%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GRP642+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 : n001.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 01:12:47 EDT 2023 % Result : Theorem 13.50s 2.58s % Output : Proof 19.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP642+1 : TPTP v8.1.2. Released v3.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n001.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 : Mon Aug 28 22:36:51 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.95/1.14 Prover 1: Preprocessing ... % 2.95/1.14 Prover 4: Preprocessing ... % 3.61/1.18 Prover 5: Preprocessing ... % 3.61/1.18 Prover 6: Preprocessing ... % 3.61/1.18 Prover 0: Preprocessing ... % 3.61/1.18 Prover 2: Preprocessing ... % 3.61/1.18 Prover 3: Preprocessing ... % 7.16/1.71 Prover 1: Warning: ignoring some quantifiers % 7.76/1.76 Prover 5: Proving ... % 7.76/1.80 Prover 1: Constructing countermodel ... % 8.35/1.83 Prover 3: Warning: ignoring some quantifiers % 8.35/1.85 Prover 2: Proving ... % 8.35/1.86 Prover 3: Constructing countermodel ... % 8.35/1.88 Prover 6: Proving ... % 13.50/2.58 Prover 5: proved (1936ms) % 13.50/2.58 % 13.50/2.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.50/2.58 % 13.50/2.58 Prover 2: stopped % 13.50/2.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.50/2.58 Prover 6: stopped % 13.50/2.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.50/2.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.50/2.58 Prover 3: stopped % 13.50/2.59 Prover 4: Warning: ignoring some quantifiers % 13.50/2.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.52/2.68 Prover 10: Preprocessing ... % 14.52/2.68 Prover 7: Preprocessing ... % 14.52/2.68 Prover 8: Preprocessing ... % 14.52/2.69 Prover 4: Constructing countermodel ... % 14.52/2.71 Prover 11: Preprocessing ... % 14.52/2.73 Prover 0: Proving ... % 14.52/2.73 Prover 0: stopped % 14.52/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.25/2.78 Prover 7: Warning: ignoring some quantifiers % 15.44/2.79 Prover 10: Warning: ignoring some quantifiers % 15.44/2.79 Prover 7: Constructing countermodel ... % 15.44/2.80 Prover 13: Preprocessing ... % 15.44/2.82 Prover 10: Constructing countermodel ... % 15.44/2.84 Prover 8: Warning: ignoring some quantifiers % 15.44/2.88 Prover 13: Warning: ignoring some quantifiers % 15.44/2.88 Prover 8: Constructing countermodel ... % 15.44/2.90 Prover 13: Constructing countermodel ... % 18.01/3.21 Prover 7: Found proof (size 42) % 18.01/3.21 Prover 7: proved (631ms) % 18.01/3.21 Prover 10: stopped % 18.01/3.21 Prover 13: stopped % 18.01/3.21 Prover 4: stopped % 18.01/3.21 Prover 8: stopped % 18.01/3.21 Prover 1: stopped % 19.00/3.35 Prover 11: Warning: ignoring some quantifiers % 19.00/3.37 Prover 11: Constructing countermodel ... % 19.12/3.38 Prover 11: stopped % 19.12/3.38 % 19.12/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.12/3.38 % 19.12/3.39 % SZS output start Proof for theBenchmark % 19.12/3.39 Assumptions after simplification: % 19.12/3.39 --------------------------------- % 19.12/3.39 % 19.12/3.39 (d1_latsubgr) % 19.37/3.43 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 19.37/3.43 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | % 19.37/3.43 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0) = v2 & % 19.37/3.43 k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & % 19.37/3.43 ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~ % 19.37/3.43 $i(v1) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 19.37/3.43 v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 