%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG215+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 : n028.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 : Wed Aug 30 16:39:58 EDT 2023 % Result : Theorem 31.19s 5.04s % Output : Proof 51.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG215+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 : n028.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 06:21:39 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.06/1.34 Prover 4: Preprocessing ... % 4.06/1.34 Prover 1: Preprocessing ... % 4.46/1.38 Prover 0: Preprocessing ... % 4.46/1.38 Prover 2: Preprocessing ... % 4.46/1.38 Prover 5: Preprocessing ... % 4.46/1.39 Prover 3: Preprocessing ... % 4.46/1.39 Prover 6: Preprocessing ... % 9.69/2.19 Prover 1: Warning: ignoring some quantifiers % 9.69/2.25 Prover 5: Proving ... % 10.98/2.27 Prover 1: Constructing countermodel ... % 10.98/2.28 Prover 2: Proving ... % 12.13/2.43 Prover 3: Warning: ignoring some quantifiers % 12.27/2.46 Prover 3: Constructing countermodel ... % 12.79/2.52 Prover 6: Proving ... % 22.95/3.90 Prover 3: gave up % 22.95/3.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.99/4.04 Prover 7: Preprocessing ... % 24.58/4.21 Prover 7: Warning: ignoring some quantifiers % 25.80/4.26 Prover 7: Constructing countermodel ... % 29.60/4.80 Prover 1: gave up % 29.60/4.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 30.31/4.94 Prover 8: Preprocessing ... % 31.19/5.04 Prover 2: proved (4409ms) % 31.19/5.04 % 31.19/5.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.19/5.04 % 31.19/5.05 Prover 5: stopped % 31.19/5.06 Prover 6: stopped % 31.19/5.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 31.19/5.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 31.19/5.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 32.43/5.13 Prover 8: Warning: ignoring some quantifiers % 32.43/5.18 Prover 8: Constructing countermodel ... % 32.43/5.19 Prover 10: Preprocessing ... % 32.43/5.22 Prover 13: Preprocessing ... % 33.17/5.23 Prover 11: Preprocessing ... % 33.72/5.32 Prover 10: Warning: ignoring some quantifiers % 33.72/5.35 Prover 10: Constructing countermodel ... % 33.72/5.35 Prover 13: Warning: ignoring some quantifiers % 34.27/5.37 Prover 13: Constructing countermodel ... % 43.10/6.53 Prover 4: Warning: ignoring some quantifiers % 44.91/6.76 Prover 4: Constructing countermodel ... % 47.94/7.18 Prover 7: Found proof (size 84) % 47.94/7.18 Prover 7: proved (3275ms) % 47.94/7.18 Prover 13: stopped % 47.94/7.18 Prover 8: stopped % 47.94/7.18 Prover 10: stopped % 47.94/7.18 Prover 4: stopped % 47.94/7.18 Prover 11: stopped % 50.04/7.71 Prover 0: Proving ... % 50.04/7.71 Prover 0: stopped % 50.04/7.71 % 50.04/7.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 50.04/7.71 % 50.04/7.73 % SZS output start Proof for theBenchmark % 50.04/7.74 Assumptions after simplification: % 50.04/7.74 --------------------------------- % 50.04/7.74 % 50.04/7.74 (d1_rmod_5) % 50.64/7.80 $i(k1_xboole_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 50.64/7.80 (k1_rlvect_1(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ % 50.64/7.80 v5_vectsp_2(v1, v0) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ % 50.64/7.80 v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ % 50.64/7.80 v6_rlvect_1(v1) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ % 50.64/7.80 v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ % 50.64/7.80 v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | % 50.64/7.80 ? [v3: $i] : ? [v4: $i] : (u1_struct_0(v1) = v3 & k1_zfmisc_1(v3) = v4 & % 50.64/7.80 $i(v4) & $i(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = % 50.64/7.80 k1_xboole_0 | ~ (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ $i(v5) | % 50.64/7.80 ~ m2_rmod_4(v6, v0, v1, v5) | ~ m1_subset_1(v5, v4) | ~ v1_rmod_5(v5, % 50.64/7.80 v0, v1) | ? [v8: $i] : ( ~ (v8 = v2) & k5_rmod_4(v0, v1, v6) = v8 & % 50.64/7.80 $i(v8))) & ! [v5: $i] : ! [v6: $i] : ( ~ (k5_rmod_4(v0, v1, v6) = % 50.64/7.80 v2) | ~ $i(v6) | ~ $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) | ~ % 50.64/7.80 m1_subset_1(v5, v4) | ~ v1_rmod_5(v5, v0, v1) | k2_rmod_4(v0, v1, v6) = % 50.64/7.81 k1_xboole_0) & ! [v5: $i] : ( ~ $i(v5) | ~ m1_subset_1(v5, v4) | % 50.64/7.81 v1_rmod_5(v5, v0, v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = % 50.64/7.81 k1_xboole_0) & k5_rmod_4(v0, v1, v6) = v2 & k2_rmod_4(v0, v1, v6) = % 50.64/7.81 v7 & $i(v7) & $i(v6) & $i(v2) & m2_rmod_4(v6, v0, v1, v5))))) & ! % 50.64/7.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (u1_struct_0(v1) = v2) | ~ $i(v1) % 50.64/7.81 | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ % 50.64/7.81 l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ % 50.64/7.81 v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 50.64/7.81 v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 50.64/7.81 v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 50.64/7.81 v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : ? [v4: % 50.64/7.81 $i] : (k1_rlvect_1(v1) = v4 & k1_zfmisc_1(v2) = v3 & $i(v4) & $i(v3) & ! % 50.64/7.81 [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = k1_xboole_0 | ~ % 50.64/7.81 (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ m2_rmod_4(v6, % 50.64/7.81 v0, v1, v5) | ~ m1_subset_1(v5, v3) | ~ v1_rmod_5(v5, v0, v1) | ? % 50.64/7.81 [v8: $i] : ( ~ (v8 = v4) & k5_rmod_4(v0, v1, v6) = v8 & $i(v8))) & ! % 50.64/7.81 [v5: $i] : ! [v6: $i] : ( ~ (k5_rmod_4(v0, v1, v6) = v4) | ~ $i(v6) | ~ % 50.64/7.81 $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) | ~ m1_subset_1(v5, v3) | ~ % 50.64/7.81 v1_rmod_5(v5, v0, v1) | k2_rmod_4(v0, v1, v6) = k1_xboole_0) & ! [v5: % 50.64/7.81 $i] : ( ~ $i(v5) | ~ m1_subset_1(v5, v3) | v1_rmod_5(v5, v0, v1) | ? % 50.64/7.81 [v6: $i] : ? [v7: $i] : ( ~ (v7 = k1_xboole_0) & k5_rmod_4(v0, v1, v6) % 50.64/7.81 = v4 & k2_rmod_4(v0, v1, v6) = v7 & $i(v7) & $i(v6) & m2_rmod_4(v6, % 50.64/7.81 v0, v1, v5))))) % 50.64/7.81 % 50.64/7.81 (d5_rmod_4) % 50.64/7.