43/3.74 | v4_group_1(all_59_8) & v3_group_1(all_59_8) & ~ v3_struct_0(all_59_8) % 22.43/3.74 | % 22.43/3.74 | ALPHA: (13) implies: % 22.43/3.75 | (14) ~ (all_59_0 = all_59_2) % 22.43/3.75 | (15) ~ v3_struct_0(all_59_8) % 22.43/3.75 | (16) v3_group_1(all_59_8) % 22.43/3.75 | (17) v4_group_1(all_59_8) % 22.43/3.75 | (18) l1_group_1(all_59_8) % 22.43/3.75 | (19) v1_group_1(all_59_6) % 22.43/3.75 | (20) v1_group_1(all_59_4) % 22.43/3.75 | (21) m1_group_2(all_59_6, all_59_8) % 22.78/3.75 | (22) m1_group_2(all_59_4, all_59_8) % 22.78/3.75 | (23) $i(all_59_8) % 22.78/3.75 | (24) $i(all_59_7) % 22.78/3.75 | (25) $i(all_59_6) % 22.78/3.75 | (26) $i(all_59_4) % 22.78/3.75 | (27) k3_xboole_0(all_59_5, all_59_1) = all_59_0 % 22.78/3.75 | (28) k9_group_2(all_59_8, all_59_6, all_59_4) = all_59_3 % 22.78/3.75 | (29) k1_funct_1(all_59_7, all_59_6) = all_59_5 % 22.78/3.75 | (30) k1_funct_1(all_59_7, all_59_4) = all_59_1 % 22.78/3.75 | (31) k1_funct_1(all_59_7, all_59_3) = all_59_2 % 22.78/3.75 | (32) k1_latsubgr(all_59_8) = all_59_7 % 22.78/3.75 | % 22.78/3.75 | GROUND_INST: instantiating (5) with all_59_8, all_59_6, all_59_4, all_59_3, % 22.78/3.75 | simplifying with (15), (16), (17), (18), (21), (22), (23), (25), % 22.78/3.75 | (26), (28) gives: % 22.78/3.75 | (33) m1_group_2(all_59_3, all_59_8) % 22.78/3.75 | % 22.78/3.75 | GROUND_INST: instantiating (4) with all_59_8, all_59_6, all_59_4, all_59_3, % 22.78/3.75 | simplifying with (15), (16), (17), (18), (21), (22), (23), (25), % 22.78/3.75 | (26), (28) gives: % 22.78/3.75 | (34) v1_group_1(all_59_3) % 22.78/3.75 | % 22.78/3.75 | GROUND_INST: instantiating (6) with all_59_8, all_59_7, all_59_6, all_59_5, % 22.78/3.75 | all_59_4, all_59_1, simplifying with (15), (16), (17), (18), % 22.78/3.75 | (19), (20), (21), (22), (23), (25), (26), (29), (30), (32) gives: % 22.78/3.75 | (35) ? [v0: $i] : ? [v1: $i] : (k9_group_2(all_59_8, all_59_6, all_59_4) % 22.78/3.75 | = v0 & k3_xboole_0(all_59_5, all_59_1) = v1 & u1_struct_0(v0) = v1 & % 22.78/3.75 | $i(v1) & $i(v0)) % 22.78/3.75 | % 22.78/3.75 | GROUND_INST: instantiating (3) with all_59_8, all_59_7, simplifying with (15), % 22.78/3.75 | (16), (17), (18), (23), (32) gives: % 22.78/3.75 | (36) v1_funct_1(all_59_7) % 22.78/3.75 | % 22.78/3.75 | GROUND_INST: instantiating (2) with all_59_8, all_59_7, simplifying with (15), % 22.78/3.75 | (16), (17), (18), (23), (32) gives: % 22.78/3.75 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_59_8) = v0 & % 22.78/3.75 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_59_8) = v1 & $i(v2) & $i(v1) % 22.78/3.75 | & $i(v0) & m2_relset_1(all_59_7, v0, v2) & v1_funct_2(all_59_7, v0, % 22.78/3.75 | v2)) % 22.78/3.75 | % 22.78/3.75 | GROUND_INST: instantiating (1) with all_59_8, all_59_7, simplifying with (15), % 22.78/3.75 | (16), (17), (18), (23), (32) gives: % 22.78/3.76 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_59_8) = v0 & % 22.78/3.76 