19.37/3.43 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 19.37/3.43 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ m2_relset_1(v1, v2, % 19.37/3.43 v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~ % 19.37/3.43 m1_group_2(v5, v0) | ~ v1_group_1(v5) | (k1_funct_1(v1, v5) = v6 & % 19.37/3.43 $i(v6))) & ! [v5: $i] : (v5 = v1 | ~ $i(v5) | ~ m2_relset_1(v5, v2, % 19.37/3.43 v4) | ~ v1_funct_2(v5, v2, v4) | ~ v1_funct_1(v5) | ? [v6: $i] : ? % 19.37/3.43 [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & % 19.37/3.43 u1_struct_0(v6) = v8 & $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) & % 19.37/3.43 v1_group_1(v6))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_group_3(v0) = % 19.37/3.43 v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ % 19.37/3.43 v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.37/3.43 (k1_latsubgr(v0) = v4 & k1_zfmisc_1(v2) = v3 & u1_struct_0(v0) = v2 & $i(v4) % 19.37/3.43 & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) = % 19.37/3.43 v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1, % 19.37/3.43 v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 19.37/3.43 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ % 19.37/3.43 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~ % 19.37/3.43 v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ % 19.37/3.43 v1_group_1(v5) | (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 % 19.37/3.43 = v4 | ~ $i(v5) | ~ m2_relset_1(v5, v1, v3) | ~ v1_funct_2(v5, v1, % 19.37/3.43 v3) | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( % 19.37/3.43 ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8) % 19.37/3.43 & $i(v7) & $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6))))) & ! [v0: % 19.37/3.43 $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 19.37/3.43 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | % 19.37/3.43 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_latsubgr(v0) = v4 & % 19.37/3.43 k1_group_3(v0) = v2 & k1_zfmisc_1(v1) = v3 & $i(v4) & $i(v3) & $i(v2) & ! % 19.37/3.43 [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ $i(v5) | ~ % 19.37/3.43 m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4) % 19.37/3.43 | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | (u1_struct_0(v5) = v6 & % 19.37/3.43 $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ (u1_struct_0(v5) = v6) | ~ % 19.37/3.43 $i(v5) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ % 19.37/3.43 v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 19.37/3.43 (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v4 | ~ $i(v5) % 19.37/3.43 | ~ m2_relset_1(v5, v2, v3) | ~ v1_funct_2(v5, v2, v3) | ~ % 19.37/3.43 v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) % 19.37/3.43 & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8) & $i(v7) & % 19.37/3.43 $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6))))) % 19.37/3.43 % 19.37/3.43 (dt_k1_latsubgr) % 19.37/3.43 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 19.37/3.43 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_funct_1(v1) | % 19.37/3.43 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | % 19.37/3.43 ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 19.37/3.43 v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0) % 19.37/3.43 = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & % 19.37/3.43 $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, v2, v4))) & ! [v0: $i] % 19.37/3.43 : ! [v1: $i] : ( ~ (k1_group_3(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ % 19.37/3.43 v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: % 19.37/3.43 $i] : ? [v4: $i] : (k1_latsubgr(v0) = v2 & k1_zfmisc_1(v3) = v4 & % 19.37/3.43 u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v1, v4) % 19.37/3.43 & v1_funct_2(v2, v1, v4) & v1_funct_1(v2))) & ! [v0: $i] : ! [v1: $i] : % 19.37/3.43 ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) % 19.37/3.43 | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 19.37/3.43 $i] : (k1_latsubgr(v0) = v2 & k1_group_3(v0) = v3 & k1_zfmisc_1(v1) = v4 & % 19.37/3.43 $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v3, v4) & v1_funct_2(v2, v3, % 19.37/3.43 v4) & v1_funct_1(v2))) % 19.37/3.43 % 19.37/3.43 (dt_l1_group_1) % 19.37/3.44 ! [v0: $i] : ( ~ $i(v0) | ~ l1_group_1(v0) | l1_struct_0(v0)) % 19.37/3.44 % 19.37/3.44 (dt_m1_group_2) % 19.37/3.44 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) | % 19.37/3.44 ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0)) % 19.37/3.44 & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) | % 19.37/3.44 ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0)) & % 19.37/3.44 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) | ~ % 19.37/3.44 l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0)) % 19.37/3.44 % 19.37/3.44 (fc1_struct_0) % 19.37/3.44 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 19.37/3.44 l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0)) % 19.37/3.44 % 19.37/3.44 (rc1_xboole_0) % 19.37/3.44 ? [v0: $i] : ($i(v0) & v1_xboole_0(v0)) % 19.37/3.44 % 19.37/3.44 (t20_latsubgr) % 19.37/3.44 $i(k1_xboole_0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_latsubgr(v0) = % 19.37/3.44 v1 & k1_funct_1(v1, v2) = k1_xboole_0 & $i(v2) & $i(v1) & $i(v0) & % 19.37/3.44 m1_group_2(v2, v0) & v1_group_1(v2) & l1_group_1(v0) & v4_group_1(v0) & % 19.37/3.44 v3_group_1(v0) & ~ v3_struct_0(v0)) % 19.37/3.44 % 19.37/3.44 (t6_boole) % 19.37/3.44 $i(k1_xboole_0) & ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~ % 19.37/3.44 v1_xboole_0(v0)) % 19.37/3.44 % 19.37/3.44 (function-axioms) % 19.37/3.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.37/3.44 (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: $i] : ! % 19.37/3.44 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = % 19.37/3.44 v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.37/3.44 $i] : ! [v3: $i] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~ % 19.37/3.44 (g1_group_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 19.37/3.44 v0 | ~ (k1_latsubgr(v2) = v1) | ~ (k1_latsubgr(v2) = v0)) & ! [v0: $i] : % 19.37/3.44 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_group_3(v2) = v1) | ~ % 19.37/3.44 (k1_group_3(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 19.37/3.44 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! % 19.37/3.44 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_group_1(v2) = v1) | ~ % 19.37/3.44 (u1_group_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 19.37/3.44 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 19.37/3.44 % 19.37/3.44 Further assumptions not needed in the proof: % 19.37/3.44 -------------------------------------------- % 19.37/3.44 abstractness_v1_group_1, antisymmetry_r2_hidden, cc1_funct_2, cc1_relset_1, % 19.37/3.44 cc5_funct_2, cc6_funct_2, dt_g1_group_1, dt_k1_funct_1, dt_k1_group_3, % 19.37/3.44 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_l1_struct_0, dt_m1_relset_1, % 19.37/3.44 dt_m1_subset_1, dt_m2_relset_1, dt_u1_group_1, dt_u1_struct_0, % 19.37/3.44 existence_l1_group_1, existence_l1_struct_0, existence_m1_group_2, % 19.37/3.44 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1, % 