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (a_3_0_rmod_4(v0, % 50.64/7.81 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_rmod_4(v2, v0, % 50.64/7.81 v1) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ l3_vectsp_1(v0) % 50.64/7.81 | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ % 50.64/7.81 v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ v6_rlvect_1(v0) | ~ % 50.64/7.81 v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~ % 50.64/7.81 v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | v3_struct_0(v1) % 50.64/7.81 | v3_struct_0(v0) | (k2_rmod_4(v0, v1, v2) = v3 & $i(v3))) & ! [v0: $i] : % 50.64/7.81 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k2_rmod_4(v0, v1, v2) = v3) | ~ % 50.64/7.81 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_rmod_4(v2, v0, v1) | ~ % 50.64/7.81 l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ l3_vectsp_1(v0) | ~ % 50.64/7.81 v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ % 50.64/7.81 v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ v6_rlvect_1(v0) | ~ % 50.64/7.81 v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~ % 50.64/7.81 v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | v3_struct_0(v1) % 50.64/7.81 | v3_struct_0(v0) | (a_3_0_rmod_4(v0, v1, v2) = v3 & $i(v3))) % 50.64/7.81 % 50.64/7.81 (d7_rmod_4) % 50.64/7.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (u1_struct_0(v1) = v2) | ~ % 50.76/7.82 $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ % 50.76/7.82 l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ % 50.76/7.82 v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 50.76/7.82 v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 50.76/7.82 v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 50.76/7.82 v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : % 50.76/7.82 (k1_zfmisc_1(v2) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 50.76/7.82 ~ (k2_rmod_4(v0, v1, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 50.76/7.82 r1_tarski(v6, v4) | ~ m1_rmod_4(v5, v0, v1) | ~ m1_subset_1(v4, v3) | % 50.76/7.82 m2_rmod_4(v5, v0, v1, v4)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 50.76/7.82 ~ (k2_rmod_4(v0, v1, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 50.76/7.82 m1_rmod_4(v5, v0, v1) | ~ m2_rmod_4(v5, v0, v1, v4) | ~ % 50.76/7.82 m1_subset_1(v4, v3) | r1_tarski(v6, v4)))) % 50.76/7.82 % 50.76/7.82 (dt_k1_subset_1) % 50.76/7.82 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_subset_1(v0) = v1) | ~ $i(v0) | % 50.76/7.82 v1_xboole_0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_subset_1(v0) = v1) | % 50.76/7.82 ~ $i(v0) | ? [v2: $i] : (k1_zfmisc_1(v0) = v2 & $i(v2) & m1_subset_1(v1, % 50.76/7.82 v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ % 50.76/7.82 $i(v0) | ? [v2: $i] : (k1_subset_1(v0) = v2 & $i(v2) & m1_subset_1(v2, % 50.76/7.82 v1))) % 50.76/7.82 % 50.76/7.82 (dt_m2_rmod_4) % 50.79/7.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 50.79/7.82 $i] : ( ~ (u1_struct_0(v1) = v3) | ~ (k1_zfmisc_1(v3) = v4) | ~ $i(v5) | % 50.79/7.82 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v5, v0, v1, v2) | ~ % 50.79/7.82 m1_subset_1(v2, v4) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ % 50.79/7.82 l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ % 50.79/7.82 v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 50.79/7.82 v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 50.79/7.82 v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 50.79/7.82 v3_rlvect_1(v0) | m1_rmod_4(v5, v0, v1) | v3_struct_0(v1) | v3_struct_0(v0)) % 50.79/7.82 % 50.79/7.82 (rc2_subset_1) % 50.79/7.82 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ $i(v0) | ? [v2: % 50.79/7.82 $i] : ($i(v2) & v1_xboole_0(v2) & m1_subset_1(v2, v1))) % 50.79/7.82 % 50.79/7.82 (t3_xboole_1) % 50.79/7.83 $i(k1_xboole_0) & ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~ % 50.79/7.83 r1_tarski(v0, k1_xboole_0)) % 50.79/7.83 % 50.79/7.83 (t4_rmod_5) % 50.79/7.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (k1_subset_1(v2) = v3 % 50.79/7.83 & u1_struct_0(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & l1_vectsp_2(v1, % 50.79/7.83 v0) & v5_vectsp_2(v1, v0) & l3_vectsp_1(v0) & v8_vectsp_1(v0) & % 50.79/7.83 v7_vectsp_1(v0) & v6_vectsp_1(v0) & v4_group_1(v0) & v6_rlvect_1(v1) & % 50.79/7.83 v6_rlvect_1(v0) & v5_rlvect_1(v1) & v5_rlvect_1(v0) & v4_rlvect_1(v1) & % 50.79/7.83 v4_rlvect_1(v0) & v3_rlvect_1(v1) & v3_rlvect_1(v0) & ~ v1_rmod_5(v3, v0, % 50.79/7.83 v1) & ~ v3_struct_0(v1) & ~ v3_struct_0(v0)) % 50.79/7.83 % 50.79/7.83 (t6_boole) % 50.79/7.83 $i(k1_xboole_0) & ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~ % 50.79/7.83 v1_xboole_0(v0)) % 50.79/7.83 % 50.79/7.83 (function-axioms) % 50.79/7.