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_59_8) = v1 & $i(v2) & $i(v1) % 22.78/3.76 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (k1_funct_1(all_59_7, v3) % 22.78/3.76 | = v4) | ~ $i(v3) | ~ $i(all_59_7) | ~ m2_relset_1(all_59_7, % 22.78/3.76 | v0, v2) | ~ v1_funct_2(all_59_7, v0, v2) | ~ % 22.78/3.76 | v1_funct_1(all_59_7) | ~ m1_group_2(v3, all_59_8) | ~ % 22.78/3.76 | v1_group_1(v3) | (u1_struct_0(v3) = v4 & $i(v4))) & ! [v3: $i] : % 22.78/3.76 | ! [v4: $i] : ( ~ (u1_struct_0(v3) = v4) | ~ $i(v3) | ~ % 22.78/3.76 | $i(all_59_7) | ~ m2_relset_1(all_59_7, v0, v2) | ~ % 22.78/3.76 | v1_funct_2(all_59_7, v0, v2) | ~ v1_funct_1(all_59_7) | ~ % 22.78/3.76 | m1_group_2(v3, all_59_8) | ~ v1_group_1(v3) | % 22.78/3.76 | (k1_funct_1(all_59_7, v3) = v4 & $i(v4))) & ! [v3: any] : (v3 = % 22.78/3.76 | all_59_7 | ~ $i(v3) | ~ m2_relset_1(v3, v0, v2) | ~ % 22.78/3.76 | v1_funct_2(v3, v0, v2) | ~ v1_funct_1(v3) | ? [v4: $i] : ? [v5: % 22.78/3.76 | $i] : ? [v6: $i] : ( ~ (v6 = v5) & k1_funct_1(v3, v4) = v5 & % 22.78/3.76 | u1_struct_0(v4) = v6 & $i(v6) & $i(v5) & $i(v4) & m1_group_2(v4, % 22.78/3.76 | all_59_8) & v1_group_1(v4)))) % 22.78/3.76 | % 22.78/3.76 | DELTA: instantiating (35) with fresh symbols all_77_0, all_77_1 gives: % 22.78/3.76 | (39) k9_group_2(all_59_8, all_59_6, all_59_4) = all_77_1 & % 22.78/3.76 | k3_xboole_0(all_59_5, all_59_1) = all_77_0 & u1_struct_0(all_77_1) = % 22.78/3.76 | all_77_0 & $i(all_77_0) & $i(all_77_1) % 22.78/3.76 | % 22.78/3.76 | ALPHA: (39) implies: % 22.78/3.76 | (40) $i(all_77_1) % 22.78/3.76 | (41) u1_struct_0(all_77_1) = all_77_0 % 22.78/3.76 | (42) k3_xboole_0(all_59_5, all_59_1) = all_77_0 % 22.78/3.76 | (43) k9_group_2(all_59_8, all_59_6, all_59_4) = all_77_1 % 22.78/3.76 | % 22.78/3.76 | DELTA: instantiating (37) with fresh symbols all_83_0, all_83_1, all_83_2 % 22.78/3.76 | gives: % 22.78/3.76 | (44) k1_group_3(all_59_8) = all_83_2 & k1_zfmisc_1(all_83_1) = all_83_0 & % 22.78/3.76 | u1_struct_0(all_59_8) = all_83_1 & $i(all_83_0) & $i(all_83_1) & % 22.78/3.76 | $i(all_83_2) & m2_relset_1(all_59_7, all_83_2, all_83_0) & % 22.78/3.76 | v1_funct_2(all_59_7, all_83_2, all_83_0) % 22.78/3.76 | % 22.78/3.76 | ALPHA: (44) implies: % 22.78/3.76 | (45) v1_funct_2(all_59_7, all_83_2, all_83_0) % 22.78/3.76 | (46) m2_relset_1(all_59_7, all_83_2, all_83_0) % 22.78/3.76 | (47) u1_struct_0(all_59_8) = all_83_1 % 22.78/3.76 | (48) k1_zfmisc_1(all_83_1) = all_83_0 % 22.78/3.76 | (49) k1_group_3(all_59_8) = all_83_2 % 22.78/3.76 | % 22.78/3.76 | DELTA: instantiating (38) with fresh symbols all_85_0, all_85_1, all_85_2 % 22.78/3.76 | gives: % 22.78/3.76 | (50) k1_group_3(all_59_8) = all_85_2 & k1_zfmisc_1(all_85_1) = all_85_0 & % 22.78/3.76 | u1_struct_0(all_59_8) = all_85_1 & $i(all_85_0) & $i(all_85_1) & % 22.78/3.76 | $i(all_85_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_funct_1(all_59_7, % 22.78/3.76 | v0) = v1) | ~ $i(v0) | ~ $i(all_59_7) | ~ % 22.78/3.76 | m2_relset_1(all_59_7, all_85_2, all_85_0) | ~ v1_funct_2(all_59_7, % 22.78/3.76 | all_85_2, all_85_0) | ~ v1_funct_1(all_59_7) | ~ m1_group_2(v0, % 22.78/3.76 | all_59_8) | ~ v1_group_1(v0) | (u1_struct_0(v0) = v1 & $i(v1))) & % 22.78/3.76 | ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | % 22.78/3.76 | ~ $i(all_59_7) | ~ m2_relset_1(all_59_7, all_85_2, all_85_0) | ~ % 22.78/3.76 | v1_funct_2(all_59_7, all_85_2, all_85_0) | ~ v1_funct_1(all_59_7) | % 22.78/3.76 | ~ m1_group_2(v0, all_59_8) | ~ v1_group_1(v0) | % 22.78/3.76 | (k1_funct_1(all_59_7, v0) = v1 & $i(v1))) & ! [v0: any] : (v0 = % 22.78/3.76 | all_59_7 | ~ $i(v0) | ~ m2_relset_1(v0, all_85_2, all_85_0) | ~ % 22.78/3.76 | v1_funct_2(v0, all_85_2, all_85_0) | ~ v1_funct_1(v0) | ? [v1: $i] % 22.78/3.76 | : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & k1_funct_1(v0, v1) = % 22.78/3.76 | v2 & u1_struct_0(v1) = v3 & $i(v3) & $i(v2) & $i(v1) & % 22.78/3.76 | m1_group_2(v1, all_59_8) & v1_group_1(v1))) % 22.78/3.76 | % 22.78/3.76 | ALPHA: (50) implies: % 22.78/3.76 | (51) u1_struct_0(all_59_8) = all_85_1 % 22.78/3.76 | (52) k1_zfmisc_1(all_85_1) = all_85_0 % 22.78/3.76 | (53) k1_group_3(all_59_8) = all_85_2 % 22.78/3.76 | (54) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | % 22.78/3.76 | ~ $i(all_59_7) | ~ m2_relset_1(all_59_7, all_85_2, all_85_0) | ~ % 22.78/3.76 | v1_funct_2(all_59_7, all_85_2, all_85_0) | ~ v1_funct_1(all_59_7) | % 22.78/3.76 | ~ m1_group_2(v0, all_59_8) | ~ v1_group_1(v0) | % 22.78/3.76 | (k1_funct_1(all_59_7, v0) = v1 & $i(v1))) % 22.78/3.76 | % 22.78/3.76 | GROUND_INST: instantiating (7) with all_83_1, all_85_1, all_59_8, simplifying % 22.78/3.76 | with (47), (51) gives: % 22.78/3.76 | (55) all_85_1 = all_83_1 % 22.78/3.76 | % 22.78/3.76 | GROUND_INST: instantiating (8) with all_83_0, all_85_0, all_83_1, simplifying % 22.78/3.76 | with (48) gives: % 22.78/3.76 | (56) all_85_0 = all_83_0 | ~ (k1_zfmisc_1(all_83_1) = all_85_0) % 22.78/3.76 | % 22.78/3.76 | GROUND_INST: instantiating (10) with all_59_0, all_77_0, all_59_1, all_59_5, % 22.78/3.76 | simplifying with (27), (42) gives: % 22.78/3.76 | (57) all_77_0 = all_59_0 % 22.78/3.76 | % 22.78/3.76 | GROUND_INST: instantiating (12) with all_59_3, all_77_1, all_59_4, all_59_6, % 22.78/3.76 | all_59_8, simplifying with (28), (43) gives: % 22.78/3.76 | (58) all_77_1 = all_59_3 % 22.78/3.76 | % 22.78/3.76 | GROUND_INST: instantiating (9) with all_83_2, all_85_2, all_59_8, simplifying % 22.78/3.76 | with (49), (53) gives: % 22.78/3.76 | (59) all_85_2 = all_83_2 % 22.78/3.76 | % 22.78/3.76 | REDUCE: (52), (55) imply: % 22.78/3.76 | (60) k1_zfmisc_1(all_83_1) = all_85_0 % 22.78/3.76 | % 22.78/3.76 | REDUCE: (41), (57), (58) imply: % 22.78/3.76 | (61) u1_struct_0(all_59_3) = all_59_0 % 22.78/3.76 | % 22.78/3.76 | REDUCE: (40), (58) imply: % 22.78/3.76 | (62) $i(all_59_3) % 22.78/3.76 | % 22.78/3.76 | BETA: splitting (56) gives: % 22.78/3.77 | % 22.78/3.77 | Case 1: % 22.78/3.77 | | % 22.78/3.77 | | (63) ~ (k1_zfmisc_1(all_83_1) = all_85_0) % 22.78/3.77 | | % 22.78/3.77 | | PRED_UNIFY: (60), (63) imply: % 22.78/3.77 | | (64) $false % 22.78/3.77 | | % 22.78/3.77 | | CLOSE: (64) is inconsistent. % 22.78/3.77 | | % 22.78/3.77 | Case 2: % 22.78/3.77 | | % 22.78/3.77 | | (65) all_85_0 = all_83_0 % 22.78/3.77 | | % 22.78/3.77 | | GROUND_INST: instantiating (54) with all_59_3, all_59_0, simplifying with % 22.78/3.77 | | (24), (33), (34), (36), (61), (62) gives: % 22.78/3.77 | | (66) ~ m2_relset_1(all_59_7, all_85_2, all_85_0) | ~ % 22.78/3.77 | | v1_funct_2(all_59_7, all_85_2, all_85_0) | (k1_funct_1(all_59_7, % 22.78/3.77 | | all_59_3) = all_59_0 & $i(all_59_0)) % 22.78/3.77 | | % 22.78/3.77 | | BETA: splitting (66) gives: % 22.78/3.77 | | % 22.78/3.77 | | Case 1: % 22.78/3.77 | | | % 22.78/3.77 | | | (67) ~ m2_relset_1(all_59_7, all_85_2, all_85_0) % 22.78/3.77 | | | % 22.78/3.77 | | | REDUCE: (59), (65), (67) imply: % 22.78/3.77 | | | (68) ~ m2_relset_1(all_59_7, all_83_2, all_83_0) % 22.78/3.77 | | | % 22.78/3.77 | | | PRED_UNIFY: (46), (68) imply: % 22.78/3.77 | | | (69) $false % 22.78/3.77 | | | % 22.78/3.77 | | | CLOSE: (69) is inconsistent. % 22.78/3.77 | | | % 22.78/3.77 | | Case 2: % 22.78/3.77 | | | % 22.78/3.77 | | | (70) ~ v1_funct_2(all_59_7, all_85_2, all_85_0) | % 22.78/3.77 | | | (k1_funct_1(all_59_7, all_59_3) = all_59_0 & $i(all_59_0)) % 22.78/3.77 | | | % 22.78/3.77 | | | BETA: splitting (70) gives: % 22.78/3.77 | | | % 22.78/3.77 | | | Case 1: % 22.78/3.77 | | | | % 22.78/3.77 | | | | (71) ~ v1_funct_2(all_59_7, all_85_2, all_85_0) % 22.78/3.77 | | | | % 22.78/3.77 | | | | REDUCE: (59), (65), (71) imply: % 22.78/3.77 | | | | (72) ~ v1_funct_2(all_59_7, all_83_2, all_83_0) % 22.78/3.77 | | | | % 22.78/3.77 | | | | PRED_UNIFY: (45), (72) imply: % 22.78/3.77 | | | | (73) $false % 22.78/3.77 | | | | % 22.78/3.77 | | | | CLOSE: (73) is inconsistent. % 22.78/3.77 | | | | % 22.78/3.77 | | | Case 2: % 22.78/3.77 | | | | % 22.90/3.77 | | | | (74) k1_funct_1(all_59_7, all_59_3) = all_59_0 & $i(all_59_0) % 22.90/3.77 | | | | % 22.90/3.77 | | | | ALPHA: (74) implies: % 22.90/3.77 | | | | (75) k1_funct_1(all_59_7, all_59_3) = all_59_0 % 22.90/3.77 | | | | % 22.90/3.77 | | | | GROUND_INST: instantiating (11) with all_59_2, all_59_0, all_59_3, % 22.90/3.77 | | | | all_59_7, simplifying with (31), (75) gives: % 22.90/3.77 | | | | (76) all_59_0 = all_59_2 % 22.90/3.77 | | | | % 22.90/3.77 | | | | REDUCE: (14), (76) imply: % 22.90/3.77 | | | | (77) $false % 22.90/3.77 | | | | % 22.90/3.77 | | | | CLOSE: (77) is inconsistent. % 22.90/3.77 | | | | % 22.90/3.77 | | | End of split % 22.90/3.77 | | | % 22.90/3.77 | | End of split % 22.90/3.77 | | % 22.90/3.77 | End of split % 22.90/3.77 | % 22.90/3.77 End of proof % 22.90/3.77 % SZS output end Proof for theBenchmark % 22.90/3.77 % 22.90/3.77 3172ms %------------------------------------------------------------------------------