19.37/3.44 fc1_group_3, fc1_subset_1, fc1_xboole_0, fc4_subset_1, free_g1_group_1, % 19.37/3.44 rc1_funct_2, rc1_subset_1, rc2_partfun1, rc2_subset_1, rc2_xboole_0, % 19.37/3.44 rc3_struct_0, rc5_struct_0, redefinition_m2_relset_1, reflexivity_r1_tarski, % 19.37/3.44 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t7_boole, t8_boole % 19.37/3.44 % 19.37/3.44 Those formulas are unsatisfiable: % 19.37/3.44 --------------------------------- % 19.37/3.44 % 19.37/3.44 Begin of proof % 19.37/3.44 | % 19.37/3.44 | ALPHA: (d1_latsubgr) implies: % 19.37/3.45 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 19.37/3.45 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 19.37/3.45 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.37/3.45 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & % 19.37/3.45 | $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ % 19.37/3.45 | (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ % 19.37/3.45 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 19.37/3.45 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 19.37/3.45 | (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( % 19.37/3.45 | ~ (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ % 19.37/3.45 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~ % 19.37/3.45 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | % 19.37/3.45 | (k1_funct_1(v1, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v1 | ~ % 19.37/3.45 | $i(v5) | ~ m2_relset_1(v5, v2, v4) | ~ v1_funct_2(v5, v2, v4) | % 19.37/3.45 | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ % 19.37/3.45 | (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & % 19.37/3.45 | $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) & % 19.37/3.45 | v1_group_1(v6))))) % 19.37/3.45 | % 19.37/3.45 | ALPHA: (dt_k1_latsubgr) implies: % 19.37/3.45 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 19.37/3.45 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 19.37/3.45 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.37/3.45 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & % 19.37/3.45 | $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, % 19.37/3.45 | v2, v4))) % 19.37/3.45 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~ % 19.37/3.45 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | % 19.37/3.45 | v1_funct_1(v1) | v3_struct_0(v0)) % 19.37/3.45 | % 19.37/3.45 | ALPHA: (dt_m1_group_2) implies: % 19.37/3.45 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, % 19.37/3.45 | v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | % 19.37/3.45 | v3_struct_0(v0)) % 19.37/3.45 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, % 19.37/3.45 | v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | % 19.37/3.45 | v3_struct_0(v0)) % 19.37/3.45 | % 19.37/3.45 | ALPHA: (t6_boole) implies: % 19.37/3.45 | (6) ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~ v1_xboole_0(v0)) % 19.37/3.45 | % 19.37/3.45 | ALPHA: (t20_latsubgr) implies: % 19.37/3.45 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_latsubgr(v0) = v1 & % 19.37/3.45 | k1_funct_1(v1, v2) = k1_xboole_0 & $i(v2) & $i(v1) & $i(v0) & % 19.37/3.45 | m1_group_2(v2, v0) & v1_group_1(v2) & l1_group_1(v0) & v4_group_1(v0) % 19.37/3.45 | & v3_group_1(v0) & ~ v3_struct_0(v0)) % 19.37/3.45 | % 19.37/3.45 | ALPHA: (function-axioms) implies: % 19.37/3.45 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.37/3.45 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 19.37/3.46 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.37/3.46 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 