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 50.79/7.84 $i] : (v1 = v0 | ~ (k8_funct_2(v5, v4, v3, v2) = v1) | ~ (k8_funct_2(v5, % 50.79/7.84 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 50.79/7.84 $i] : ! [v4: $i] : (v1 = v0 | ~ (a_3_0_rmod_4(v4, v3, v2) = v1) | ~ % 50.79/7.84 (a_3_0_rmod_4(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 50.79/7.84 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (k5_rmod_4(v4, v3, v2) = v1) | ~ % 50.79/7.84 (k5_rmod_4(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 50.79/7.84 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (k2_rmod_4(v4, v3, v2) = v1) | ~ % 50.79/7.84 (k2_rmod_4(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 50.79/7.84 [v3: $i] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = % 50.79/7.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 50.79/7.84 ~ (k1_funct_2(v3, v2) = v1) | ~ (k1_funct_2(v3, v2) = v0)) & ! [v0: $i] : % 50.79/7.84 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k1_fraenkel(v3, v2) = % 50.79/7.84 v1) | ~ (k1_fraenkel(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 50.79/7.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ % 50.79/7.84 (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 50.79/7.84 = v0 | ~ (k1_subset_1(v2) = v1) | ~ (k1_subset_1(v2) = v0)) & ! [v0: $i] % 50.79/7.84 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_rlvect_1(v2) = v1) | ~ % 50.79/7.84 (k1_rlvect_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 50.79/7.84 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! % 50.79/7.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ % 50.79/7.84 (k1_zfmisc_1(v2) = v0)) % 50.79/7.84 % 50.79/7.84 Further assumptions not needed in the proof: % 50.79/7.84 -------------------------------------------- % 50.79/7.84 antisymmetry_r2_hidden, cc1_relset_1, dt_k1_fraenkel, dt_k1_funct_1, % 50.79/7.84 dt_k1_funct_2, dt_k1_rlvect_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_rmod_4, % 50.79/7.84 dt_k2_zfmisc_1, dt_k5_rmod_4, dt_k8_funct_2, dt_l1_group_1, dt_l1_rlvect_1, % 50.79/7.84 dt_l1_struct_0, dt_l1_vectsp_1, dt_l1_vectsp_2, dt_l2_struct_0, dt_l2_vectsp_1, % 50.79/7.84 dt_l3_vectsp_1, dt_m1_fraenkel, dt_m1_relset_1, dt_m1_rmod_4, dt_m1_subset_1, % 50.79/7.84 dt_m2_fraenkel, dt_m2_relset_1, dt_u1_struct_0, existence_l1_group_1, % 50.79/7.84 existence_l1_rlvect_1, existence_l1_struct_0, existence_l1_vectsp_1, % 50.79/7.84 existence_l1_vectsp_2, existence_l2_struct_0, existence_l2_vectsp_1, % 50.79/7.84 existence_l3_vectsp_1, existence_m1_fraenkel, existence_m1_relset_1, % 50.79/7.84 existence_m1_rmod_4, existence_m1_subset_1, existence_m2_fraenkel, % 50.79/7.84 existence_m2_relset_1, existence_m2_rmod_4, fc1_struct_0, fc1_subset_1, % 50.79/7.84 fc1_xboole_0, fc4_subset_1, fraenkel_a_3_0_rmod_4, rc1_subset_1, rc1_xboole_0, % 50.79/7.84 rc2_rlvect_2, rc2_xboole_0, rc3_struct_0, rc4_struct_0, rc5_struct_0, % 50.79/7.84 rc9_vectsp_2, redefinition_k1_fraenkel, redefinition_k8_funct_2, % 50.79/7.84 redefinition_m2_fraenkel, redefinition_m2_relset_1, reflexivity_r1_tarski, % 50.79/7.84 t1_subset, t2_subset, t2_tarski, t3_subset, t4_subset, t5_subset, t7_boole, % 50.79/7.84 t8_boole % 50.79/7.84 % 50.79/7.84 Those formulas are unsatisfiable: % 50.79/7.84 --------------------------------- % 50.79/7.84 % 50.79/7.84 Begin of proof % 50.79/7.84 | % 50.79/7.84 | ALPHA: (d1_rmod_5) implies: % 50.79/7.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (u1_struct_0(v1) = v2) | % 50.79/7.85 | ~ $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, % 50.79/7.85 | v0) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) % 50.79/7.85 | | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 50.79/7.85 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 50.79/7.85 | v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 50.79/7.85 | v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : % 50.79/7.85 | ? [v4: $i] : (k1_rlvect_1(v1) = v4 & k1_zfmisc_1(v2) = v3 & $i(v4) & % 50.79/7.85 | $i(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = % 50.79/7.85 | k1_xboole_0 | ~ (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ % 50.79/7.85 | $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) | ~ m1_subset_1(v5, v3) | % 50.79/7.85 | ~ v1_rmod_5(v5, v0, v1) | ? [v8: $i] : ( ~ (v8 = v4) & % 50.79/7.85 | k5_rmod_4(v0, v1, v6) = v8 & $i(v8))) & ! [v5: $i] : ! [v6: % 50.79/7.85 | $i] : ( ~ (k5_rmod_4(v0, v1, v6) = v4) | ~ $i(v6) | ~ $i(v5) | % 50.79/7.85 | ~ m2_rmod_4(v6, v0, v1, v5) | ~ m1_subset_1(v5, v3) | ~ % 50.79/7.85 | v1_rmod_5(v5, v0, v1) | k2_rmod_4(v0, v1, v6) = k1_xboole_0) & ! % 50.79/7.85 | [v5: $i] : ( ~ $i(v5) | ~ m1_subset_1(v5, v3) | v1_rmod_5(v5, v0, % 50.79/7.85 | v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = k1_xboole_0) & % 50.79/7.85 | k5_rmod_4(v0, v1, v6) = v4 & k2_rmod_4(v0, v1, v6) = v7 & % 50.79/7.85 | $i(v7) & $i(v6) & m2_rmod_4(v6, v0, v1, v5))))) % 50.79/7.