%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG214+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 : n014.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 20.70s 3.58s % Output : Proof 35.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG214+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 : n014.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 03:59:16 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.71/1.21 Prover 1: Preprocessing ... % 3.71/1.21 Prover 4: Preprocessing ... % 4.10/1.24 Prover 2: Preprocessing ... % 4.10/1.24 Prover 3: Preprocessing ... % 4.10/1.24 Prover 6: Preprocessing ... % 4.10/1.24 Prover 5: Preprocessing ... % 4.10/1.24 Prover 0: Preprocessing ... % 9.83/2.08 Prover 5: Proving ... % 9.83/2.09 Prover 2: Proving ... % 9.83/2.10 Prover 1: Warning: ignoring some quantifiers % 9.83/2.17 Prover 1: Constructing countermodel ... % 10.77/2.20 Prover 3: Warning: ignoring some quantifiers % 10.77/2.23 Prover 3: Constructing countermodel ... % 11.61/2.28 Prover 6: Proving ... % 20.70/3.58 Prover 2: proved (2969ms) % 20.70/3.58 % 20.70/3.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.70/3.58 % 20.70/3.58 Prover 5: stopped % 20.70/3.58 Prover 6: stopped % 20.70/3.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.70/3.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.70/3.58 Prover 0: stopped % 20.70/3.58 Prover 3: stopped % 20.70/3.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.70/3.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.70/3.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.05/3.73 Prover 10: Preprocessing ... % 22.05/3.74 Prover 11: Preprocessing ... % 22.05/3.75 Prover 7: Preprocessing ... % 22.05/3.76 Prover 8: Preprocessing ... % 22.05/3.77 Prover 13: Preprocessing ... % 23.08/3.84 Prover 10: Warning: ignoring some quantifiers % 23.08/3.86 Prover 10: Constructing countermodel ... % 23.08/3.86 Prover 7: Warning: ignoring some quantifiers % 23.08/3.90 Prover 7: Constructing countermodel ... % 23.78/3.94 Prover 13: Warning: ignoring some quantifiers % 23.78/3.97 Prover 8: Warning: ignoring some quantifiers % 23.78/3.97 Prover 13: Constructing countermodel ... % 23.78/3.99 Prover 8: Constructing countermodel ... % 28.60/4.58 Prover 7: Found proof (size 60) % 28.60/4.58 Prover 7: proved (999ms) % 28.60/4.58 Prover 1: stopped % 28.60/4.58 Prover 8: stopped % 28.60/4.58 Prover 13: stopped % 28.60/4.58 Prover 10: stopped % 28.60/4.59 Prover 11: stopped % 34.27/5.96 Prover 4: Warning: ignoring some quantifiers % 34.90/6.15 Prover 4: Constructing countermodel ... % 35.37/6.16 Prover 4: stopped % 35.37/6.16 % 35.37/6.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 35.37/6.16 % 35.37/6.18 % SZS output start Proof for theBenchmark % 35.37/6.19 Assumptions after simplification: % 35.37/6.19 --------------------------------- % 35.37/6.19 % 35.37/6.19 (d1_rmod_5) % 35.55/6.26 $i(k1_xboole_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 35.55/6.26 (k1_rlvect_1(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ % 35.55/6.26 v5_vectsp_2(v1, v0) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ % 35.55/6.26 v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ % 35.55/6.26 v6_rlvect_1(v1) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ % 35.55/6.26 v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ % 35.55/6.26 v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | % 35.55/6.26 ? [v3: $i] : ? [v4: $i] : (u1_struct_0(v1) = v3 & k1_zfmisc_1(v3) = v4 & % 35.55/6.26 $i(v4) & $i(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = % 35.55/6.26 k1_xboole_0 | ~ (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ $i(v5) | % 35.55/6.26 ~ m2_rmod_4(v6, v0, v1, v5) | ~ v1_rmod_5(v5, v0, v1) | ~ % 35.55/6.26 m1_subset_1(v5, v4) | ? [v8: $i] : ( ~ (v8 = v2) & k5_rmod_4(v0, v1, % 35.55/6.26 v6) = v8 & $i(v8))) & ! [v5: $i] : ! [v6: $i] : ( ~ (k5_rmod_4(v0, % 35.55/6.26 v1, v6) = v2) | ~ $i(v6) | ~ $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) % 35.55/6.26 | ~ v1_rmod_5(v5, v0, v1) | ~ m1_subset_1(v5, v4) | k2_rmod_4(v0, v1, % 35.55/6.26 v6) = k1_xboole_0) & ! [v5: $i] : ( ~ $i(v5) | ~ m1_subset_1(v5, v4) % 35.55/6.26 | v1_rmod_5(v5, v0, v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = % 35.55/6.26 