19.37/3.46 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.37/3.46 | (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0)) % 19.37/3.46 | % 19.37/3.46 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_38_0 gives: % 19.37/3.46 | (11) $i(all_38_0) & v1_xboole_0(all_38_0) % 19.37/3.46 | % 19.37/3.46 | ALPHA: (11) implies: % 19.37/3.46 | (12) v1_xboole_0(all_38_0) % 19.37/3.46 | (13) $i(all_38_0) % 19.37/3.46 | % 19.37/3.46 | DELTA: instantiating (7) with fresh symbols all_51_0, all_51_1, all_51_2 % 19.37/3.46 | gives: % 19.37/3.46 | (14) k1_latsubgr(all_51_2) = all_51_1 & k1_funct_1(all_51_1, all_51_0) = % 19.37/3.46 | k1_xboole_0 & $i(all_51_0) & $i(all_51_1) & $i(all_51_2) & % 19.37/3.46 | m1_group_2(all_51_0, all_51_2) & v1_group_1(all_51_0) & % 19.37/3.46 | l1_group_1(all_51_2) & v4_group_1(all_51_2) & v3_group_1(all_51_2) & % 19.37/3.46 | ~ v3_struct_0(all_51_2) % 19.37/3.46 | % 19.37/3.46 | ALPHA: (14) implies: % 19.37/3.46 | (15) ~ v3_struct_0(all_51_2) % 19.37/3.46 | (16) v3_group_1(all_51_2) % 19.37/3.46 | (17) v4_group_1(all_51_2) % 19.37/3.46 | (18) l1_group_1(all_51_2) % 19.37/3.46 | (19) v1_group_1(all_51_0) % 19.37/3.46 | (20) m1_group_2(all_51_0, all_51_2) % 19.37/3.46 | (21) $i(all_51_2) % 19.37/3.46 | (22) $i(all_51_1) % 19.37/3.46 | (23) $i(all_51_0) % 19.37/3.46 | (24) k1_funct_1(all_51_1, all_51_0) = k1_xboole_0 % 19.37/3.46 | (25) k1_latsubgr(all_51_2) = all_51_1 % 19.37/3.46 | % 19.37/3.46 | GROUND_INST: instantiating (4) with all_51_2, all_51_0, simplifying with (15), % 19.37/3.46 | (16), (18), (20), (21), (23) gives: % 19.37/3.46 | (26) l1_group_1(all_51_0) % 19.37/3.46 | % 19.37/3.46 | GROUND_INST: instantiating (6) with all_38_0, simplifying with (12), (13) % 19.37/3.46 | gives: % 19.37/3.46 | (27) all_38_0 = k1_xboole_0 % 19.37/3.46 | % 19.37/3.46 | GROUND_INST: instantiating (3) with all_51_2, all_51_1, simplifying with (15), % 19.37/3.46 | (16), (17), (18), (21), (25) gives: % 19.37/3.46 | (28) v1_funct_1(all_51_1) % 19.37/3.46 | % 19.37/3.46 | GROUND_INST: instantiating (2) with all_51_2, all_51_1, simplifying with (15), % 19.37/3.46 | (16), (17), (18), (21), (25) gives: % 19.37/3.46 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_51_2) = v0 & % 19.37/3.46 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_51_2) = v1 & $i(v2) & $i(v1) % 19.37/3.46 | & $i(v0) & m2_relset_1(all_51_1, v0, v2) & v1_funct_2(all_51_1, v0, % 19.37/3.46 | v2)) % 19.37/3.46 | % 19.37/3.46 | GROUND_INST: instantiating (1) with all_51_2, all_51_1, simplifying with (15), % 19.37/3.46 | (16), (17), (18), (21), (25) gives: % 19.37/3.47 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_51_2) = v0 & % 19.37/3.47 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_51_2) = v1 & $i(v2) & $i(v1) % 19.37/3.47 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (k1_funct_1(all_51_1, v3) % 19.37/3.47 | = v4) | ~ $i(v3) | ~ $i(all_51_1) | ~ m2_relset_1(all_51_1, % 19.37/3.47 | v0, v2) | ~ v1_funct_2(all_51_1, v0, v2) | ~ % 19.37/3.47 | v1_funct_1(all_51_1) | ~ m1_group_2(v3, all_51_2) | ~ % 19.37/3.47 | v1_group_1(v3) | (u1_struct_0(v3) = v4 & $i(v4))) & ! [v3: $i] : % 19.37/3.47 | ! [v4: $i] : ( ~ (u1_struct_0(v3) = v4) | ~ $i(v3) | ~ % 19.37/3.47 | $i(all_51_1) | ~ m2_relset_1(all_51_1, v0, v2) | ~ % 19.37/3.47 | v1_funct_2(all_51_1, v0, v2) | ~ v1_funct_1(all_51_1) | ~ % 19.37/3.47 | m1_group_2(v3, all_51_2) | ~ v1_group_1(v3) | % 19.37/3.47 | (k1_funct_1(all_51_1, v3) = v4 & $i(v4))) & ! [v3: any] : (v3 = % 19.37/3.47 | all_51_1 | ~ $i(v3) | ~ m2_relset_1(v3, v0, v2) | ~ % 19.37/3.47 | v1_funct_2(v3, v0, v2) | ~ v1_funct_1(v3) | ? [v4: $i] : ? [v5: % 19.37/3.47 | $i] : ? [v6: $i] : ( ~ (v6 = v5) & k1_funct_1(v3, v4) = v5 & % 19.37/3.47 | u1_struct_0(v4) = v6 & $i(v6) & $i(v5) & $i(v4) & m1_group_2(v4, % 19.37/3.47 | all_51_2) & v1_group_1(v4)))) % 19.37/3.47 | % 19.37/3.47 | DELTA: instantiating (29) with fresh symbols all_65_0, all_65_1, all_65_2 % 19.37/3.47 | gives: % 19.37/3.47 | (31) k1_group_3(all_51_2) = all_65_2 & k1_zfmisc_1(all_65_1) = all_65_0 & % 19.37/3.47 | u1_struct_0(all_51_2) = all_65_1 & $i(all_65_0) & $i(all_65_1) & % 19.37/3.47 | $i(all_65_2) & m2_relset_1(all_51_1, all_65_2, all_65_0) & % 19.37/3.47 | v1_funct_2(all_51_1, all_65_2, all_65_0) % 19.37/3.47 | % 19.37/3.47 | ALPHA: (31) implies: % 19.37/3.47 | (32) v1_funct_2(all_51_1, all_65_2, all_65_0) % 19.37/3.47 | (33) m2_relset_1(all_51_1, all_65_2, all_65_0) % 19.37/3.47 | (34) u1_struct_0(all_51_2) = all_65_1 % 19.37/3.47 | (35) k1_zfmisc_1(all_65_1) = all_65_0 % 19.37/3.47 | (36) k1_group_3(all_51_2) = all_65_2 % 19.37/3.47 | % 19.37/3.47 | DELTA: instantiating (30) with fresh symbols all_67_0, all_67_1, all_67_2 % 19.37/3.47 | gives: % 19.37/3.47 | (37) k1_group_3(all_51_2) = all_67_2 & k1_zfmisc_1(all_67_1) = all_67_0 & % 19.37/3.47 | u1_struct_0(all_51_2) = all_67_1 & $i(all_67_0) & $i(all_67_1) & % 19.37/3.47 | $i(all_67_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_funct_1(all_51_1, % 19.37/3.47 | v0) = v1) | ~ $i(v0) | ~ $i(all_51_1) | ~ % 19.37/3.47 | m2_relset_1(all_51_1, all_67_2, all_67_0) | ~ v1_funct_2(all_51_1, % 19.37/3.47 | all_67_2, all_67_0) | ~ v1_funct_1(all_51_1) | ~ m1_group_2(v0, % 19.37/3.47 | all_51_2) | ~ v1_group_1(v0) | (u1_struct_0(v0) = v1 & $i(v1))) & % 19.37/3.47 | ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | % 19.37/3.47 | ~ $i(all_51_1) | ~ m2_relset_1(all_51_1, all_67_2, all_67_0) | ~ % 19.37/3.47 | v1_funct_2(all_51_1, all_67_2, all_67_0) | ~ v1_funct_1(all_51_1) | % 19.37/3.47 | ~ m1_group_2(v0, all_51_2) | ~ v1_group_1(v0) | % 19.37/3.47 | (k1_funct_1(all_51_1, v0) = v1 & $i(v1))) & ! [v0: any] : (v0 = % 19.37/3.47 | all_51_1 | ~ $i(v0) | ~ m2_relset_1(v0, all_67_2, all_67_0) | ~ % 19.37/3.47 | v1_funct_2(v0, all_67_2, all_67_0) | ~ v1_funct_1(v0) | ? [v1: $i] % 19.37/3.47 | : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & k1_funct_1(v0, v1) = % 19.37/3.47 | v2 & u1_struct_0(v1) = v3 & $i(v3) & $i(v2) & $i(v1) & % 19.37/3.47 | m1_group_2(v1, all_51_2) & v1_group_1(v1))) % 19.37/3.47 | % 19.37/3.47 | ALPHA: (37) implies: % 19.37/3.47 | (38) u1_struct_0(all_51_2) = all_67_1 % 19.37/3.47 | (39) k1_zfmisc_1(all_67_1) = all_67_0 % 19.37/3.47 | (40) k1_group_3(all_51_2) = all_67_2 % 19.37/3.47 | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_funct_1(all_51_1, v0) = v1) | ~ % 19.37/3.48 | $i(v0) | ~ $i(all_51_1) | ~ m2_relset_1(all_51_1, all_67_2, % 19.37/3.48 | all_67_0) | ~ v1_funct_2(all_51_1, all_67_2, all_67_0) | ~ % 19.37/3.48 | v1_funct_1(all_51_1) | ~ m1_group_2(v0, all_51_2) | ~ % 19.37/3.48 | v1_group_1(v0) | (u1_struct_0(v0) = v1 & $i(v1))) % 19.37/3.48 | % 19.37/3.48 | REDUCE: (12), (27) imply: % 19.37/3.48 | (42) v1_xboole_0(k1_xboole_0) % 19.37/3.48 | % 19.37/3.48 | GROUND_INST: instantiating (8) with all_65_1, all_67_1, all_51_2, simplifying % 19.37/3.48 | with (34), (38) gives: % 19.37/3.48 | (43) all_67_1 = all_65_1 % 19.37/3.48 | % 19.37/3.48 | GROUND_INST: instantiating (9) with all_65_0, all_67_0, all_65_1, simplifying % 19.37/3.48 | with (35) gives: % 19.37/3.48 | (44) all_67_0 = all_65_0 | ~ (k1_zfmisc_1(all_65_1) = all_67_0) % 19.37/3.48 | % 19.37/3.48 | GROUND_INST: instantiating (10) with all_65_2, all_67_2, all_51_2, simplifying % 19.37/3.48 | with (36), (40) gives: % 19.37/3.48 | (45) all_67_2 = all_65_2 % 19.37/3.48 | % 19.37/3.48 | REDUCE: (39), (43) imply: % 19.37/3.48 | (46) k1_zfmisc_1(all_65_1) = all_67_0 % 19.37/3.48 | % 19.37/3.48 | BETA: splitting (44) gives: % 19.37/3.48 | % 19.37/3.48 | Case 1: % 19.37/3.48 | | % 19.37/3.48 | | (47) ~ (k1_zfmisc_1(all_65_1) = all_67_0) % 19.37/3.48 | | % 19.37/3.48 | | PRED_UNIFY: (46), (47) imply: % 19.37/3.48 | | (48) $false % 19.37/3.48 | | % 19.37/3.48 | | CLOSE: (48) is inconsistent. % 19.37/3.48 | | % 19.37/3.48 | Case 2: % 19.37/3.48 | | % 19.37/3.48 | | (49) all_67_0 = all_65_0 % 19.37/3.48 | | % 19.37/3.48 | | GROUND_INST: instantiating (dt_l1_group_1) with all_51_0, simplifying with % 19.37/3.48 | | (23), (26) gives: % 19.37/3.48 | | (50) l1_struct_0(all_51_0) % 19.37/3.48 | | % 19.37/3.48 | | GROUND_INST: instantiating (41) with all_51_0, k1_xboole_0, simplifying with % 19.37/3.48 | | (19), (20), (22), (23), (24), (28) gives: % 19.37/3.48 | | (51) ~ m2_relset_1(all_51_1, all_67_2, all_67_0) | ~ % 19.37/3.48 | | v1_funct_2(all_51_1, all_67_2, all_67_0) | (u1_struct_0(all_51_0) = % 19.37/3.48 | | k1_xboole_0 & $i(k1_xboole_0)) % 19.37/3.48 | | % 19.37/3.48 | | BETA: splitting (51) gives: % 19.37/3.48 | | % 19.37/3.48 | | Case 1: % 19.37/3.48 | | | % 19.37/3.48 | | | (52) ~ m2_relset_1(all_51_1, all_67_2, all_67_0) % 19.37/3.48 | | | % 19.37/3.48 | | | REDUCE: (45), (49), (52) imply: % 19.37/3.48 | | | (53) ~ m2_relset_1(all_51_1, all_65_2, all_65_0) % 19.37/3.48 | | | % 19.37/3.48 | | | PRED_UNIFY: (33), (53) imply: % 19.37/3.48 | | | (54) $false % 19.37/3.48 | | | % 19.37/3.48 | | | CLOSE: (54) is inconsistent. % 19.37/3.48 | | | % 19.37/3.48 | | Case 2: % 19.37/3.48 | | | % 19.37/3.48 | | | (55) ~ v1_funct_2(all_51_1, all_67_2, all_67_0) | % 19.37/3.48 | | | (u1_struct_0(all_51_0) = k1_xboole_0 & $i(k1_xboole_0)) % 19.37/3.48 | | | % 19.37/3.48 | | | BETA: splitting (55) gives: % 19.37/3.48 | | | % 19.37/3.48 | | | Case 1: % 19.37/3.48 | | | | % 19.37/3.48 | | | | (56) ~ v1_funct_2(all_51_1, all_67_2, all_67_0) % 19.37/3.48 | | | | % 19.37/3.48 | | | | REDUCE: (45), (49), (56) imply: % 19.37/3.48 | | | | (57) ~ v1_funct_2(all_51_1, all_65_2, all_65_0) % 19.37/3.48 | | | | % 19.37/3.48 | | | | PRED_UNIFY: (32), (57) imply: % 19.37/3.48 | | | | (58) $false % 19.37/3.48 | | | | % 19.37/3.48 | | | | CLOSE: (58) is inconsistent. % 19.37/3.48 | | | | % 19.37/3.48 | | | Case 2: % 19.37/3.48 | | | | % 19.37/3.48 | | | | (59) u1_struct_0(all_51_0) = k1_xboole_0 & $i(k1_xboole_0) % 19.37/3.48 | | | | % 19.37/3.48 | | | | ALPHA: (59) implies: % 19.37/3.48 | | | | (60) u1_struct_0(all_51_0) = k1_xboole_0 % 19.37/3.48 | | | | % 19.37/3.48 | | | | GROUND_INST: instantiating (fc1_struct_0) with all_51_0, k1_xboole_0, % 19.37/3.48 | | | | simplifying with (23), (42), (50), (60) gives: % 19.37/3.48 | | | | (61) v3_struct_0(all_51_0) % 19.37/3.48 | | | | % 19.37/3.48 | | | | GROUND_INST: instantiating (5) with all_51_2, all_51_0, simplifying with % 19.37/3.48 | | | | (15), (16), (18), (20), (21), (23), (61) gives: % 19.37/3.48 | | | | (62) $false % 19.37/3.48 | | | | % 19.37/3.48 | | | | CLOSE: (62) is inconsistent. % 19.37/3.48 | | | | % 19.37/3.48 | | | End of split % 19.37/3.48 | | | % 19.37/3.48 | | End of split % 19.37/3.48 | | % 19.37/3.48 | End of split % 19.37/3.48 | % 19.37/3.48 End of proof % 19.37/3.49 % SZS output end Proof for theBenchmark % 19.37/3.49 % 19.37/3.49 2875ms %------------------------------------------------------------------------------