%------------------------------------------------------------------------------ % 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 : n031.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 12.05s 2.45s % Output : Proof 25.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % 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 % 0.19/0.35 % Computer : n031.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Sun Aug 27 11:50:39 EDT 2023 % 0.19/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.24/1.16 Prover 1: Preprocessing ... % 3.24/1.16 Prover 4: Preprocessing ... % 3.46/1.20 Prover 3: Preprocessing ... % 3.46/1.20 Prover 5: Preprocessing ... % 3.46/1.20 Prover 0: Preprocessing ... % 3.46/1.20 Prover 6: Preprocessing ... % 3.46/1.21 Prover 2: Preprocessing ... % 8.48/1.90 Prover 1: Warning: ignoring some quantifiers % 8.48/2.04 Prover 3: Warning: ignoring some quantifiers % 9.51/2.04 Prover 1: Constructing countermodel ... % 9.51/2.05 Prover 4: Constructing countermodel ... % 9.51/2.08 Prover 6: Proving ... % 9.51/2.08 Prover 0: Proving ... % 9.51/2.08 Prover 3: Constructing countermodel ... % 10.28/2.21 Prover 5: Proving ... % 11.21/2.29 Prover 2: Proving ... % 12.05/2.45 Prover 3: proved (1808ms) % 12.05/2.45 % 12.05/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.05/2.45 % 12.05/2.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.46/2.46 Prover 2: stopped % 12.46/2.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.46/2.46 Prover 6: stopped % 12.46/2.46 Prover 5: stopped % 12.46/2.47 Prover 0: stopped % 12.46/2.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.46/2.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.46/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.46/2.53 Prover 7: Preprocessing ... % 13.17/2.55 Prover 11: Preprocessing ... % 13.17/2.57 Prover 8: Preprocessing ... % 13.17/2.58 Prover 13: Preprocessing ... % 13.17/2.59 Prover 10: Preprocessing ... % 15.36/2.85 Prover 7: Constructing countermodel ... % 15.36/2.85 Prover 10: Constructing countermodel ... % 15.36/2.88 Prover 8: Warning: ignoring some quantifiers % 15.36/2.91 Prover 8: Constructing countermodel ... % 15.36/2.92 Prover 11: Constructing countermodel ... % 17.34/3.10 Prover 13: Warning: ignoring some quantifiers % 17.34/3.13 Prover 13: Constructing countermodel ... % 24.98/4.13 Prover 7: Found proof (size 66) % 24.98/4.13 Prover 7: proved (1675ms) % 24.98/4.13 Prover 4: stopped % 24.98/4.13 Prover 11: stopped % 24.98/4.13 Prover 10: stopped % 24.98/4.13 Prover 13: stopped % 24.98/4.13 Prover 1: stopped % 24.98/4.13 Prover 8: stopped % 24.98/4.13 % 24.98/4.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.98/4.14 % 24.98/4.14 % SZS output start Proof for theBenchmark % 24.98/4.14 Assumptions after simplification: % 24.98/4.14 --------------------------------- % 24.98/4.14 % 24.98/4.14 (arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1) % 25.27/4.17 $i(c_2Ecomplex_2Ecomplex__inv_2E0) & $i(tyop_2Erealax_2Ereal) & ? [v0: $i] : % 25.27/4.17 ? [v1: $i] : ? [v2: $i] : (tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, % 25.27/4.17 tyop_2Erealax_2Ereal) = v0 & tyop_2Emin_2Efun(v0, v0) = v1 & s(v1, % 25.27/4.17 c_2Ecomplex_2Ecomplex__inv_2E0) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: % 25.27/4.17 $i] : ! [v4: $i] : ( ~ (s(v0, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? % 25.27/4.17 [v6: $i] : ? [v7: $i] : (c_2Ecomplex_2Ecomplex__inv_2E1(v4) = v5 & % 25.27/4.17 app_2E2(v2, v4) = v7 & s(v0, v7) = v6 & s(v0, v5) = v6 & $i(v7) & $i(v6) % 25.27/4.17 & $i(v5)))) % 25.27/4.17 % 25.27/4.17 (arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1) % 25.27/4.17 $i(c_2Ecomplex_2Ecomplex__of__num_2E0) & $i(tyop_2Enum_2Enum) & % 25.27/4.17 $i(tyop_2Erealax_2Ereal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 25.27/4.17 (tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = v0 & % 25.27/4.17 tyop_2Emin_2Efun(tyop_2Enum_2Enum, v0) = v1 & s(v1, % 25.27/4.17 c_2Ecomplex_2Ecomplex__of__num_2E0) = v2 & $i(v2) & $i(v1) & $i(v0) & ! % 25.27/4.17 [v3: $i] : ! [v4: $i] : ( ~ (s(tyop_2Enum_2Enum, v3) = v4) | ~ $i(v3) | ? % 25.27/4.17 [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 25.27/4.17 (c_2Ecomplex_2Ecomplex__of__num_2E1(v4) = v5 & app_2E2(v2, v4) = v7 & % 25.27/4.17 s(v0, v7) = v6 & s(v0, v5) = v6 & $i(v7) & $i(v6) & $i(v5)))) % 25.27/4.17 % 25.27/4.17 (thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) % 25.27/4.17 $i(c_2Enum_2E0_2E0) & $i(tyop_2Enum_2Enum) & $i(tyop_2Erealax_2Ereal) & ? % 25.27/4.17 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 25.27/4.17 (c_2Ecomplex_2Ecomplex__of__num_2E1(v1) = v2 & % 25.27/4.17 tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = v0 & s(v0, % 25.27/4.17 v2) = v3 & s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0) = v1 & $i(v3) & $i(v2) & % 25.27/4.17 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ (s(v0, v4) = v5) % 25.27/4.17 | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v3) & % 25.27/4.17 c_2Ecomplex_2Ecomplex__inv_2E1(v5) = v6 & s(v0, v6) = v7 & $i(v7) & % 25.27/4.17 $i(v6))) & ! [v4: $i] : ( ~ (s(v0, v4) = v3) | ~ $i(v4) | ? [v5: $i] % 25.27/4.17 : (c_2Ecomplex_2Ecomplex__inv_2E1(v3) = v5 & s(v0, v5) = v3 & $i(v5)))) % 25.27/4.17 % 25.27/4.17 (thm_2Ecomplex_2ECOMPLEX__INV__NZ) % 25.27/4.18 $i(c_2Enum_2E0_2E0) & $i(tyop_2Enum_2Enum) & $i(tyop_2Erealax_2Ereal) & ? % 25.27/4.18 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 25.27/4.18 : ? [v6: $i] : ( ~ (v5 = v3) & c_2Ecomplex_2Ecomplex__of__num_2E1(v1) = v2 & % 25.27/4.18 tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = v0 & % 25.27/4.18 c_2Ecomplex_2Ecomplex__inv_2E1(v5) = v6 & s(v0, v6) = v3 & s(v0, v4) = v5 & % 25.27/4.18 s(v0, v2) = v3 & s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0) = v1 & $i(v6) & $i(v5) % 25.27/4.18 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 25.27/4.18 % 25.27/4.18 (function-axioms) % 25.27/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.27/4.18 (tyop_2Epair_2Eprod(v3, v2) = v1) | ~ (tyop_2Epair_2Eprod(v3, v2) = v0)) & % 25.27/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.27/4.18 (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v0)) & ! % 25.27/4.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.27/4.18 (c_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_3D_3E_2E2(v3, v2) % 25.27/4.18 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 25.27/4.18 | ~ (c_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | ~ (c_2Ebool_2E_5C_2F_2E2(v3, % 25.27/4.