k1_xboole_0) & k5_rmod_4(v0, v1, v6) = v2 & k2_rmod_4(v0, v1, v6) = % 35.55/6.26 v7 & $i(v7) & $i(v6) & $i(v2) & m2_rmod_4(v6, v0, v1, v5))))) & ! % 35.55/6.26 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (u1_struct_0(v1) = v2) | ~ $i(v1) % 35.55/6.26 | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ % 35.55/6.26 l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ % 35.55/6.26 v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 35.55/6.26 v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 35.55/6.26 v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 35.55/6.26 v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : ? [v4: % 35.55/6.26 $i] : (k1_rlvect_1(v1) = v4 & k1_zfmisc_1(v2) = v3 & $i(v4) & $i(v3) & ! % 35.55/6.26 [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = k1_xboole_0 | ~ % 35.55/6.26 (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ m2_rmod_4(v6, % 35.55/6.26 v0, v1, v5) | ~ v1_rmod_5(v5, v0, v1) | ~ m1_subset_1(v5, v3) | ? % 35.55/6.26 [v8: $i] : ( ~ (v8 = v4) & k5_rmod_4(v0, v1, v6) = v8 & $i(v8))) & ! % 35.55/6.26 [v5: $i] : ! [v6: $i] : ( ~ (k5_rmod_4(v0, v1, v6) = v4) | ~ $i(v6) | ~ % 35.55/6.26 $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) | ~ v1_rmod_5(v5, v0, v1) | ~ % 35.55/6.26 m1_subset_1(v5, v3) | k2_rmod_4(v0, v1, v6) = k1_xboole_0) & ! [v5: $i] % 35.55/6.26 : ( ~ $i(v5) | ~ m1_subset_1(v5, v3) | v1_rmod_5(v5, v0, v1) | ? [v6: % 35.55/6.26 $i] : ? [v7: $i] : ( ~ (v7 = k1_xboole_0) & k5_rmod_4(v0, v1, v6) = % 35.55/6.26 v4 & k2_rmod_4(v0, v1, v6) = v7 & $i(v7) & $i(v6) & m2_rmod_4(v6, v0, % 35.55/6.26 v1, v5))))) % 35.55/6.26 % 35.55/6.26 (t25_rmod_4) % 35.55/6.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (u1_struct_0(v1) = v2) | ~ % 35.55/6.27 $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ % 35.55/6.27 l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ % 35.55/6.27 v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 35.55/6.27 v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 35.55/6.27 v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 35.55/6.27 v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : % 35.55/6.27 (k1_zfmisc_1(v2) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 35.55/6.27 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ m2_rmod_4(v6, v0, v1, v4) | ~ % 35.55/6.27 r1_tarski(v4, v5) | ~ m1_subset_1(v5, v3) | ~ m1_subset_1(v4, v3) | % 35.55/6.27 m2_rmod_4(v6, v0, v1, v5)))) % 35.55/6.27 % 35.55/6.27 (t2_rmod_5) % 35.55/6.27 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 35.55/6.27 $i] : (u1_struct_0(v1) = v2 & k1_zfmisc_1(v2) = v3 & $i(v5) & $i(v4) & % 35.55/6.27 $i(v3) & $i(v2) & $i(v1) & $i(v0) & v1_rmod_5(v5, v0, v1) & r1_tarski(v4, % 35.55/6.27 v5) & m1_subset_1(v5, v3) & m1_subset_1(v4, v3) & l1_vectsp_2(v1, v0) & % 35.55/6.27 v5_vectsp_2(v1, v0) & l3_vectsp_1(v0) & v8_vectsp_1(v0) & v7_vectsp_1(v0) & % 35.55/6.27 v6_vectsp_1(v0) & v4_group_1(v0) & v6_rlvect_1(v1) & v6_rlvect_1(v0) & % 35.55/6.27 v5_rlvect_1(v1) & v5_rlvect_1(v0) & v4_rlvect_1(v1) & v4_rlvect_1(v0) & % 35.55/6.27 v3_rlvect_1(v1) & v3_rlvect_1(v0) & ~ v1_rmod_5(v4, v0, v1) & ~ % 35.55/6.27 v3_struct_0(v1) & ~ v3_struct_0(v0)) % 35.55/6.27 % 35.55/6.27 (function-axioms) % 35.55/6.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 35.55/6.28 $i] : (v1 = v0 | ~ (k8_funct_2(v5, v4, v3, v2) = v1) | ~ (k8_funct_2(v5, % 35.55/6.28 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 35.55/6.28 $i] : ! [v4: $i] : (v1 = v0 | ~ (a_3_0_rmod_4(v4, v3, v2) = v1) | ~ % 35.55/6.28 (a_3_0_rmod_4(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 35.55/6.28 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (k5_rmod_4(v4, v3, v2) = v1) | ~ % 35.55/6.28 (k5_rmod_4(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 35.55/6.28 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (k2_rmod_4(v4, v3, v2) = v1) | ~ % 35.55/6.28 (k2_rmod_4(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 35.55/6.28 [v3: $i] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = % 35.55/6.28 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 35.55/6.28 ~ (k1_funct_2(v3, v2) = v1) | ~ (k1_funct_2(v3, v2) = v0)) & ! [v0: $i] : % 35.55/6.28 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k1_fraenkel(v3, v2) = % 35.55/6.28 v1) | ~ (k1_fraenkel(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 35.55/6.28 $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ % 35.55/6.28 (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 35.55/6.28 = v0 | ~ (k1_rlvect_1(v2) = v1) | ~ (k1_rlvect_1(v2) = v0)) & ! [v0: $i] % 35.55/6.28 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~ % 35.55/6.28 (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 35.55/6.28 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 35.55/6.28 % 35.55/6.28 Further assumptions not needed in the proof: % 35.55/6.28 -------------------------------------------- % 35.55/6.28 antisymmetry_r2_hidden, cc1_relset_1, d5_rmod_4, dt_k1_fraenkel, dt_k1_funct_1, % 35.55/6.28 dt_k1_funct_2, dt_k1_rlvect_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_rmod_4, % 35.55/6.28 dt_k2_zfmisc_1, dt_k5_rmod_4, dt_k8_funct_2, dt_l1_group_1, dt_l1_rlvect_1, % 35.55/6.28 dt_l1_struct_0, dt_l1_vectsp_1, dt_l1_vectsp_2, dt_l2_struct_0, dt_l2_vectsp_1, % 35.55/6.28 dt_l3_vectsp_1, dt_m1_fraenkel, dt_m1_relset_1, dt_m1_rmod_4, dt_m1_subset_1, % 35.55/6.28 dt_m2_fraenkel, dt_m2_relset_1, dt_m2_rmod_4, dt_u1_struct_0, % 35.55/6.28 existence_l1_group_1, existence_l1_rlvect_1, existence_l1_struct_0, % 35.55/6.28 existence_l1_vectsp_1, existence_l1_vectsp_2, existence_l2_struct_0, % 35.55/6.28 existence_l2_vectsp_1, existence_l3_vectsp_1, existence_m1_fraenkel, % 35.55/6.28 existence_m1_relset_1, existence_m1_rmod_4, existence_m1_subset_1, % 35.55/6.28 existence_m2_fraenkel, existence_m2_relset_1, existence_m2_rmod_4, fc1_struct_0, % 35.55/6.28 fc1_subset_1, fc1_xboole_0, fc4_subset_1, fraenkel_a_3_0_rmod_4, rc1_subset_1, % 35.55/6.28 rc1_xboole_0, rc2_rlvect_2, rc2_subset_1, rc2_xboole_0, rc3_struct_0, % 35.55/6.28 rc4_struct_0, rc5_struct_0, rc9_vectsp_2, redefinition_k1_fraenkel, % 35.55/6.28 redefinition_k8_funct_2, redefinition_m2_fraenkel, redefinition_m2_relset_1, % 35.55/6.28 reflexivity_r1_tarski, t1_subset, t2_subset, t2_tarski, t3_subset, t4_subset, % 35.55/6.28 t5_subset, t6_boole, t7_boole, t8_boole % 35.55/6.28 % 35.55/6.28 Those formulas are unsatisfiable: % 35.55/6.28 --------------------------------- % 35.55/6.28 % 35.55/6.28 Begin of proof % 35.55/6.28 | % 35.55/6.28 | ALPHA: (d1_rmod_5) implies: % 35.55/6.28 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (u1_struct_0(v1) = v2) | % 35.55/6.28 | ~ $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, % 35.55/6.28 | v0) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) % 35.55/6.28 | | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 35.55/6.28 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 35.55/6.28 | v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 35.55/6.28 | v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : % 35.55/6.28 | ? [v4: $i] : (k1_rlvect_1(v1) = v4 & k1_zfmisc_1(v2) = v3 & $i(v4) & % 35.55/6.28 | $i(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = % 35.55/6.28 | k1_xboole_0 | ~ (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ % 35.55/6.28 | $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) | ~ v1_rmod_5(v5, v0, v1) % 35.55/6.28 | | ~ m1_subset_1(v5, v3) | ? [v8: $i] : ( ~ (v8 = v4) & % 35.55/6.28 | k5_rmod_4(v0, v1, v6) = v8 & $i(v8))) & ! [v5: $i] : ! [v6: % 35.55/6.28 | $i] : ( ~ (k5_rmod_4(v0, v1, v6) = v4) | ~ $i(v6) | ~ $i(v5) | % 35.55/6.28 | ~ m2_rmod_4(v6, v0, v1, v5) | ~ v1_rmod_5(v5, v0, v1) | ~ % 35.55/6.28 | m1_subset_1(v5, v3) | k2_rmod_4(v0, v1, v6) = k1_xboole_0) & ! % 35.55/6.28 | [v5: $i] : ( ~ $i(v5) | ~ m1_subset_1(v5, v3) | v1_rmod_5(v5, v0, % 35.55/6.28 | v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = k1_xboole_0) & % 35.55/6.28 | k5_rmod_4(v0, v1, v6) = v4 & k2_rmod_4(v0, v1, v6) = v7 & % 35.55/6.28 | $i(v7) & $i(v6) & m2_rmod_4(v6, v0, v1, v5))))) % 35.55/6.29 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_rlvect_1(v1) = v2) | % 35.55/6.29 | ~ $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, % 35.55/6.29 | v0) | ~ l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) % 35.55/6.29 | | ~ v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ % 35.55/6.29 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ % 35.55/6.29 | v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ % 35.55/6.29 | v3_rlvect_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v3: $i] : % 35.55/6.29 | ? [v4: $i] : (u1_struct_0(v1) = v3 & k1_zfmisc_1(v3) = v4 & $i(v4) & % 35.55/6.29 | $i(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = % 35.55/6.29 | k1_xboole_0 | ~ (k2_rmod_4(v0, v1, v6) = v7) | ~ $i(v6) | ~ % 35.55/6.29 | $i(v5) | ~ m2_rmod_4(v6, v0, v1, v5) | ~ v1_rmod_5(v5, v0, v1) % 35.55/6.29 | | ~ m1_subset_1(v5, v4) | ? [v8: $i] : ( ~ (v8 = v2) & % 35.55/6.29 | k5_rmod_4(v0, v1, v6) = v8 & $i(v8))) & ! [v5: $i] : ! [v6: % 35.55/6.29 | $i] : ( ~ (k5_rmod_4(v0, v1, v6) = v2) | ~ $i(v6) | ~ $i(v5) | % 35.55/6.29 | ~ m2_rmod_4(v6, v0, v1, v5) | ~ v1_rmod_5(v5, v0, v1) | ~ % 35.55/6.29 | m1_subset_1(v5, v4) | k2_rmod_4(v0, v1, v6) = k1_xboole_0) & ! % 35.55/6.29 | [v5: $i] : ( ~ $i(v5) | ~ m1_subset_1(v5, v4) | v1_rmod_5(v5, v0, % 35.55/6.29 | v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = k1_xboole_0) & % 35.55/6.29 | k5_rmod_4(v0, v1, v6) = v2 & k2_rmod_4(v0, v1, v6) = v7 & % 35.55/6.29 | $i(v7) & $i(v6) & $i(v2) & m2_rmod_4(v6, v0, v1, v5))))) % 35.55/6.29 | % 35.55/6.29 | ALPHA: (function-axioms) implies: % 35.55/6.29 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 35.55/6.29 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 35.55/6.29 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 35.55/6.29 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 35.55/6.29 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 35.55/6.29 | (v1 = v0 | ~ (k2_rmod_4(v4, v3, v2) = v1) | ~ (k2_rmod_4(v4, v3, v2) % 35.55/6.29 | = v0)) % 35.55/6.29 | % 35.55/6.29 | DELTA: instantiating (t2_rmod_5) with fresh symbols all_78_0, all_78_1, % 35.55/6.29 | all_78_2, all_78_3, all_78_4, all_78_5 gives: % 35.55/6.29 | (6) u1_struct_0(all_78_4) = all_78_3 & k1_zfmisc_1(all_78_3) = all_78_2 & % 35.55/6.29 | $i(all_78_0) & $i(all_78_1) & $i(all_78_2) & $i(all_78_3) & % 35.55/6.29 | $i(all_78_4) & $i(all_78_5) & v1_rmod_5(all_78_0, all_78_5, all_78_4) & % 35.55/6.29 | r1_tarski(all_78_1, all_78_0) & m1_subset_1(all_78_0, all_78_2) & % 35.55/6.29 | m1_subset_1(all_78_1, all_78_2) & l1_vectsp_2(all_78_4, all_78_5) & % 35.55/6.29 | v5_vectsp_2(all_78_4, all_78_5) & l3_vectsp_1(all_78_5) & % 35.55/6.29 | v8_vectsp_1(all_78_5) & v7_vectsp_1(all_78_5) & v6_vectsp_1(all_78_5) & % 35.55/6.29 | v4_group_1(all_78_5) & v6_rlvect_1(all_78_4) & v6_rlvect_1(all_78_5) & % 35.55/6.29 | v5_rlvect_1(all_78_4) & v5_rlvect_1(all_78_5) & v4_rlvect_1(all_78_4) & % 35.55/6.29 | v4_rlvect_1(all_78_5) & v3_rlvect_1(all_78_4) & v3_rlvect_1(all_78_5) & % 35.55/6.29 | ~ v1_rmod_5(all_78_1, all_78_5, all_78_4) & ~ v3_struct_0(all_78_4) & % 35.55/6.29 | ~ v3_struct_0(all_78_5) % 35.55/6.29 | % 35.55/6.29 | ALPHA: (6) implies: % 35.55/6.29 | (7) ~ v3_struct_0(all_78_5) % 35.55/6.29 | (8) ~ v3_struct_0(all_78_4) % 35.55/6.29 | (9) ~ v1_rmod_5(all_78_1, all_78_5, all_78_4) % 35.55/6.29 | (10) v3_rlvect_1(all_78_5) % 35.55/6.29 | (11) v3_rlvect_1(all_78_4) % 35.55/6.29 | (12) v4_rlvect_1(all_78_5) % 35.55/6.29 | (13) v4_rlvect_1(all_78_4) % 35.55/6.29 | (14) v5_rlvect_1(all_78_5) % 35.55/6.29 | (15) v5_rlvect_1(all_78_4) % 35.55/6.30 | (16) v6_rlvect_1(all_78_5) % 35.55/6.30 | (17) v6_rlvect_1(all_78_4) % 35.55/6.30 | (18) v4_group_1(all_78_5) % 35.55/6.30 | (19) v6_vectsp_1(all_78_5) % 35.55/6.30 | (20) v7_vectsp_1(all_78_5) % 35.55/6.30 | (21) v8_vectsp_1(all_78_5) % 35.55/6.30 | (22) l3_vectsp_1(all_78_5) % 35.55/6.30 | (23) v5_vectsp_2(all_78_4, all_78_5) % 35.55/6.30 | (24) l1_vectsp_2(all_78_4, all_78_5) % 35.55/6.30 | (25) m1_subset_1(all_78_1, all_78_2) % 35.55/6.30 | (26) m1_subset_1(all_78_0, all_78_2) % 35.55/6.30 | (27) r1_tarski(all_78_1, all_78_0) % 35.55/6.30 | (28) v1_rmod_5(all_78_0, all_78_5, all_78_4) % 35.55/6.30 | (29) $i(all_78_5) % 35.55/6.30 | (30) $i(all_78_4) % 35.55/6.30 | (31) $i(all_78_1) % 35.55/6.30 | (32) $i(all_78_0) % 35.55/6.30 | (33) k1_zfmisc_1(all_78_3) = all_78_2 % 35.55/6.30 | (34) u1_struct_0(all_78_4) = all_78_3 % 35.55/6.30 | % 35.55/6.30 | GROUND_INST: instantiating (1) with all_78_5, all_78_4, all_78_3, simplifying % 35.55/6.30 | with (7), (8), (10), (11), (12), (13), (14), (15), (16), (17), % 35.55/6.30 | (18), (19), (20), (21), (22), (23), (24), (29), (30), (34) gives: % 35.55/6.30 | (35) ? [v0: $i] : ? [v1: $i] : (k1_rlvect_1(all_78_4) = v1 & % 35.55/6.30 | k1_zfmisc_1(all_78_3) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 35.55/6.30 | $i] : ! [v4: $i] : (v4 = k1_xboole_0 | ~ (k2_rmod_4(all_78_5, % 35.55/6.30 | all_78_4, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ m2_rmod_4(v3, % 35.55/6.30 | all_78_5, all_78_4, v2) | ~ v1_rmod_5(v2, all_78_5, all_78_4) | % 35.55/6.30 | ~ m1_subset_1(v2, v0) | ? [v5: $i] : ( ~ (v5 = v1) & % 35.55/6.30 | k5_rmod_4(all_78_5, all_78_4, v3) = v5 & $i(v5))) & ! [v2: $i] % 35.55/6.30 | : ! [v3: $i] : ( ~ (k5_rmod_4(all_78_5, all_78_4, v3) = v1) | ~ % 35.55/6.30 | $i(v3) | ~ $i(v2) | ~ m2_rmod_4(v3, all_78_5, all_78_4, v2) | ~ % 35.55/6.30 | v1_rmod_5(v2, all_78_5, all_78_4) | ~ m1_subset_1(v2, v0) | % 35.55/6.30 | k2_rmod_4(all_78_5, all_78_4, v3) = k1_xboole_0) & ! [v2: $i] : ( % 35.55/6.30 | ~ $i(v2) | ~ m1_subset_1(v2, v0) | v1_rmod_5(v2, all_78_5, % 35.55/6.30 | all_78_4) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = k1_xboole_0) & % 35.55/6.30 | k5_rmod_4(all_78_5, all_78_4, v3) = v1 & k2_rmod_4(all_78_5, % 35.55/6.30 | all_78_4, v3) = v4 & $i(v4) & $i(v3) & m2_rmod_4(v3, all_78_5, % 35.55/6.30 | all_78_4, v2)))) % 35.55/6.30 | % 35.55/6.30 | GROUND_INST: instantiating (t25_rmod_4) with all_78_5, all_78_4, all_78_3, % 35.55/6.30 | simplifying with (7), (8), (10), (11), (12), (13), (14), (15), % 35.55/6.30 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (29), (30), % 35.55/6.30 | (34) gives: % 35.55/6.30 | (36) ? [v0: $i] : (k1_zfmisc_1(all_78_3) = v0 & $i(v0) & ! [v1: $i] : ! % 35.55/6.30 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 35.55/6.30 | m2_rmod_4(v3, all_78_5, all_78_4, v1) | ~ r1_tarski(v1, v2) | ~ % 35.55/6.30 | m1_subset_1(v2, v0) | ~ m1_subset_1(v1, v0) | m2_rmod_4(v3, % 35.55/6.30 | all_78_5, all_78_4, v2))) % 35.55/6.30 | % 35.55/6.30 | DELTA: instantiating (36) with fresh symbol all_108_0 gives: % 35.55/6.31 | (37) k1_zfmisc_1(all_78_3) = all_108_0 & $i(all_108_0) & ! [v0: $i] : ! % 35.55/6.31 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 35.55/6.31 | m2_rmod_4(v2, all_78_5, all_78_4, v0) | ~ r1_tarski(v0, v1) | ~ % 35.55/6.31 | m1_subset_1(v1, all_108_0) | ~ m1_subset_1(v0, all_108_0) | % 35.55/6.31 | m2_rmod_4(v2, all_78_5, all_78_4, v1)) % 35.55/6.31 | % 35.55/6.31 | ALPHA: (37) implies: % 35.55/6.31 | (38) k1_zfmisc_1(all_78_3) = all_108_0 % 35.55/6.31 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 35.55/6.31 | $i(v0) | ~ m2_rmod_4(v2, all_78_5, all_78_4, v0) | ~ r1_tarski(v0, % 35.55/6.31 | v1) | ~ m1_subset_1(v1, all_108_0) | ~ m1_subset_1(v0, % 35.55/6.31 | all_108_0) | m2_rmod_4(v2, all_78_5, all_78_4, v1)) % 35.55/6.31 | % 35.55/6.31 | DELTA: instantiating (35) with fresh symbols all_111_0, all_111_1 gives: % 35.55/6.31 | (40) k1_rlvect_1(all_78_4) = all_111_0 & k1_zfmisc_1(all_78_3) = all_111_1 % 35.55/6.31 | & $i(all_111_0) & $i(all_111_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 35.55/6.31 | $i] : (v2 = k1_xboole_0 | ~ (k2_rmod_4(all_78_5, all_78_4, v1) = % 35.55/6.31 | v2) | ~ $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, all_78_5, all_78_4, % 35.55/6.31 | v0) | ~ v1_rmod_5(v0, all_78_5, all_78_4) | ~ m1_subset_1(v0, % 35.55/6.31 | all_111_1) | ? [v3: any] : ( ~ (v3 = all_111_0) & % 35.55/6.31 | k5_rmod_4(all_78_5, all_78_4, v1) = v3 & $i(v3))) & ! [v0: $i] : % 35.55/6.31 | ! [v1: $i] : ( ~ (k5_rmod_4(all_78_5, all_78_4, v1) = all_111_0) | ~ % 35.55/6.31 | $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, all_78_5, all_78_4, v0) | ~ % 35.55/6.31 | v1_rmod_5(v0, all_78_5, all_78_4) | ~ m1_subset_1(v0, all_111_1) | % 35.55/6.31 | k2_rmod_4(all_78_5, all_78_4, v1) = k1_xboole_0) & ! [v0: $i] : ( ~ % 35.55/6.31 | $i(v0) | ~ m1_subset_1(v0, all_111_1) | v1_rmod_5(v0, all_78_5, % 35.55/6.31 | all_78_4) | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = k1_xboole_0) & % 35.55/6.31 | k5_rmod_4(all_78_5, all_78_4, v1) = all_111_0 & % 35.55/6.31 | k2_rmod_4(all_78_5, all_78_4, v1) = v2 & $i(v2) & $i(v1) & % 35.55/6.31 | m2_rmod_4(v1, all_78_5, all_78_4, v0))) % 35.55/6.31 | % 35.55/6.31 | ALPHA: (40) implies: % 35.55/6.31 | (41) k1_zfmisc_1(all_78_3) = all_111_1 % 35.55/6.31 | (42) k1_rlvect_1(all_78_4) = all_111_0 % 35.55/6.31 | (43) ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_111_1) | % 35.55/6.31 | v1_rmod_5(v0, all_78_5, all_78_4) | ? [v1: $i] : ? [v2: $i] : ( ~ % 35.55/6.31 | (v2 = k1_xboole_0) & k5_rmod_4(all_78_5, all_78_4, v1) = all_111_0 % 35.55/6.31 | & k2_rmod_4(all_78_5, all_78_4, v1) = v2 & $i(v2) & $i(v1) & % 35.55/6.31 | m2_rmod_4(v1, all_78_5, all_78_4, v0))) % 35.55/6.31 | (44) ! [v0: $i] : ! [v1: $i] : ( ~ (k5_rmod_4(all_78_5, all_78_4, v1) = % 35.55/6.31 | all_111_0) | ~ $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, all_78_5, % 35.55/6.31 | all_78_4, v0) | ~ v1_rmod_5(v0, all_78_5, all_78_4) | ~ % 35.55/6.31 | m1_subset_1(v0, all_111_1) | k2_rmod_4(all_78_5, all_78_4, v1) = % 35.55/6.31 | k1_xboole_0) % 35.55/6.31 | % 35.55/6.31 | GROUND_INST: instantiating (43) with all_78_1, simplifying with (9), (31) % 35.55/6.31 | gives: % 35.55/6.31 | (45) ~ m1_subset_1(all_78_1, all_111_1) | ? [v0: $i] : ? [v1: $i] : ( ~ % 35.55/6.31 | (v1 = k1_xboole_0) & k5_rmod_4(all_78_5, all_78_4, v0) = all_111_0 & % 35.55/6.31 | k2_rmod_4(all_78_5, all_78_4, v0) = v1 & $i(v1) & $i(v0) & % 35.55/6.31 | m2_rmod_4(v0, all_78_5, all_78_4, all_78_1)) % 35.55/6.31 | % 35.55/6.31 | GROUND_INST: instantiating (3) with all_78_2, all_111_1, all_78_3, simplifying % 35.55/6.31 | with (33), (41) gives: % 35.55/6.31 | (46) all_111_1 = all_78_2 % 35.55/6.31 | % 35.55/6.31 | GROUND_INST: instantiating (3) with all_108_0, all_111_1, all_78_3, % 35.55/6.31 | simplifying with (38), (41) gives: % 35.55/6.31 | (47) all_111_1 = all_108_0 % 35.55/6.31 | % 35.55/6.31 | COMBINE_EQS: (46), (47) imply: % 35.55/6.31 | (48) all_108_0 = all_78_2 % 35.55/6.31 | % 35.55/6.32 | BETA: splitting (45) gives: % 35.55/6.32 | % 35.55/6.32 | Case 1: % 35.55/6.32 | | % 35.55/6.32 | | (49) ~ m1_subset_1(all_78_1, all_111_1) % 35.55/6.32 | | % 35.55/6.32 | | REDUCE: (46), (49) imply: % 35.55/6.32 | | (50) ~ m1_subset_1(all_78_1, all_78_2) % 35.55/6.32 | | % 35.55/6.32 | | PRED_UNIFY: (25), (50) imply: % 35.55/6.32 | | (51) $false % 35.55/6.32 | | % 35.55/6.32 | | CLOSE: (51) is inconsistent. % 35.55/6.32 | | % 35.55/6.32 | Case 2: % 35.55/6.32 | | % 35.55/6.32 | | (52) m1_subset_1(all_78_1, all_111_1) % 35.55/6.32 | | (53) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = k1_xboole_0) & % 35.55/6.32 | | k5_rmod_4(all_78_5, all_78_4, v0) = all_111_0 & % 35.55/6.32 | | k2_rmod_4(all_78_5, all_78_4, v0) = v1 & $i(v1) & $i(v0) & % 35.55/6.32 | | m2_rmod_4(v0, all_78_5, all_78_4, all_78_1)) % 35.55/6.32 | | % 35.55/6.32 | | DELTA: instantiating (53) with fresh symbols all_122_0, all_122_1 gives: % 35.55/6.32 | | (54) ~ (all_122_0 = k1_xboole_0) & k5_rmod_4(all_78_5, all_78_4, % 35.55/6.32 | | all_122_1) = all_111_0 & k2_rmod_4(all_78_5, all_78_4, all_122_1) % 35.55/6.32 | | = all_122_0 & $i(all_122_0) & $i(all_122_1) & m2_rmod_4(all_122_1, % 35.55/6.32 | | all_78_5, all_78_4, all_78_1) % 35.55/6.32 | | % 35.55/6.32 | | ALPHA: (54) implies: % 35.55/6.32 | | (55) ~ (all_122_0 = k1_xboole_0) % 35.55/6.32 | | (56) m2_rmod_4(all_122_1, all_78_5, all_78_4, all_78_1) % 35.55/6.32 | | (57) $i(all_122_1) % 35.55/6.32 | | (58) k2_rmod_4(all_78_5, all_78_4, all_122_1) = all_122_0 % 35.55/6.32 | | (59) k5_rmod_4(all_78_5, all_78_4, all_122_1) = all_111_0 % 35.55/6.32 | | % 35.55/6.32 | | GROUND_INST: instantiating (39) with all_78_1, all_78_0, all_122_1, % 35.55/6.32 | | simplifying with (27), (31), (32), (56), (57) gives: % 35.55/6.32 | | (60) ~ m1_subset_1(all_78_0, all_108_0) | ~ m1_subset_1(all_78_1, % 35.55/6.32 | | all_108_0) | m2_rmod_4(all_122_1, all_78_5, all_78_4, all_78_0) % 35.55/6.32 | | % 35.55/6.32 | | GROUND_INST: instantiating (2) with all_78_5, all_78_4, all_111_0, % 35.55/6.32 | | simplifying with (7), (8), (10), (11), (12), (13), (14), (15), % 35.55/6.32 | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (29), % 35.55/6.32 | | (30), (42) gives: % 35.55/6.32 | | (61) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_78_4) = v0 & % 35.55/6.32 | | k1_zfmisc_1(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] % 35.55/6.32 | | : ! [v4: $i] : (v4 = k1_xboole_0 | ~ (k2_rmod_4(all_78_5, % 35.55/6.32 | | all_78_4, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 35.55/6.32 | | m2_rmod_4(v3, all_78_5, all_78_4, v2) | ~ v1_rmod_5(v2, % 35.55/6.32 | | all_78_5, all_78_4) | ~ m1_subset_1(v2, v1) | ? [v5: any] : % 35.55/6.32 | | ( ~ (v5 = all_111_0) & k5_rmod_4(all_78_5, all_78_4, v3) = v5 & % 35.55/6.32 | | $i(v5))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 35.55/6.32 | | (k5_rmod_4(all_78_5, all_78_4, v3) = all_111_0) | ~ $i(v3) | ~ % 35.55/6.32 | | $i(v2) | ~ m2_rmod_4(v3, all_78_5, all_78_4, v2) | ~ % 35.55/6.32 | | v1_rmod_5(v2, all_78_5, all_78_4) | ~ m1_subset_1(v2, v1) | % 35.55/6.32 | | k2_rmod_4(all_78_5, all_78_4, v3) = k1_xboole_0) & ! [v2: $i] : % 35.55/6.33 | | ( ~ $i(v2) | ~ m1_subset_1(v2, v1) | v1_rmod_5(v2, all_78_5, % 35.55/6.33 | | all_78_4) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = k1_xboole_0) % 35.55/6.33 | | & k5_rmod_4(all_78_5, all_78_4, v3) = all_111_0 & % 35.55/6.33 | | k2_rmod_4(all_78_5, all_78_4, v3) = v4 & $i(v4) & $i(v3) & % 35.55/6.33 | | $i(all_111_0) & m2_rmod_4(v3, all_78_5, all_78_4, v2)))) % 35.55/6.33 | | % 35.55/6.33 | | DELTA: instantiating (61) with fresh symbols all_144_0, all_144_1 gives: % 35.55/6.33 | | (62) u1_struct_0(all_78_4) = all_144_1 & k1_zfmisc_1(all_144_1) = % 35.55/6.33 | | all_144_0 & $i(all_144_0) & $i(all_144_1) & ! [v0: $i] : ! [v1: % 35.55/6.33 | | $i] : ! [v2: $i] : (v2 = k1_xboole_0 | ~ (k2_rmod_4(all_78_5, % 35.55/6.33 | | all_78_4, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, % 35.55/6.33 | | all_78_5, all_78_4, v0) | ~ v1_rmod_5(v0, all_78_5, all_78_4) | % 35.55/6.33 | | ~ m1_subset_1(v0, all_144_0) | ? [v3: any] : ( ~ (v3 = % 35.55/6.33 | | all_111_0) & k5_rmod_4(all_78_5, all_78_4, v1) = v3 & $i(v3))) % 35.55/6.33 | | & ! [v0: $i] : ! [v1: $i] : ( ~ (k5_rmod_4(all_78_5, all_78_4, v1) % 35.55/6.33 | | = all_111_0) | ~ $i(v1) | ~ $i(v0) | ~ m2_rmod_4(v1, % 35.55/6.33 | | all_78_5, all_78_4, v0) | ~ v1_rmod_5(v0, all_78_5, all_78_4) | % 35.55/6.33 | | ~ m1_subset_1(v0, all_144_0) | k2_rmod_4(all_78_5, all_78_4, v1) % 35.55/6.33 | | = k1_xboole_0) & ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, % 35.55/6.33 | | all_144_0) | v1_rmod_5(v0, all_78_5, all_78_4) | ? [v1: $i] : % 35.55/6.33 | | ? [v2: $i] : ( ~ (v2 = k1_xboole_0) & k5_rmod_4(all_78_5, % 35.55/6.33 | | all_78_4, v1) = all_111_0 & k2_rmod_4(all_78_5, all_78_4, v1) % 35.55/6.33 | | = v2 & $i(v2) & $i(v1) & $i(all_111_0) & m2_rmod_4(v1, all_78_5, % 35.55/6.33 | | all_78_4, v0))) % 35.55/6.33 | | % 35.55/6.33 | | ALPHA: (62) implies: % 35.55/6.33 | | (63) k1_zfmisc_1(all_144_1) = all_144_0 % 35.55/6.33 | | (64) u1_struct_0(all_78_4) = all_144_1 % 35.55/6.33 | | (65) ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_144_0) | % 35.55/6.33 | | v1_rmod_5(v0, all_78_5, all_78_4) | ? [v1: $i] : ? [v2: $i] : ( % 35.55/6.33 | | ~ (v2 = k1_xboole_0) & k5_rmod_4(all_78_5, all_78_4, v1) = % 35.55/6.33 | | all_111_0 & k2_rmod_4(all_78_5, all_78_4, v1) = v2 & $i(v2) & % 35.55/6.33 | | $i(v1) & $i(all_111_0) & m2_rmod_4(v1, all_78_5, all_78_4, v0))) % 35.55/6.33 | | % 35.55/6.33 | | GROUND_INST: instantiating (65) with all_78_1, simplifying with (9), (31) % 35.55/6.33 | | gives: % 35.55/6.33 | | (66) ~ m1_subset_1(all_78_1, all_144_0) | ? [v0: $i] : ? [v1: $i] : ( % 35.55/6.33 | | ~ (v1 = k1_xboole_0) & k5_rmod_4(all_78_5, all_78_4, v0) = % 35.55/6.33 | | all_111_0 & k2_rmod_4(all_78_5, all_78_4, v0) = v1 & $i(v1) & % 35.55/6.33 | | $i(v0) & $i(all_111_0) & m2_rmod_4(v0, all_78_5, all_78_4, % 35.55/6.33 | | all_78_1)) % 35.55/6.33 | | % 35.55/6.33 | | BETA: splitting (60) gives: % 35.55/6.33 | | % 35.55/6.33 | | Case 1: % 35.55/6.33 | | | % 35.55/6.33 | | | (67) ~ m1_subset_1(all_78_0, all_108_0) % 35.55/6.33 | | | % 35.55/6.33 | | | REDUCE: (48), (67) imply: % 35.55/6.33 | | | (68) ~ m1_subset_1(all_78_0, all_78_2) % 35.55/6.33 | | | % 35.55/6.33 | | | PRED_UNIFY: (26), (68) imply: % 35.55/6.33 | | | (69) $false % 35.55/6.33 | | | % 35.55/6.33 | | | CLOSE: (69) is inconsistent. % 35.55/6.33 | | | % 35.55/6.33 | | Case 2: % 35.55/6.33 | | | % 35.55/6.33 | | | (70) m1_subset_1(all_78_0, all_108_0) % 35.55/6.33 | | | (71) ~ m1_subset_1(all_78_1, all_108_0) | m2_rmod_4(all_122_1, % 35.55/6.33 | | | all_78_5, all_78_4, all_78_0) % 35.55/6.33 | | | % 35.55/6.33 | | | BETA: splitting (71) gives: % 35.55/6.33 | | | % 35.55/6.33 | | | Case 1: % 35.55/6.33 | | | | % 35.55/6.33 | | | | (72) ~ m1_subset_1(all_78_1, all_108_0) % 35.55/6.33 | | | | % 35.55/6.33 | | | | REDUCE: (48), (72) imply: % 35.55/6.33 | | | | (73) ~ m1_subset_1(all_78_1, all_78_2) % 