%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP019_1 : TPTP v8.1.2. Bugfixed v7.5.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 04:08:55 EDT 2023 % Result : Theorem 11.55s 2.41s % Output : Proof 15.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP019_1 : TPTP v8.1.2. Bugfixed v7.5.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Sun Aug 27 13:58:27 EDT 2023 % 0.17/0.35 % CPUTime : % 0.19/0.58 ________ _____ % 0.19/0.58 ___ __ \_________(_)________________________________ % 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.58 (2023-06-19) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2023 % 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.58 Amanda Stjerna. % 0.19/0.58 Free software under BSD-3-Clause. % 0.19/0.58 % 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.59 Running up to 7 provers in parallel. % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.34/1.29 Prover 4: Preprocessing ... % 4.34/1.29 Prover 1: Preprocessing ... % 4.34/1.33 Prover 5: Preprocessing ... % 4.34/1.33 Prover 6: Preprocessing ... % 4.34/1.33 Prover 0: Preprocessing ... % 4.34/1.33 Prover 3: Preprocessing ... % 4.34/1.33 Prover 2: Preprocessing ... % 9.52/2.10 Prover 1: Warning: ignoring some quantifiers % 9.52/2.15 Prover 3: Warning: ignoring some quantifiers % 9.52/2.15 Prover 4: Warning: ignoring some quantifiers % 9.52/2.17 Prover 1: Constructing countermodel ... % 9.52/2.19 Prover 3: Constructing countermodel ... % 9.52/2.19 Prover 6: Proving ... % 9.52/2.21 Prover 0: Proving ... % 9.52/2.22 Prover 5: Proving ... % 10.64/2.23 Prover 4: Constructing countermodel ... % 11.55/2.36 Prover 2: Proving ... % 11.55/2.40 Prover 3: proved (1796ms) % 11.55/2.40 % 11.55/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.55/2.41 % 11.55/2.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.55/2.41 Prover 0: stopped % 11.55/2.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.55/2.41 Prover 5: stopped % 12.32/2.42 Prover 6: proved (1801ms) % 12.32/2.42 % 12.32/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.32/2.42 % 12.32/2.43 Prover 2: stopped % 12.32/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.32/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.32/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.89/2.53 Prover 8: Preprocessing ... % 12.89/2.54 Prover 10: Preprocessing ... % 12.89/2.55 Prover 11: Preprocessing ... % 12.89/2.55 Prover 7: Preprocessing ... % 12.89/2.56 Prover 13: Preprocessing ... % 14.46/2.72 Prover 1: Found proof (size 19) % 14.64/2.72 Prover 1: proved (2117ms) % 14.64/2.72 Prover 4: stopped % 14.64/2.74 Prover 10: Warning: ignoring some quantifiers % 14.64/2.74 Prover 7: Warning: ignoring some quantifiers % 14.64/2.75 Prover 13: stopped % 14.64/2.76 Prover 10: Constructing countermodel ... % 14.64/2.77 Prover 7: Constructing countermodel ... % 14.64/2.78 Prover 10: stopped % 14.64/2.79 Prover 7: stopped % 14.64/2.79 Prover 8: Warning: ignoring some quantifiers % 14.64/2.81 Prover 8: Constructing countermodel ... % 15.31/2.82 Prover 8: stopped % 15.31/2.85 Prover 11: Warning: ignoring some quantifiers % 15.31/2.86 Prover 11: Constructing countermodel ... % 15.31/2.87 Prover 11: stopped % 15.31/2.87 % 15.31/2.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.31/2.87 % 15.31/2.87 % SZS output start Proof for theBenchmark % 15.31/2.88 Assumptions after simplification: % 15.31/2.88 --------------------------------- % 15.31/2.88 % 15.31/2.88 (thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) % 15.68/2.90 mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) & ? [v0: % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.90 : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = v0 & % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0) % 15.68/2.90 & ! [v1: % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.90 : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0) | ~ % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1)) % 15.68/2.90 & ! [v1: % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.90 : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = v1))) % 15.68/2.90 % 15.68/2.90 (thm_2Ecomplex_2ECOMPLEX__INV__NZ) % 15.68/2.90 mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) & ? [v0: % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.90 : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = v0 & % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0) % 15.68/2.90 & ? [v1: % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.90 : ( ~ (v1 = v0) & mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0 & % 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1))) % 15.68/2.90 % 15.68/2.90 (function-axioms) % 15.68/2.92 ! [v0: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v2: mono_2Etyop_2Enum_2Enum] : ! [v3: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : (v1 = v0 | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3, % 15.68/2.92 v2) = v1) | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3, % 15.68/2.92 v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v2: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v3: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : (v1 = v0 | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3, % 15.68/2.92 v2) = v1) | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3, % 15.68/2.92 v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 15.68/2.92 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 15.68/2.92 [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 15.68/2.92 : (v1 = v0 | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3, % 15.68/2.92 v2) = v1) | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3, % 15.68/2.92 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: % 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 = % 15.68/2.92 v0 | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 15.68/2.92 v2) = v1) | ~ % 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3, % 15.68/2.92 v2) = v0)) & ! [v0: d] : ! [v1: d] : ! [v2: d] : ! [v3: d] : (v1 = % 15.68/2.92 v0 | ~ (tyop_2Epair_2Eprod(v3, v2) = v1) | ~ (tyop_2Epair_2Eprod(v3, v2) = % 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 = v0 | ~ % 15.68/2.92 (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v0)) & ! % 15.68/2.92 [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 15.68/2.92 ~ (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~ % 15.68/2.92 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 15.68/2.92 ~ (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | ~ % 15.68/2.92 (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: % 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | % 15.68/2.92 ~ (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | ~ % 15.68/2.92 (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: d] : ! [v1: d] : ! % 15.68/2.92 [v2: d] : ! [v3: d] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~ % 15.68/2.92 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : % 15.68/2.92 ! [v3: du] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = v0)) % 15.68/2.92 & ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~ (s(v3, % 15.68/2.92 v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v2: mono_2Etyop_2Enum_2Enum] : (v1 = v0 | ~ % 15.68/2.92 (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v1) | ~ % 15.68/2.92 (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v2: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v2) = v1) | ~ % 15.68/2.92 (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~ % 15.68/2.92 (j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.92 : (v1 = v0 | ~ % 15.68/2.92 (i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2) % 15.68/2.92 = v0)) & ! [v0: mono_2Etyop_2Enum_2Enum] : ! [v1: % 15.68/2.92 mono_2Etyop_2Enum_2Enum] : ! [v2: du] : (v1 = v0 | ~ % 15.68/2.92 (j_mono_2Etyop_2Enum_2Enum(v2) = v1) | ~ (j_mono_2Etyop_2Enum_2Enum(v2) = % 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Enum_2Enum] : (v1 = % 15.68/2.92 v0 | ~ (i_mono_2Etyop_2Enum_2Enum(v2) = v1) | ~ % 15.68/2.92 (i_mono_2Etyop_2Enum_2Enum(v2) = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : (v1 = v0 | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29] % 15.68/2.92 : (v1 = v0 | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2) % 15.68/2.92 = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 15.68/2.92 : ! [v1: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] % 15.68/2.92 : (v1 = v0 | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 15.68/2.92 = v1) | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2) % 15.68/2.92 = v0)) & ! [v0: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 15.68/2.92 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ! % 15.68/2.92 [v2: du] : (v1 = v0 | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 15.68/2.92 v1) | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 = % 15.68/2.92 v0 | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 15.68/2.92 v1) | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) = % 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = % 15.68/2.92 v0 | ~ (i_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~ % 15.68/2.92 (i_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: % 15.68/2.92 du] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = v1) | ~ % 15.68/2.92 (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1 % 15.68/2.92 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_21_2E1(v2) = v0)) % 15.68/2.92 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! % 15.68/2.92 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~ % 15.68/2.92 (j_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : % 15.68/2.92 ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = % 15.68/2.92 v0 | ~ (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~ % 15.68/2.92 (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.68/2.92 MultipleValueBool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ % 15.68/2.92 (p(v2) = v1) | ~ (p(v2) = v0)) % 15.68/2.92 % 15.68/2.92 Further assumptions not needed in the proof: % 15.68/2.92 -------------------------------------------- % 15.68/2.92 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, % 15.68/2.92 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1, % 15.68/2.92 arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1, % 15.68/2.92 arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, % 15.68/2.92 arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, % 15.68/2.92 arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, ij_2Emono_2Etyop_2Emin_2Ebool, % 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, % 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29, % 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29, % 15.68/2.92 ij_2Emono_2Etyop_2Enum_2Enum, % 15.68/2.92 ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, % 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Ebool, % 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, % 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29, % 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29, % 15.68/2.92 ji_2Emono_2Etyop_2Enum_2Enum, % 15.68/2.92 ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, % 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool, % 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, % 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, % 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, % 15.68/2.92 reserved_2Eho_2Ebool__cases__ax, reserved_2Eho_2Eboolext, % 15.68/2.92 