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_rlvect_1(v1) = v2) | % 50.79/7.85 | ~ $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, % 50.79/7.85 | v0) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) % 50.79/7.85 | | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 50.79/7.85 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 50.79/7.85 | v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 50.79/7.85 | v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : % 50.79/7.85 | ? [v4: $i] : (u1_struct_0(v1) = v3 & k1_zfmisc_1(v3) = v4 & $i(v4) & % 50.79/7.85 | $i(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = % 50.79/7.85 | k1_xboole_0 | ~ (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ % 50.79/7.85 | $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) | ~ m1_subset_1(v5, v4) | % 50.79/7.85 | ~ v1_rmod_5(v5, v0, v1) | ? [v8: $i] : ( ~ (v8 = v2) & % 50.79/7.85 | k5_rmod_4(v0, v1, v6) = v8 & $i(v8))) & ! [v5: $i] : ! [v6: % 50.79/7.85 | $i] : ( ~ (k5_rmod_4(v0, v1, v6) = v2) | ~ $i(v6) | ~ $i(v5) | % 50.79/7.85 | ~ m2_rmod_4(v6, v0, v1, v5) | ~ m1_subset_1(v5, v4) | ~ % 50.79/7.85 | v1_rmod_5(v5, v0, v1) | k2_rmod_4(v0, v1, v6) = k1_xboole_0) & ! % 50.79/7.85 | [v5: $i] : ( ~ $i(v5) | ~ m1_subset_1(v5, v4) | v1_rmod_5(v5, v0, % 50.79/7.85 | v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = k1_xboole_0) & % 50.79/7.85 | k5_rmod_4(v0, v1, v6) = v2 & k2_rmod_4(v0, v1, v6) = v7 & % 50.79/7.85 | $i(v7) & $i(v6) & $i(v2) & m2_rmod_4(v6, v0, v1, v5))))) % 50.79/7.85 | % 50.79/7.85 | ALPHA: (d5_rmod_4) implies: % 50.79/7.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 50.79/7.85 | (k2_rmod_4(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 50.79/7.85 | m1_rmod_4(v2, v0, v1) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, % 50.79/7.85 | v0) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) % 50.79/7.85 | | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 50.79/7.85 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 50.79/7.85 | v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 50.79/7.85 | v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | % 50.79/7.85 | (a_3_0_rmod_4(v0, v1, v2) = v3 & $i(v3))) % 50.79/7.85 | % 50.79/7.85 | ALPHA: (dt_k1_subset_1) implies: % 50.79/7.86 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_subset_1(v0) = v1) | ~ $i(v0) | ? % 50.79/7.86 | [v2: $i] : (k1_zfmisc_1(v0) = v2 & $i(v2) & m1_subset_1(v1, v2))) % 50.79/7.86 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_subset_1(v0) = v1) | ~ $i(v0) | % 50.79/7.86 | v1_xboole_0(v1)) % 50.79/7.86 | % 50.79/7.86 | ALPHA: (t3_xboole_1) implies: % 50.79/7.86 | (6) ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~ r1_tarski(v0, % 50.79/7.86 | k1_xboole_0)) % 50.79/7.86 | % 50.79/7.86 | ALPHA: (t6_boole) implies: % 50.79/7.86 | (7) ! [v0: $i] : (v0 = k1_xboole_0 | ~ $i(v0) | ~ v1_xboole_0(v0)) % 50.79/7.86 | % 50.79/7.86 | ALPHA: (function-axioms) implies: % 50.79/7.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 50.79/7.86 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 50.79/7.86 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 50.79/7.86 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 50.79/7.86 | % 50.79/7.86 | DELTA: instantiating (t4_rmod_5) with fresh symbols all_80_0, all_80_1, % 50.79/7.86 | all_80_2, all_80_3 gives: % 50.79/7.86 | (10) k1_subset_1(all_80_1) = all_80_0 & u1_struct_0(all_80_2) = all_80_1 & % 50.79/7.86 | $i(all_80_0) & $i(all_80_1) & $i(all_80_2) & $i(all_80_3) & % 50.79/7.86 | l1_vectsp_2(all_80_2, all_80_3) & v5_vectsp_2(all_80_2, all_80_3) & % 50.79/7.86 | l3_vectsp_1(all_80_3) & v8_vectsp_1(all_80_3) & v7_vectsp_1(all_80_3) % 50.79/7.86 | & v6_vectsp_1(all_80_3) & v4_group_1(all_80_3) & v6_rlvect_1(all_80_2) % 50.79/7.86 | & v6_rlvect_1(all_80_3) & v5_rlvect_1(all_80_2) & % 50.79/7.86 | v5_rlvect_1(all_80_3) & v4_rlvect_1(all_80_2) & v4_rlvect_1(all_80_3) % 50.79/7.86 | & v3_rlvect_1(all_80_2) & v3_rlvect_1(all_80_3) & ~ % 50.79/7.86 | v1_rmod_5(all_80_0, all_80_3, all_80_2) & ~ v3_struct_0(all_80_2) & % 50.79/7.86 | ~ v3_struct_0(all_80_3) % 50.79/7.86 | % 50.79/7.86 | ALPHA: (10) implies: % 50.79/7.86 | (11) ~ v3_struct_0(all_80_3) % 50.79/7.86 | (12) ~ v3_struct_0(all_80_2) % 50.79/7.86 | (13) ~ v1_rmod_5(all_80_0, all_80_3, all_80_2) % 50.79/7.86 | (14) v3_rlvect_1(all_80_3) % 50.79/7.86 | (15) v3_rlvect_1(all_80_2) % 50.79/7.86 | (16) v4_rlvect_1(all_80_3) % 50.79/7.86 | (17) v4_rlvect_1(all_80_2) % 50.79/7.86 | (18) v5_rlvect_1(all_80_3) % 50.79/7.86 | (19) v5_rlvect_1(all_80_2) % 50.79/7.86 | (20) v6_rlvect_1(all_80_3) % 50.79/7.86 | (21) v6_rlvect_1(all_80_2) % 50.79/7.86 | (22) v4_group_1(all_80_3) % 50.79/7.86 | (23) v6_vectsp_1(all_80_3) % 50.79/7.86 | (24) v7_vectsp_1(all_80_3) % 50.79/7.86 | (25) v8_vectsp_1(all_80_3) % 50.79/7.86 | (26) l3_vectsp_1(all_80_3) % 50.79/7.86 | (27) v5_vectsp_2(all_80_2, all_80_3) % 50.79/7.86 | (28) l1_vectsp_2(all_80_2, all_80_3) % 50.79/7.86 | (29) $i(all_80_3) % 50.79/7.86 | (30) $i(all_80_2) % 50.79/7.86 | (31) $i(all_80_1) % 50.79/7.86 | (32) $i(all_80_0) % 50.79/7.86 | (33) u1_struct_0(all_80_2) = all_80_1 % 50.79/7.86 | (34) k1_subset_1(all_80_1) = all_80_0 % 50.79/7.86 | % 50.79/7.86 | GROUND_INST: instantiating (1) with all_80_3, all_80_2, all_80_1, simplifying % 50.79/7.86 | with (11), (12), (14), (15), (16), (17), (18), (19), (20), (21), % 50.79/7.86 | (22), (23), (24), (25), (26), (27), (28), (29), (30), (33) gives: % 50.79/7.87 | (35) ? [v0: $i] : ? [v1: $i] : (k1_rlvect_1(all_80_2) = v1 & % 50.79/7.87 | k1_zfmisc_1(all_80_1) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 50.79/7.87 | $i] : ! [v4: $i] : (v4 = k1_xboole_0 | ~ (k2_rmod_4(all_80_3, % 50.79/7.87 | all_80_2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ m2_rmod_4(v3, % 50.79/7.87 | all_80_3, all_80_2, v2) | ~ m1_subset_1(v2, v0) | ~ % 50.79/7.87 | v1_rmod_5(v2, all_80_3, all_80_2) | ? [v5: $i] : ( ~ (v5 = v1) & % 50.79/7.87 | k5_rmod_4(all_80_3, all_80_2, v3) = v5 & $i(v5))) & ! [v2: $i] % 50.79/7.87 | : ! [v3: $i] : ( ~ (k5_rmod_4(all_80_3, all_80_2, v3) = v1) | ~ % 50.79/7.87 | $i(v3) | ~ $i(v2) | ~ m2_rmod_4(v3, all_80_3, all_80_2, v2) | ~ % 50.79/7.87 | m1_subset_1(v2, v0) | ~ v1_rmod_5(v2, all_80_3, all_80_2) | % 50.79/7.87 | k2_rmod_4(all_80_3, all_80_2, v3) = k1_xboole_0) & ! [v2: $i] : ( % 50.79/7.87 | ~ $i(v2) | ~ m1_subset_1(v2, v0) | v1_rmod_5(v2, all_80_3, % 50.79/7.87 | all_80_2) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = k1_xboole_0) & % 50.79/7.87 | k5_rmod_4(all_80_3, all_80_2, v3) = v1 & k2_rmod_4(all_80_3, % 50.79/7.87 | all_80_2, v3) = v4 & $i(v4) & $i(v3) & m2_rmod_4(v3, all_80_3, % 50.79/7.87 | all_80_2, v2)))) % 50.79/7.87 | % 50.79/7.87 | GROUND_INST: instantiating (d7_rmod_4) with all_80_3, all_80_2, all_80_1, % 50.79/7.87 | simplifying with (11), (12), (14), (15), (16), (17), (18), (19), % 50.79/7.87 | (20), (21), (22), (23), (24), (25), (26), (27), (28), (29), (30), % 50.79/7.87 | (33) gives: % 50.79/7.87 | (36) ? [v0: $i] : (k1_zfmisc_1(all_80_1) = v0 & $i(v0) & ! [v1: $i] : ! % 50.79/7.87 | [v2: $i] : ! [v3: $i] : ( ~ (k2_rmod_4(all_80_3, all_80_2, v2) = % 50.79/7.87 | v3) | ~ $i(v2) | ~ $i(v1) | ~ r1_tarski(v3, v1) | ~ % 50.79/7.87 | m1_rmod_4(v2, all_80_3, all_80_2) | ~ m1_subset_1(v1, v0) | % 50.79/7.87 | m2_rmod_4(v2, all_80_3, all_80_2, v1)) & ! [v1: $i] : ! [v2: $i] % 50.79/7.87 | : ! [v3: $i] : ( ~ (k2_rmod_4(all_80_3, all_80_2, v2) = v3) | ~ % 50.79/7.87 | $i(v2) | ~ $i(v1) | ~ m1_rmod_4(v2, all_80_3, all_80_2) | ~ % 50.79/7.87 | m2_rmod_4(v2, all_80_3, all_80_2, v1) | ~ m1_subset_1(v1, v0) | % 50.79/7.87 | r1_tarski(v3, v1))) % 50.79/7.87 | % 50.79/7.87 | GROUND_INST: instantiating (5) with all_80_1, all_80_0, simplifying with (31), % 50.79/7.87 | (34) gives: % 50.79/7.87 | (37) v1_xboole_0(all_80_0) % 50.79/7.87 | % 50.79/7.87 | GROUND_INST: instantiating (4) with all_80_1, all_80_0, simplifying with (31), % 50.79/7.87 | (34) gives: % 50.79/7.87 | (38) ? [v0: $i] : (k1_zfmisc_1(all_80_1) = v0 & $i(v0) & % 50.79/7.87 | m1_subset_1(all_80_0, v0)) % 50.79/7.87 | % 50.79/7.87 | DELTA: instantiating (38) with fresh symbol all_100_0 gives: % 50.79/7.87 | (39) k1_zfmisc_1(all_80_1) = all_100_0 & $i(all_100_0) & % 50.79/7.87 | m1_subset_1(all_80_0, all_100_0) % 50.79/7.87 | % 50.79/7.87 | ALPHA: (39) implies: % 50.79/7.87 | (40) m1_subset_1(all_80_0, all_100_0) % 50.79/7.87 | (41) k1_zfmisc_1(all_80_1) = all_100_0 % 50.79/7.87 | % 50.79/7.87 | DELTA: instantiating (36) with fresh symbol all_106_0 gives: % 50.79/7.87 | (42) k1_zfmisc_1(all_80_1) = all_106_0 & $i(all_106_0) & ! [v0: $i] : ! % 50.79/7.87 | [v1: $i] : ! [v2: $i] : ( ~ (k2_rmod_4(all_80_3, all_80_2, v1) = v2) % 50.79/7.87 | | ~ $i(v1) | ~ $i(v0) | ~ r1_tarski(v2, v0) | ~ m1_rmod_4(v1, % 50.79/7.87 | all_80_3, all_80_2) | ~ m1_subset_1(v0, all_106_0) | % 50.79/7.87 | m2_rmod_4(v1, all_80_3, all_80_2, v0)) & ! [v0: $i] : ! [v1: $i] : % 50.79/7.87 | ! [v2: $i] : ( ~ (k2_rmod_4(all_80_3, all_80_2, v1) = v2) | ~ $i(v1) % 50.79/7.87 | | ~ $i(v0) | ~ m1_rmod_4(v1, all_80_3, all_80_2) | ~ % 50.79/7.87 | m2_rmod_4(v1, all_80_3, all_80_2, v0) | ~ m1_subset_1(v0, % 50.79/7.87 | all_106_0) | r1_tarski(v2, v0)) % 50.79/7.87 | % 50.79/7.87 | ALPHA: (42) implies: % 50.79/7.87 | (43) k1_zfmisc_1(all_80_1) = all_106_0 % 50.79/7.87 | (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k2_rmod_4(all_80_3, % 50.79/7.87 | all_80_2, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_rmod_4(v1, % 50.79/7.87 | all_80_3, all_80_2) | ~ m2_rmod_4(v1, all_80_3, all_80_2, v0) | % 50.79/7.87 | ~ m1_subset_1(v0, all_106_0) | r1_tarski(v2, v0)) % 50.79/7.87 | % 50.79/7.87 | DELTA: instantiating (35) with fresh symbols all_109_0, all_109_1 gives: % 50.79/7.88 | (45) k1_rlvect_1(all_80_2) = all_109_0 & k1_zfmisc_1(all_80_1) = all_109_1 % 50.79/7.88 | & $i(all_109_0) & $i(all_109_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 50.79/7.88 | $i] : (v2 = k1_xboole_0 | ~ (k2_rmod_4(all_80_3, all_80_2, v1) = % 50.79/7.88 | v2) | ~ $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, all_80_3, all_80_2, % 50.79/7.88 | v0) | ~ m1_subset_1(v0, all_109_1) | ~ v1_rmod_5(v0, all_80_3, % 50.79/7.88 | all_80_2) | ? [v3: any] : ( ~ (v3 = all_109_0) & % 50.79/7.88 | k5_rmod_4(all_80_3, all_80_2, v1) = v3 & $i(v3))) & ! [v0: $i] : % 50.79/7.88 | ! [v1: $i] : ( ~ (k5_rmod_4(all_80_3, all_80_2, v1) = all_109_0) | ~ % 50.79/7.88 | $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, all_80_3, all_80_2, v0) | ~ % 50.79/7.88 | m1_subset_1(v0, all_109_1) | ~ v1_rmod_5(v0, all_80_3, all_80_2) | % 50.79/7.88 | k2_rmod_4(all_80_3, all_80_2, v1) = k1_xboole_0) & ! [v0: $i] : ( ~ % 50.79/7.88 | $i(v0) | ~ m1_subset_1(v0, all_109_1) | v1_rmod_5(v0, all_80_3, % 