35.55/6.33 | | | | % 35.55/6.33 | | | | PRED_UNIFY: (25), (73) imply: % 35.55/6.33 | | | | (74) $false % 35.55/6.33 | | | | % 35.55/6.33 | | | | CLOSE: (74) is inconsistent. % 35.55/6.33 | | | | % 35.55/6.33 | | | Case 2: % 35.55/6.33 | | | | % 35.55/6.33 | | | | (75) m1_subset_1(all_78_1, all_108_0) % 35.55/6.33 | | | | (76) m2_rmod_4(all_122_1, all_78_5, all_78_4, all_78_0) % 35.55/6.33 | | | | % 35.55/6.34 | | | | GROUND_INST: instantiating (3) with all_78_2, all_144_0, all_78_3, % 35.55/6.34 | | | | simplifying with (33) gives: % 35.55/6.34 | | | | (77) all_144_0 = all_78_2 | ~ (k1_zfmisc_1(all_78_3) = all_144_0) % 35.55/6.34 | | | | % 35.55/6.34 | | | | GROUND_INST: instantiating (4) with all_78_3, all_144_1, all_78_4, % 35.55/6.34 | | | | simplifying with (34), (64) gives: % 35.55/6.34 | | | | (78) all_144_1 = all_78_3 % 35.55/6.34 | | | | % 35.55/6.34 | | | | REDUCE: (63), (78) imply: % 35.55/6.34 | | | | (79) k1_zfmisc_1(all_78_3) = all_144_0 % 35.55/6.34 | | | | % 35.55/6.34 | | | | BETA: splitting (77) gives: % 35.55/6.34 | | | | % 35.55/6.34 | | | | Case 1: % 35.55/6.34 | | | | | % 35.55/6.34 | | | | | (80) ~ (k1_zfmisc_1(all_78_3) = all_144_0) % 35.55/6.34 | | | | | % 35.55/6.34 | | | | | PRED_UNIFY: (79), (80) imply: % 35.55/6.34 | | | | | (81) $false % 35.55/6.34 | | | | | % 35.55/6.34 | | | | | CLOSE: (81) is inconsistent. % 35.55/6.34 | | | | | % 35.55/6.34 | | | | Case 2: % 35.55/6.34 | | | | | % 35.55/6.34 | | | | | (82) all_144_0 = all_78_2 % 35.55/6.34 | | | | | % 35.55/6.34 | | | | | BETA: splitting (66) gives: % 35.55/6.34 | | | | | % 35.55/6.34 | | | | | Case 1: % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | (83) ~ m1_subset_1(all_78_1, all_144_0) % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | REDUCE: (82), (83) imply: % 35.55/6.34 | | | | | | (84) ~ m1_subset_1(all_78_1, all_78_2) % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | PRED_UNIFY: (25), (84) imply: % 35.55/6.34 | | | | | | (85) $false % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | CLOSE: (85) is inconsistent. % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | Case 2: % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | GROUND_INST: instantiating (44) with all_78_0, all_122_1, % 35.55/6.34 | | | | | | simplifying with (28), (32), (57), (59), (76) gives: % 35.55/6.34 | | | | | | (86) ~ m1_subset_1(all_78_0, all_111_1) | k2_rmod_4(all_78_5, % 35.55/6.34 | | | | | | all_78_4, all_122_1) = k1_xboole_0 % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | BETA: splitting (86) gives: % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | | Case 1: % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | (87) k2_rmod_4(all_78_5, all_78_4, all_122_1) = k1_xboole_0 % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | GROUND_INST: instantiating (5) with all_122_0, k1_xboole_0, % 35.55/6.34 | | | | | | | all_122_1, all_78_4, all_78_5, simplifying with (58), % 35.55/6.34 | | | | | | | (87) gives: % 35.55/6.34 | | | | | | | (88) all_122_0 = k1_xboole_0 % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | REDUCE: (55), (88) imply: % 35.55/6.34 | | | | | | | (89) $false % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | CLOSE: (89) is inconsistent. % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | Case 2: % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | (90) ~ m1_subset_1(all_78_0, all_111_1) % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | REDUCE: (46), (90) imply: % 35.55/6.34 | | | | | | | (91) ~ m1_subset_1(all_78_0, all_78_2) % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | PRED_UNIFY: (26), (91) imply: % 35.55/6.34 | | | | | | | (92) $false % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | | CLOSE: (92) is inconsistent. % 35.55/6.34 | | | | | | | % 35.55/6.34 | | | | | | End of split % 35.55/6.34 | | | | | | % 35.55/6.34 | | | | | End of split % 35.55/6.34 | | | | | % 35.55/6.34 | | | | End of split % 35.55/6.34 | | | | % 35.55/6.34 | | | End of split % 35.55/6.34 | | | % 35.55/6.34 | | End of split % 35.55/6.34 | | % 35.55/6.34 | End of split % 35.55/6.34 | % 35.55/6.34 End of proof % 35.55/6.34 % SZS output end Proof for theBenchmark % 35.55/6.34 % 35.55/6.34 5751ms %------------------------------------------------------------------------------