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ei__thm, reserved_2Eho_2Ek__thm, % 15.68/2.92 reserved_2Eho_2Enotfalse, reserved_2Eho_2Es__thm, reserved_2Eho_2Etruth, % 15.68/2.92 reserved_2Elogic_2E_2F_5C, reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E, % 15.68/2.92 reserved_2Elogic_2E_5C_2F, reserved_2Elogic_2E_7E, reserved_2Equant_2E_21, % 15.68/2.92 reserved_2Equant_2E_3F, thm_2Ebool_2EFORALL__SIMP, thm_2Ebool_2EIMP__CLAUSES, % 15.68/2.92 thm_2Ebool_2ETRUTH % 15.68/2.92 % 15.68/2.92 Those formulas are unsatisfiable: % 15.68/2.92 --------------------------------- % 15.68/2.92 % 15.68/2.92 Begin of proof % 15.68/2.93 | % 15.68/2.93 | ALPHA: (thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) implies: % 15.68/2.93 | (1) ? [v0: % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.93 | : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = % 15.68/2.93 | v0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0) % 15.68/2.93 | & ! [v1: % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.93 | : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0) | ~ % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1)) % 15.68/2.93 | & ! [v1: % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.93 | : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = v1))) % 15.68/2.93 | % 15.68/2.93 | ALPHA: (thm_2Ecomplex_2ECOMPLEX__INV__NZ) implies: % 15.68/2.93 | (2) ? [v0: % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.93 | : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = % 15.68/2.93 | v0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0) % 15.68/2.93 | & ? [v1: % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.93 | : ( ~ (v1 = v0) & mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1))) % 15.68/2.93 | % 15.68/2.93 | ALPHA: (function-axioms) implies: % 15.68/2.93 | (3) ! [v0: % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.93 | : ! [v1: % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] % 15.68/2.93 | : ! [v2: mono_2Etyop_2Enum_2Enum] : (v1 = v0 | ~ % 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v1) | ~ % 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v0)) % 15.68/2.93 | % 15.68/2.93 | DELTA: instantiating (2) with fresh symbol all_52_0 gives: % 15.68/2.93 | (4) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = % 15.68/2.93 | all_52_0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_52_0) % 15.68/2.93 | & ? [v0: any] : ( ~ (v0 = all_52_0) & % 15.68/2.93 | mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_52_0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)) % 15.68/2.93 | % 15.68/2.93 | ALPHA: (4) implies: % 15.68/2.93 | (5) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = % 15.68/2.93 | all_52_0 % 15.68/2.93 | (6) ? [v0: any] : ( ~ (v0 = all_52_0) & % 15.68/2.93 | mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_52_0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)) % 15.68/2.93 | % 15.68/2.93 | DELTA: instantiating (1) with fresh symbol all_62_0 gives: % 15.68/2.93 | (7) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = % 15.68/2.93 | all_62_0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_62_0) % 15.68/2.93 | & ! [v0: any] : (v0 = all_62_0 | ~ % 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_62_0) | ~ % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)) % 15.68/2.93 | & ! [v0: int] : (v0 = all_62_0 | ~ % 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_62_0) = v0)) % 15.68/2.93 | % 15.68/2.93 | ALPHA: (7) implies: % 15.68/2.93 | (8) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = % 15.68/2.93 | all_62_0 % 15.68/2.93 | (9) ! [v0: any] : (v0 = all_62_0 | ~ % 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_62_0) | ~ % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)) % 15.68/2.93 | % 15.68/2.93 | DELTA: instantiating (6) with fresh symbol all_104_0 gives: % 15.68/2.93 | (10) ~ (all_104_0 = all_52_0) & % 15.68/2.93 | mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_52_0 & % 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_104_0) % 15.68/2.93 | % 15.68/2.93 | ALPHA: (10) implies: % 15.68/2.93 | (11) ~ (all_104_0 = all_52_0) % 15.68/2.93 | (12) mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_104_0) % 15.68/2.93 | (13) mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_52_0 % 15.68/2.93 | % 15.68/2.94 | GROUND_INST: instantiating (3) with all_52_0, all_62_0, % 15.68/2.94 | mono_2Ec_2Enum_2E0_2E0, simplifying with (5), (8) gives: % 15.68/2.94 | (14) all_62_0 = all_52_0 % 15.68/2.94 | % 15.68/2.94 | GROUND_INST: instantiating (9) with all_104_0, simplifying with (12) gives: % 15.68/2.94 | (15) all_104_0 = all_62_0 | ~ % 15.68/2.94 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_62_0) % 15.68/2.94 | % 15.68/2.94 | BETA: splitting (15) gives: % 15.68/2.94 | % 15.68/2.94 | Case 1: % 15.68/2.94 | | % 15.68/2.94 | | (16) ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_62_0) % 15.68/2.94 | | % 15.68/2.94 | | REDUCE: (14), (16) imply: % 15.68/2.94 | | (17) ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_52_0) % 15.68/2.94 | | % 15.68/2.94 | | PRED_UNIFY: (13), (17) imply: % 15.68/2.94 | | (18) $false % 15.68/2.94 | | % 15.68/2.94 | | CLOSE: (18) is inconsistent. % 15.68/2.94 | | % 15.68/2.94 | Case 2: % 15.68/2.94 | | % 15.68/2.94 | | (19) all_104_0 = all_62_0 % 15.68/2.94 | | % 15.68/2.94 | | COMBINE_EQS: (14), (19) imply: % 15.68/2.94 | | (20) all_104_0 = all_52_0 % 15.68/2.94 | | % 15.68/2.94 | | REDUCE: (11), (20) imply: % 15.68/2.94 | | (21) $false % 15.68/2.94 | | % 15.68/2.94 | | CLOSE: (21) is inconsistent. % 15.68/2.94 | | % 15.68/2.94 | End of split % 15.68/2.94 | % 15.68/2.94 End of proof % 15.68/2.94 % SZS output end Proof for theBenchmark % 15.68/2.94 % 15.68/2.94 2357ms %------------------------------------------------------------------------------