50.79/7.88 | all_80_2) | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = k1_xboole_0) & % 50.79/7.88 | k5_rmod_4(all_80_3, all_80_2, v1) = all_109_0 & % 50.79/7.88 | k2_rmod_4(all_80_3, all_80_2, v1) = v2 & $i(v2) & $i(v1) & % 50.79/7.88 | m2_rmod_4(v1, all_80_3, all_80_2, v0))) % 50.79/7.88 | % 50.79/7.88 | ALPHA: (45) implies: % 50.79/7.88 | (46) k1_zfmisc_1(all_80_1) = all_109_1 % 50.79/7.88 | (47) k1_rlvect_1(all_80_2) = all_109_0 % 50.79/7.88 | (48) ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_109_1) | % 50.79/7.88 | v1_rmod_5(v0, all_80_3, all_80_2) | ? [v1: $i] : ? [v2: $i] : ( ~ % 50.79/7.88 | (v2 = k1_xboole_0) & k5_rmod_4(all_80_3, all_80_2, v1) = all_109_0 % 50.79/7.88 | & k2_rmod_4(all_80_3, all_80_2, v1) = v2 & $i(v2) & $i(v1) & % 50.79/7.88 | m2_rmod_4(v1, all_80_3, all_80_2, v0))) % 50.79/7.88 | % 50.79/7.88 | GROUND_INST: instantiating (8) with all_106_0, all_109_1, all_80_1, % 50.79/7.88 | simplifying with (43), (46) gives: % 50.79/7.88 | (49) all_109_1 = all_106_0 % 50.79/7.88 | % 50.79/7.88 | GROUND_INST: instantiating (8) with all_100_0, all_109_1, all_80_1, % 50.79/7.88 | simplifying with (41), (46) gives: % 50.79/7.88 | (50) all_109_1 = all_100_0 % 50.79/7.88 | % 50.79/7.88 | COMBINE_EQS: (49), (50) imply: % 50.79/7.88 | (51) all_106_0 = all_100_0 % 50.79/7.88 | % 50.79/7.88 | SIMP: (51) implies: % 50.79/7.88 | (52) all_106_0 = all_100_0 % 50.79/7.88 | % 50.79/7.88 | GROUND_INST: instantiating (48) with all_80_0, simplifying with (13), (32) % 50.79/7.88 | gives: % 50.79/7.88 | (53) ~ m1_subset_1(all_80_0, all_109_1) | ? [v0: $i] : ? [v1: $i] : ( ~ % 50.79/7.88 | (v1 = k1_xboole_0) & k5_rmod_4(all_80_3, all_80_2, v0) = all_109_0 & % 50.79/7.88 | k2_rmod_4(all_80_3, all_80_2, v0) = v1 & $i(v1) & $i(v0) & % 50.79/7.88 | m2_rmod_4(v0, all_80_3, all_80_2, all_80_0)) % 50.79/7.88 | % 50.79/7.88 | GROUND_INST: instantiating (7) with all_80_0, simplifying with (32), (37) % 50.79/7.88 | gives: % 50.79/7.88 | (54) all_80_0 = k1_xboole_0 % 50.79/7.88 | % 50.79/7.88 | GROUND_INST: instantiating (rc2_subset_1) with all_80_1, all_100_0, % 50.79/7.88 | simplifying with (31), (41) gives: % 50.79/7.88 | (55) ? [v0: $i] : ($i(v0) & v1_xboole_0(v0) & m1_subset_1(v0, all_100_0)) % 50.79/7.88 | % 50.79/7.88 | GROUND_INST: instantiating (2) with all_80_3, all_80_2, all_109_0, simplifying % 50.79/7.88 | with (11), (12), (14), (15), (16), (17), (18), (19), (20), (21), % 50.79/7.88 | (22), (23), (24), (25), (26), (27), (28), (29), (30), (47) gives: % 50.79/7.88 | (56) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_80_2) = v0 & % 50.79/7.88 | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : % 50.79/7.88 | ! [v4: $i] : (v4 = k1_xboole_0 | ~ (k2_rmod_4(all_80_3, all_80_2, % 50.79/7.88 | v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ m2_rmod_4(v3, all_80_3, % 50.79/7.88 | all_80_2, v2) | ~ m1_subset_1(v2, v1) | ~ v1_rmod_5(v2, % 50.79/7.88 | all_80_3, all_80_2) | ? [v5: any] : ( ~ (v5 = all_109_0) & % 50.79/7.88 | k5_rmod_4(all_80_3, all_80_2, v3) = v5 & $i(v5))) & ! [v2: $i] % 50.79/7.88 | : ! [v3: $i] : ( ~ (k5_rmod_4(all_80_3, all_80_2, v3) = all_109_0) % 50.79/7.88 | | ~ $i(v3) | ~ $i(v2) | ~ m2_rmod_4(v3, all_80_3, all_80_2, v2) % 50.79/7.88 | | ~ m1_subset_1(v2, v1) | ~ v1_rmod_5(v2, all_80_3, all_80_2) | % 50.79/7.88 | k2_rmod_4(all_80_3, all_80_2, v3) = k1_xboole_0) & ! [v2: $i] : ( % 50.79/7.88 | ~ $i(v2) | ~ m1_subset_1(v2, v1) | v1_rmod_5(v2, all_80_3, % 50.79/7.88 | all_80_2) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = k1_xboole_0) & % 50.79/7.88 | k5_rmod_4(all_80_3, all_80_2, v3) = all_109_0 & % 50.79/7.88 | k2_rmod_4(all_80_3, all_80_2, v3) = v4 & $i(v4) & $i(v3) & % 50.79/7.88 | $i(all_109_0) & m2_rmod_4(v3, all_80_3, all_80_2, v2)))) % 50.79/7.88 | % 50.79/7.88 | DELTA: instantiating (55) with fresh symbol all_130_0 gives: % 50.79/7.89 | (57) $i(all_130_0) & v1_xboole_0(all_130_0) & m1_subset_1(all_130_0, % 50.79/7.89 | all_100_0) % 50.79/7.89 | % 50.79/7.89 | ALPHA: (57) implies: % 50.79/7.89 | (58) m1_subset_1(all_130_0, all_100_0) % 50.79/7.89 | (59) v1_xboole_0(all_130_0) % 50.79/7.89 | (60) $i(all_130_0) % 50.79/7.89 | % 50.79/7.89 | DELTA: instantiating (56) with fresh symbols all_138_0, all_138_1 gives: % 50.79/7.89 | (61) u1_struct_0(all_80_2) = all_138_1 & k1_zfmisc_1(all_138_1) = all_138_0 % 50.79/7.89 | & $i(all_138_0) & $i(all_138_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 50.79/7.89 | $i] : (v2 = k1_xboole_0 | ~ (k2_rmod_4(all_80_3, all_80_2, v1) = % 50.79/7.89 | v2) | ~ $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, all_80_3, all_80_2, % 50.79/7.89 | v0) | ~ m1_subset_1(v0, all_138_0) | ~ v1_rmod_5(v0, all_80_3, % 50.79/7.89 | all_80_2) | ? [v3: any] : ( ~ (v3 = all_109_0) & % 50.79/7.89 | k5_rmod_4(all_80_3, all_80_2, v1) = v3 & $i(v3))) & ! [v0: $i] : % 50.79/7.89 | ! [v1: $i] : ( ~ (k5_rmod_4(all_80_3, all_80_2, v1) = all_109_0) | ~ % 50.79/7.89 | $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, all_80_3, all_80_2, v0) | ~ % 50.79/7.89 | m1_subset_1(v0, all_138_0) | ~ v1_rmod_5(v0, all_80_3, all_80_2) | % 50.79/7.89 | k2_rmod_4(all_80_3, all_80_2, v1) = k1_xboole_0) & ! [v0: $i] : ( ~ % 50.79/7.89 | $i(v0) | ~ m1_subset_1(v0, all_138_0) | v1_rmod_5(v0, all_80_3, % 50.79/7.89 | all_80_2) | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = k1_xboole_0) & % 50.79/7.89 | k5_rmod_4(all_80_3, all_80_2, v1) = all_109_0 & % 50.79/7.89 | k2_rmod_4(all_80_3, all_80_2, v1) = v2 & $i(v2) & $i(v1) & % 50.79/7.89 | $i(all_109_0) & m2_rmod_4(v1, all_80_3, all_80_2, v0))) % 50.79/7.89 | % 50.79/7.89 | ALPHA: (61) implies: % 50.79/7.89 | (62) k1_zfmisc_1(all_138_1) = all_138_0 % 50.79/7.89 | (63) u1_struct_0(all_80_2) = all_138_1 % 50.79/7.89 | (64) ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_138_0) | % 50.79/7.89 | v1_rmod_5(v0, all_80_3, all_80_2) | ? [v1: $i] : ? [v2: $i] : ( ~ % 50.79/7.89 | (v2 = k1_xboole_0) & k5_rmod_4(all_80_3, all_80_2, v1) = all_109_0 % 50.79/7.89 | & k2_rmod_4(all_80_3, all_80_2, v1) = v2 & $i(v2) & $i(v1) & % 50.79/7.89 | $i(all_109_0) & m2_rmod_4(v1, all_80_3, all_80_2, v0))) % 50.79/7.89 | % 50.79/7.89 | GROUND_INST: instantiating (64) with all_80_0, simplifying with (13), (32) % 50.79/7.89 | gives: % 50.79/7.89 | (65) ~ m1_subset_1(all_80_0, all_138_0) | ? [v0: $i] : ? [v1: $i] : ( ~ % 50.79/7.89 | (v1 = k1_xboole_0) & k5_rmod_4(all_80_3, all_80_2, v0) = all_109_0 & % 50.79/7.89 | k2_rmod_4(all_80_3, all_80_2, v0) = v1 & $i(v1) & $i(v0) & % 50.79/7.89 | $i(all_109_0) & m2_rmod_4(v0, all_80_3, all_80_2, all_80_0)) % 50.79/7.89 | % 50.79/7.89 | REDUCE: (32), (54) imply: % 50.79/7.89 | (66) $i(k1_xboole_0) % 50.79/7.89 | % 50.79/7.89 | REDUCE: (40), (54) imply: % 50.79/7.89 | (67) m1_subset_1(k1_xboole_0, all_100_0) % 50.79/7.89 | % 50.79/7.89 | REDUCE: (13), (54) imply: % 50.79/7.89 | (68) ~ v1_rmod_5(k1_xboole_0, all_80_3, all_80_2) % 50.79/7.89 | % 50.79/7.89 | BETA: splitting (53) gives: % 50.79/7.89 | % 50.79/7.89 | Case 1: % 50.79/7.89 | | % 50.79/7.89 | | (69) ~ m1_subset_1(all_80_0, all_109_1) % 50.79/7.89 | | % 50.79/7.89 | | REDUCE: (50), (54), (69) imply: % 50.79/7.89 | | (70) ~ m1_subset_1(k1_xboole_0, all_100_0) % 50.79/7.89 | | % 50.79/7.89 | | PRED_UNIFY: (67), (70) imply: % 50.79/7.89 | | (71) $false % 50.79/7.89 | | % 50.79/7.89 | | CLOSE: (71) is inconsistent. % 50.79/7.89 | | % 50.79/7.89 | Case 2: % 50.79/7.89 | | % 50.79/7.89 | | (72) m1_subset_1(all_80_0, all_109_1) % 50.79/7.89 | | (73) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = k1_xboole_0) & % 50.79/7.89 | | k5_rmod_4(all_80_3, all_80_2, v0) = all_109_0 & % 50.79/7.89 | | k2_rmod_4(all_80_3, all_80_2, v0) = v1 & $i(v1) & $i(v0) & % 50.79/7.89 | | m2_rmod_4(v0, all_80_3, all_80_2, all_80_0)) % 50.79/7.89 | | % 50.79/7.89 | | DELTA: instantiating (73) with fresh symbols all_145_0, all_145_1 gives: % 50.79/7.89 | | (74) ~ (all_145_0 = k1_xboole_0) & k5_rmod_4(all_80_3, all_80_2, % 50.79/7.89 | | all_145_1) = all_109_0 & k2_rmod_4(all_80_3, all_80_2, all_145_1) % 50.79/7.89 | | = all_145_0 & $i(all_145_0) & $i(all_145_1) & m2_rmod_4(all_145_1, % 50.79/7.89 | | all_80_3, all_80_2, all_80_0) % 50.79/7.89 | | % 50.79/7.89 | | ALPHA: (74) implies: % 50.79/7.89 | | (75) ~ (all_145_0 = k1_xboole_0) % 50.79/7.89 | | (76) m2_rmod_4(all_145_1, all_80_3, all_80_2, all_80_0) % 50.79/7.89 | | (77) $i(all_145_1) % 50.79/7.89 | | (78) k2_rmod_4(all_80_3, all_80_2, all_145_1) = all_145_0 % 50.79/7.89 | | % 50.79/7.89 | | REDUCE: (54), (76) imply: % 50.79/7.89 | | (79) m2_rmod_4(all_145_1, all_80_3, all_80_2, k1_xboole_0) % 50.79/7.89 | | % 50.79/7.89 | | GROUND_INST: instantiating (8) with all_100_0, all_138_0, all_80_1, % 50.79/7.89 | | simplifying with (41) gives: % 50.79/7.89 | | (80) all_138_0 = all_100_0 | ~ (k1_zfmisc_1(all_80_1) = all_138_0) % 50.79/7.89 | | % 50.79/7.89 | | GROUND_INST: instantiating (9) with all_80_1, all_138_1, all_80_2, % 50.79/7.89 | | simplifying with (33), (63) gives: % 50.79/7.89 | | (81) all_138_1 = all_80_1 % 50.79/7.89 | | % 50.79/7.89 | | REDUCE: (62), (81) imply: % 50.79/7.89 | | (82) k1_zfmisc_1(all_80_1) = all_138_0 % 50.79/7.89 | | % 50.79/7.89 | | BETA: splitting (80) gives: % 50.79/7.89 | | % 50.79/7.89 | | Case 1: % 50.79/7.89 | | | % 50.79/7.89 | | | (83) ~ (k1_zfmisc_1(all_80_1) = all_138_0) % 50.79/7.89 | | | % 50.79/7.90 | | | PRED_UNIFY: (82), (83) imply: % 50.79/7.90 | | | (84) $false % 50.79/7.90 | | | % 50.79/7.90 | | | CLOSE: (84) is inconsistent. % 50.79/7.90 | | | % 50.79/7.90 | | Case 2: % 50.79/7.90 | | | % 50.79/7.90 | | | (85) all_138_0 = all_100_0 % 50.79/7.90 | | | % 50.79/7.90 | | | BETA: splitting (65) gives: % 50.79/7.90 | | | % 50.79/7.90 | | | Case 1: % 50.79/7.90 | | | | % 50.79/7.90 | | | | (86) ~ m1_subset_1(all_80_0, all_138_0) % 50.79/7.90 | | | | % 50.79/7.90 | | | | REDUCE: (54), (85), (86) imply: % 50.79/7.90 | | | | (87) ~ m1_subset_1(k1_xboole_0, all_100_0) % 50.79/7.90 | | | | % 50.79/7.90 | | | | PRED_UNIFY: (67), (87) imply: % 50.79/7.90 | | | | (88) $false % 50.79/7.90 | | | | % 50.79/7.90 | | | | CLOSE: (88) is inconsistent. % 50.79/7.90 | | | | % 50.79/7.90 | | | Case 2: % 50.79/7.90 | | | | % 50.79/7.90 | | | | (89) m1_subset_1(all_80_0, all_138_0) % 50.79/7.90 | | | | % 50.79/7.90 | | | | GROUND_INST: instantiating (64) with all_130_0, simplifying with (60) % 50.79/7.90 | | | | gives: % 50.79/7.90 | | | | (90) ~ m1_subset_1(all_130_0, all_138_0) | v1_rmod_5(all_130_0, % 50.79/7.90 | | | | all_80_3, all_80_2) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 50.79/7.90 | | | | k1_xboole_0) & k5_rmod_4(all_80_3, all_80_2, v0) = all_109_0 % 50.79/7.90 | | | | & k2_rmod_4(all_80_3, all_80_2, v0) = v1 & $i(v1) & $i(v0) & % 50.79/7.90 | | | | $i(all_109_0) & m2_rmod_4(v0, all_80_3, all_80_2, all_130_0)) % 50.79/7.90 | | | | % 50.79/7.90 | | | | GROUND_INST: instantiating (dt_m2_rmod_4) with all_80_3, all_80_2, % 50.79/7.90 | | | | k1_xboole_0, all_80_1, all_100_0, all_145_1, simplifying % 50.79/7.90 | | | | with (11), (12), (14), (15), (16), (17), (18), (19), (20), % 50.79/7.90 | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29), (30), % 50.79/7.90 | | | | (33), (41), (66), (67), (77), (79) gives: % 50.79/7.90 | | | | (91) m1_rmod_4(all_145_1, all_80_3, all_80_2) % 50.79/7.90 | | | | % 50.79/7.90 | | | | GROUND_INST: instantiating (7) with all_130_0, simplifying with (59), % 50.79/7.90 | | | | (60) gives: % 50.79/7.90 | | | | (92) all_130_0 = k1_xboole_0 % 50.79/7.90 | | | | % 50.79/7.90 | | | | BETA: splitting (90) gives: % 50.79/7.90 | | | | % 50.79/7.90 | | | | Case 1: % 50.79/7.90 | | | | | % 50.79/7.90 | | | | | (93) ~ m1_subset_1(all_130_0, all_138_0) % 50.79/7.90 | | | | | % 50.79/7.90 | | | | | REDUCE: (85), (92), (93) imply: % 50.79/7.90 | | | | | (94) ~ m1_subset_1(k1_xboole_0, all_100_0) % 50.79/7.90 | | | | | % 50.79/7.90 | | | | | PRED_UNIFY: (67), (94) imply: % 50.79/7.90 | | | | | (95) $false % 50.79/7.90 | | | | | % 50.79/7.90 | | | | | CLOSE: (95) is inconsistent. % 50.79/7.90 | | | | | % 50.79/7.90 | | | | Case 2: % 50.79/7.90 | | | | | % 50.79/7.90 | | | | | (96) m1_subset_1(all_130_0, all_138_0) % 50.79/7.90 | | | | | (97) v1_rmod_5(all_130_0, all_80_3, all_80_2) | ? [v0: $i] : ? % 50.79/7.90 | | | | | [v1: $i] : ( ~ (v1 = k1_xboole_0) & k5_rmod_4(all_80_3, % 50.79/7.90 | | | | | all_80_2, v0) = all_109_0 & k2_rmod_4(all_80_3, all_80_2, % 50.79/7.90 | | | | | v0) = v1 & $i(v1) & $i(v0) & $i(all_109_0) & m2_rmod_4(v0, % 50.79/7.90 | | | | | all_80_3, all_80_2, all_130_0)) % 50.79/7.90 | | | | | % 50.79/7.90 | | | | | BETA: splitting (97) gives: % 50.79/7.90 | | | | | % 50.79/7.90 | | | | | Case 1: % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | (98) v1_rmod_5(all_130_0, all_80_3, all_80_2) % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | REDUCE: (92), (98) imply: % 50.79/7.90 | | | | | | (99) v1_rmod_5(k1_xboole_0, all_80_3, all_80_2) % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | PRED_UNIFY: (68), (99) imply: % 50.79/7.90 | | | | | | (100) $false % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | CLOSE: (100) is inconsistent. % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | Case 2: % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | GROUND_INST: instantiating (3) with all_80_3, all_80_2, all_145_1, % 50.79/7.90 | | | | | | all_145_0, simplifying with (11), (12), (14), (15), % 50.79/7.90 | | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), % 50.79/7.90 | | | | | | (25), (26), (27), (28), (29), (30), (77), (78), (91) % 50.79/7.90 | | | | | | gives: % 50.79/7.90 | | | | | | (101) a_3_0_rmod_4(all_80_3, all_80_2, all_145_1) = all_145_0 & % 50.79/7.90 | | | | | | $i(all_145_0) % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | ALPHA: (101) implies: % 50.79/7.90 | | | | | | (102) $i(all_145_0) % 50.79/7.90 | | | | | | % 50.79/7.90 | | | | | | GROUND_INST: instantiating (44) with k1_xboole_0, all_145_1, % 51.19/7.90 | | | | | | all_145_0, simplifying with (66), (77), (78), (79), % 51.19/7.90 | | | | | | (91) gives: % 51.19/7.90 | | | | | | (103) ~ m1_subset_1(k1_xboole_0, all_106_0) | % 51.19/7.90 | | | | | | r1_tarski(all_145_0, k1_xboole_0) % 51.19/7.90 | | | | | | % 51.19/7.90 | | | | | | BETA: splitting (103) gives: % 51.19/7.90 | | | | | | % 51.19/7.90 | | | | | | Case 1: % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | (104) ~ m1_subset_1(k1_xboole_0, all_106_0) % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | REDUCE: (52), (104) imply: % 51.19/7.90 | | | | | | | (105) ~ m1_subset_1(k1_xboole_0, all_100_0) % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | PRED_UNIFY: (67), (105) imply: % 51.19/7.90 | | | | | | | (106) $false % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | CLOSE: (106) is inconsistent. % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | Case 2: % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | (107) r1_tarski(all_145_0, k1_xboole_0) % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | GROUND_INST: instantiating (6) with all_145_0, simplifying with % 51.19/7.90 | | | | | | | (102), (107) gives: % 51.19/7.90 | | | | | | | (108) all_145_0 = k1_xboole_0 % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | REDUCE: (75), (108) imply: % 51.19/7.90 | | | | | | | (109) $false % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | | CLOSE: (109) is inconsistent. % 51.19/7.90 | | | | | | | % 51.19/7.90 | | | | | | End of split % 51.19/7.90 | | | | | | % 51.19/7.90 | | | | | End of split % 51.19/7.90 | | | | | % 51.19/7.90 | | | | End of split % 51.19/7.90 | | | | % 51.19/7.90 | | | End of split % 51.19/7.90 | | | % 51.19/7.90 | | End of split % 51.19/7.90 | | % 51.19/7.90 | End of split % 51.19/7.90 | % 51.19/7.90 End of proof % 51.19/7.90 % SZS output end Proof for theBenchmark % 51.19/7.90 % 51.19/7.90 7292ms %------------------------------------------------------------------------------