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 25.27/4.18 = v0 | ~ (c_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | ~ % 25.27/4.18 (c_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 25.27/4.18 $i] : ! [v3: $i] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~ % 25.27/4.18 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 25.27/4.18 ! [v3: $i] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = % 25.27/4.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 25.27/4.18 ~ (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 25.27/4.18 [v2: $i] : (v1 = v0 | ~ (c_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v1) | ~ % 25.27/4.18 (c_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 25.27/4.18 ! [v2: $i] : (v1 = v0 | ~ (c_2Ecomplex_2Ecomplex__inv_2E1(v2) = v1) | ~ % 25.27/4.18 (c_2Ecomplex_2Ecomplex__inv_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 25.27/4.18 [v2: $i] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = v1) | ~ % 25.27/4.18 (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 25.27/4.18 (v1 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_21_2E1(v2) = % 25.27/4.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 25.27/4.18 (c_2Ebool_2E_7E_2E1(v2) = v1) | ~ (c_2Ebool_2E_7E_2E1(v2) = v0)) % 25.27/4.18 % 25.27/4.18 Further assumptions not needed in the proof: % 25.27/4.18 -------------------------------------------- % 25.27/4.18 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, % 25.27/4.18 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1, % 25.27/4.18 arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, % 25.27/4.18 arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, % 25.27/4.18 reserved_2Eho_2Ebool__cases__ax, reserved_2Eho_2Eboolext, % 25.27/4.18 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ei__thm, reserved_2Eho_2Ek__thm, % 25.27/4.18 reserved_2Eho_2Enotfalse, reserved_2Eho_2Es__thm, reserved_2Eho_2Etruth, % 25.27/4.18 reserved_2Elogic_2E_2F_5C, reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E, % 25.27/4.18 reserved_2Elogic_2E_5C_2F, reserved_2Elogic_2E_7E, reserved_2Equant_2E_21, % 25.27/4.18 reserved_2Equant_2E_3F, thm_2Ebool_2EFORALL__SIMP, thm_2Ebool_2EIMP__CLAUSES, % 25.27/4.18 thm_2Ebool_2ETRUTH % 25.27/4.18 % 25.27/4.18 Those formulas are unsatisfiable: % 25.27/4.18 --------------------------------- % 25.27/4.18 % 25.27/4.18 Begin of proof % 25.27/4.18 | % 25.27/4.18 | ALPHA: (arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1) implies: % 25.27/4.18 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 25.27/4.18 | (tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = v0 & % 25.27/4.18 | tyop_2Emin_2Efun(v0, v0) = v1 & s(v1, c_2Ecomplex_2Ecomplex__inv_2E0) % 25.27/4.18 | = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 25.27/4.18 | (s(v0, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 25.27/4.18 | $i] : (c_2Ecomplex_2Ecomplex__inv_2E1(v4) = v5 & app_2E2(v2, v4) % 25.27/4.18 | = v7 & s(v0, v7) = v6 & s(v0, v5) = v6 & $i(v7) & $i(v6) & % 25.27/4.18 | $i(v5)))) % 25.27/4.18 | % 25.27/4.18 | ALPHA: (arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1) implies: % 25.27/4.18 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 25.27/4.18 | (tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = v0 & % 25.27/4.18 | tyop_2Emin_2Efun(tyop_2Enum_2Enum, v0) = v1 & s(v1, % 25.27/4.18 | c_2Ecomplex_2Ecomplex__of__num_2E0) = v2 & $i(v2) & $i(v1) & $i(v0) % 25.27/4.18 | & ! [v3: $i] : ! [v4: $i] : ( ~ (s(tyop_2Enum_2Enum, v3) = v4) | ~ % 25.27/4.18 | $i(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 25.27/4.18 | (c_2Ecomplex_2Ecomplex__of__num_2E1(v4) = v5 & app_2E2(v2, v4) = v7 % 25.27/4.18 | & s(v0, v7) = v6 & s(v0, v5) = v6 & $i(v7) & $i(v6) & $i(v5)))) % 25.27/4.18 | % 25.27/4.18 | ALPHA: (thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) implies: % 25.27/4.19 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 25.27/4.19 | (c_2Ecomplex_2Ecomplex__of__num_2E1(v1) = v2 & % 25.27/4.19 | tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = v0 & % 25.27/4.19 | s(v0, v2) = v3 & s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0) = v1 & $i(v3) & % 25.27/4.19 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 25.27/4.19 | (s(v0, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 % 25.27/4.19 | = v3) & c_2Ecomplex_2Ecomplex__inv_2E1(v5) = v6 & s(v0, v6) = % 25.27/4.19 | v7 & $i(v7) & $i(v6))) & ! [v4: $i] : ( ~ (s(v0, v4) = v3) | ~ % 25.27/4.19 | $i(v4) | ? [v5: $i] : (c_2Ecomplex_2Ecomplex__inv_2E1(v3) = v5 & % 25.27/4.19 | s(v0, v5) = v3 & $i(v5)))) % 25.27/4.19 | % 25.27/4.19 | ALPHA: (thm_2Ecomplex_2ECOMPLEX__INV__NZ) implies: % 25.27/4.19 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 25.27/4.19 | ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v3) & % 25.27/4.19 | c_2Ecomplex_2Ecomplex__of__num_2E1(v1) = v2 & % 25.27/4.19 | tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = v0 & % 25.27/4.19 | c_2Ecomplex_2Ecomplex__inv_2E1(v5) = v6 & s(v0, v6) = v3 & s(v0, v4) % 25.27/4.19 | = v5 & s(v0, v2) = v3 & s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0) = v1 & % 25.27/4.19 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 25.27/4.19 | % 25.27/4.19 | ALPHA: (function-axioms) implies: % 25.27/4.19 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 25.27/4.19 | (c_2Ecomplex_2Ecomplex__inv_2E1(v2) = v1) | ~ % 25.27/4.19 | (c_2Ecomplex_2Ecomplex__inv_2E1(v2) = v0)) % 25.27/4.19 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 25.27/4.19 | (c_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v1) | ~ % 25.27/4.19 | (c_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v0)) % 25.27/4.19 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.27/4.19 | (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) % 25.27/4.19 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.27/4.19 | (tyop_2Epair_2Eprod(v3, v2) = v1) | ~ (tyop_2Epair_2Eprod(v3, v2) = % 25.27/4.19 | v0)) % 25.27/4.19 | % 25.27/4.19 | DELTA: instantiating (2) with fresh symbols all_29_0, all_29_1, all_29_2 % 25.27/4.19 | gives: % 25.27/4.19 | (9) tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.19 | all_29_2 & tyop_2Emin_2Efun(tyop_2Enum_2Enum, all_29_2) = all_29_1 & % 25.27/4.19 | s(all_29_1, c_2Ecomplex_2Ecomplex__of__num_2E0) = all_29_0 & % 25.27/4.19 | $i(all_29_0) & $i(all_29_1) & $i(all_29_2) & ! [v0: $i] : ! [v1: $i] % 25.27/4.19 | : ( ~ (s(tyop_2Enum_2Enum, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 25.27/4.19 | [v3: $i] : ? [v4: $i] : (c_2Ecomplex_2Ecomplex__of__num_2E1(v1) = v2 % 25.27/4.19 | & app_2E2(all_29_0, v1) = v4 & s(all_29_2, v4) = v3 & s(all_29_2, % 25.27/4.19 | v2) = v3 & $i(v4) & $i(v3) & $i(v2))) % 25.27/4.19 | % 25.27/4.19 | ALPHA: (9) implies: % 25.27/4.19 | (10) tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.19 | all_29_2 % 25.27/4.19 | % 25.27/4.19 | DELTA: instantiating (1) with fresh symbols all_32_0, all_32_1, all_32_2 % 25.27/4.19 | gives: % 25.27/4.19 | (11) tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.19 | all_32_2 & tyop_2Emin_2Efun(all_32_2, all_32_2) = all_32_1 & % 25.27/4.19 | s(all_32_1, c_2Ecomplex_2Ecomplex__inv_2E0) = all_32_0 & $i(all_32_0) % 25.27/4.19 | & $i(all_32_1) & $i(all_32_2) & ! [v0: $i] : ! [v1: $i] : ( ~ % 25.27/4.19 | (s(all_32_2, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? % 25.27/4.19 | [v4: $i] : (c_2Ecomplex_2Ecomplex__inv_2E1(v1) = v2 & % 25.27/4.19 | app_2E2(all_32_0, v1) = v4 & s(all_32_2, v4) = v3 & s(all_32_2, % 25.27/4.19 | v2) = v3 & $i(v4) & $i(v3) & $i(v2))) % 25.27/4.19 | % 25.27/4.19 | ALPHA: (11) implies: % 25.27/4.19 | (12) tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.19 | all_32_2 % 25.27/4.19 | % 25.27/4.19 | DELTA: instantiating (4) with fresh symbols all_35_0, all_35_1, all_35_2, % 25.27/4.19 | all_35_3, all_35_4, all_35_5, all_35_6 gives: % 25.27/4.19 | (13) ~ (all_35_1 = all_35_3) & % 25.27/4.19 | c_2Ecomplex_2Ecomplex__of__num_2E1(all_35_5) = all_35_4 & % 25.27/4.19 | tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.19 | all_35_6 & c_2Ecomplex_2Ecomplex__inv_2E1(all_35_1) = all_35_0 & % 25.27/4.19 | s(all_35_6, all_35_0) = all_35_3 & s(all_35_6, all_35_2) = all_35_1 & % 25.27/4.19 | s(all_35_6, all_35_4) = all_35_3 & s(tyop_2Enum_2Enum, % 25.27/4.19 | c_2Enum_2E0_2E0) = all_35_5 & $i(all_35_0) & $i(all_35_1) & % 25.27/4.19 | $i(all_35_2) & $i(all_35_3) & $i(all_35_4) & $i(all_35_5) & % 25.27/4.19 | $i(all_35_6) % 25.27/4.19 | % 25.27/4.19 | ALPHA: (13) implies: % 25.27/4.19 | (14) ~ (all_35_1 = all_35_3) % 25.27/4.19 | (15) $i(all_35_2) % 25.27/4.19 | (16) s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0) = all_35_5 % 25.27/4.19 | (17) s(all_35_6, all_35_4) = all_35_3 % 25.27/4.19 | (18) s(all_35_6, all_35_2) = all_35_1 % 25.27/4.19 | (19) s(all_35_6, all_35_0) = all_35_3 % 25.27/4.19 | (20) c_2Ecomplex_2Ecomplex__inv_2E1(all_35_1) = all_35_0 % 25.27/4.19 | (21) tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.19 | all_35_6 % 25.27/4.19 | (22) c_2Ecomplex_2Ecomplex__of__num_2E1(all_35_5) = all_35_4 % 25.27/4.19 | % 25.27/4.19 | DELTA: instantiating (3) with fresh symbols all_40_0, all_40_1, all_40_2, % 25.27/4.19 | all_40_3 gives: % 25.27/4.20 | (23) c_2Ecomplex_2Ecomplex__of__num_2E1(all_40_2) = all_40_1 & % 25.27/4.20 | tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.20 | all_40_3 & s(all_40_3, all_40_1) = all_40_0 & s(tyop_2Enum_2Enum, % 25.27/4.20 | c_2Enum_2E0_2E0) = all_40_2 & $i(all_40_0) & $i(all_40_1) & % 25.27/4.20 | $i(all_40_2) & $i(all_40_3) & ! [v0: $i] : ! [v1: any] : (v1 = % 25.27/4.20 | all_40_0 | ~ (s(all_40_3, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 25.27/4.20 | [v3: any] : ( ~ (v3 = all_40_0) & c_2Ecomplex_2Ecomplex__inv_2E1(v1) % 25.27/4.20 | = v2 & s(all_40_3, v2) = v3 & $i(v3) & $i(v2))) & ! [v0: $i] : ( % 25.27/4.20 | ~ (s(all_40_3, v0) = all_40_0) | ~ $i(v0) | ? [v1: $i] : % 25.27/4.20 | (c_2Ecomplex_2Ecomplex__inv_2E1(all_40_0) = v1 & s(all_40_3, v1) = % 25.27/4.20 | all_40_0 & $i(v1))) % 25.27/4.20 | % 25.27/4.20 | ALPHA: (23) implies: % 25.27/4.20 | (24) s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0) = all_40_2 % 25.27/4.20 | (25) s(all_40_3, all_40_1) = all_40_0 % 25.27/4.20 | (26) tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal) = % 25.27/4.20 | all_40_3 % 25.27/4.20 | (27) c_2Ecomplex_2Ecomplex__of__num_2E1(all_40_2) = all_40_1 % 25.27/4.20 | (28) ! [v0: $i] : ! [v1: any] : (v1 = all_40_0 | ~ (s(all_40_3, v0) = % 25.27/4.20 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ( ~ (v3 = all_40_0) % 25.27/4.20 | & c_2Ecomplex_2Ecomplex__inv_2E1(v1) = v2 & s(all_40_3, v2) = v3 & % 25.27/4.20 | $i(v3) & $i(v2))) % 25.27/4.20 | % 25.27/4.20 | GROUND_INST: instantiating (7) with all_35_5, all_40_2, c_2Enum_2E0_2E0, % 25.27/4.20 | tyop_2Enum_2Enum, simplifying with (16), (24) gives: % 25.27/4.20 | (29) all_40_2 = all_35_5 % 25.27/4.20 | % 25.27/4.20 | GROUND_INST: instantiating (7) with all_35_3, all_35_1, all_35_4, all_35_6, % 25.27/4.20 | simplifying with (17) gives: % 25.27/4.20 | (30) all_35_1 = all_35_3 | ~ (s(all_35_6, all_35_4) = all_35_1) % 25.27/4.20 | % 25.27/4.20 | GROUND_INST: instantiating (8) with all_29_2, all_35_6, tyop_2Erealax_2Ereal, % 25.27/4.20 | tyop_2Erealax_2Ereal, simplifying with (10), (21) gives: % 25.27/4.20 | (31) all_35_6 = all_29_2 % 25.27/4.20 | % 25.27/4.20 | GROUND_INST: instantiating (8) with all_35_6, all_40_3, tyop_2Erealax_2Ereal, % 25.27/4.20 | tyop_2Erealax_2Ereal, simplifying with (21), (26) gives: % 25.27/4.20 | (32) all_40_3 = all_35_6 % 25.27/4.20 | % 25.27/4.20 | GROUND_INST: instantiating (8) with all_32_2, all_40_3, tyop_2Erealax_2Ereal, % 25.27/4.20 | tyop_2Erealax_2Ereal, simplifying with (12), (26) gives: % 25.27/4.20 | (33) all_40_3 = all_32_2 % 25.27/4.20 | % 25.27/4.20 | GROUND_INST: instantiating (6) with all_35_4, all_40_1, all_35_5, simplifying % 25.27/4.20 | with (22) gives: % 25.27/4.20 | (34) all_40_1 = all_35_4 | ~ (c_2Ecomplex_2Ecomplex__of__num_2E1(all_35_5) % 25.27/4.20 | = all_40_1) % 25.27/4.20 | % 25.27/4.20 | COMBINE_EQS: (32), (33) imply: % 25.27/4.20 | (35) all_35_6 = all_32_2 % 25.27/4.20 | % 25.27/4.20 | SIMP: (35) implies: % 25.27/4.20 | (36) all_35_6 = all_32_2 % 25.27/4.20 | % 25.27/4.20 | COMBINE_EQS: (31), (36) imply: % 25.27/4.20 | (37) all_32_2 = all_29_2 % 25.27/4.20 | % 25.27/4.20 | COMBINE_EQS: (33), (37) imply: % 25.27/4.20 | (38) all_40_3 = all_29_2 % 25.27/4.20 | % 25.27/4.20 | REDUCE: (27), (29) imply: % 25.27/4.20 | (39) c_2Ecomplex_2Ecomplex__of__num_2E1(all_35_5) = all_40_1 % 25.27/4.20 | % 25.27/4.20 | REDUCE: (25), (38) imply: % 25.27/4.20 | (40) s(all_29_2, all_40_1) = all_40_0 % 25.27/4.20 | % 25.27/4.20 | REDUCE: (19), (31) imply: % 25.27/4.20 | (41) s(all_29_2, all_35_0) = all_35_3 % 25.27/4.20 | % 25.27/4.20 | REDUCE: (18), (31) imply: % 25.27/4.20 | (42) s(all_29_2, all_35_2) = all_35_1 % 25.27/4.20 | % 25.27/4.20 | REDUCE: (17), (31) imply: % 25.27/4.20 | (43) s(all_29_2, all_35_4) = all_35_3 % 25.27/4.20 | % 25.27/4.20 | BETA: splitting (34) gives: % 25.27/4.20 | % 25.27/4.20 | Case 1: % 25.27/4.20 | | % 25.27/4.20 | | (44) ~ (c_2Ecomplex_2Ecomplex__of__num_2E1(all_35_5) = all_40_1) % 25.27/4.20 | | % 25.27/4.20 | | PRED_UNIFY: (39), (44) imply: % 25.27/4.20 | | (45) $false % 25.27/4.20 | | % 25.27/4.20 | | CLOSE: (45) is inconsistent. % 25.27/4.20 | | % 25.27/4.20 | Case 2: % 25.27/4.20 | | % 25.27/4.20 | | (46) all_40_1 = all_35_4 % 25.27/4.21 | | % 25.27/4.21 | | REDUCE: (40), (46) imply: % 25.27/4.21 | | (47) s(all_29_2, all_35_4) = all_40_0 % 25.27/4.21 | | % 25.27/4.21 | | BETA: splitting (30) gives: % 25.27/4.21 | | % 25.27/4.21 | | Case 1: % 25.27/4.21 | | | % 25.27/4.21 | | | (48) ~ (s(all_35_6, all_35_4) = all_35_1) % 25.27/4.21 | | | % 25.27/4.21 | | | REDUCE: (31), (48) imply: % 25.27/4.21 | | | (49) ~ (s(all_29_2, all_35_4) = all_35_1) % 25.27/4.21 | | | % 25.27/4.21 | | | GROUND_INST: instantiating (7) with all_35_3, all_40_0, all_35_4, % 25.27/4.21 | | | all_29_2, simplifying with (43), (47) gives: % 25.27/4.21 | | | (50) all_40_0 = all_35_3 % 25.27/4.21 | | | % 25.27/4.21 | | | PRED_UNIFY: (47), (49) imply: % 25.27/4.21 | | | (51) ~ (all_40_0 = all_35_1) % 25.27/4.21 | | | % 25.27/4.21 | | | REDUCE: (50), (51) imply: % 25.27/4.21 | | | (52) ~ (all_35_1 = all_35_3) % 25.27/4.21 | | | % 25.27/4.21 | | | GROUND_INST: instantiating (28) with all_35_2, all_35_1, simplifying with % 25.27/4.21 | | | (15) gives: % 25.27/4.21 | | | (53) all_40_0 = all_35_1 | ~ (s(all_40_3, all_35_2) = all_35_1) | ? % 25.27/4.21 | | | [v0: $i] : ? [v1: any] : ( ~ (v1 = all_40_0) & % 25.27/4.21 | | | c_2Ecomplex_2Ecomplex__inv_2E1(all_35_1) = v0 & s(all_40_3, v0) % 25.27/4.21 | | | = v1 & $i(v1) & $i(v0)) % 25.27/4.21 | | | % 25.27/4.21 | | | BETA: splitting (53) gives: % 25.27/4.21 | | | % 25.27/4.21 | | | Case 1: % 25.27/4.21 | | | | % 25.27/4.21 | | | | (54) ~ (s(all_40_3, all_35_2) = all_35_1) % 25.27/4.21 | | | | % 25.27/4.21 | | | | REDUCE: (38), (54) imply: % 25.27/4.21 | | | | (55) ~ (s(all_29_2, all_35_2) = all_35_1) % 25.27/4.21 | | | | % 25.27/4.21 | | | | PRED_UNIFY: (42), (55) imply: % 25.27/4.21 | | | | (56) $false % 25.27/4.21 | | | | % 25.27/4.21 | | | | CLOSE: (56) is inconsistent. % 25.27/4.21 | | | | % 25.27/4.21 | | | Case 2: % 25.27/4.21 | | | | % 25.27/4.21 | | | | (57) all_40_0 = all_35_1 | ? [v0: $i] : ? [v1: any] : ( ~ (v1 = % 25.27/4.21 | | | | all_40_0) & c_2Ecomplex_2Ecomplex__inv_2E1(all_35_1) = v0 & % 25.27/4.21 | | | | s(all_40_3, v0) = v1 & $i(v1) & $i(v0)) % 25.27/4.21 | | | | % 25.27/4.21 | | | | BETA: splitting (57) gives: % 25.27/4.21 | | | | % 25.27/4.21 | | | | Case 1: % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | (58) all_40_0 = all_35_1 % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | COMBINE_EQS: (50), (58) imply: % 25.27/4.21 | | | | | (59) all_35_1 = all_35_3 % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | REDUCE: (14), (59) imply: % 25.27/4.21 | | | | | (60) $false % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | CLOSE: (60) is inconsistent. % 25.27/4.21 | | | | | % 25.27/4.21 | | | | Case 2: % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | (61) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_40_0) & % 25.27/4.21 | | | | | c_2Ecomplex_2Ecomplex__inv_2E1(all_35_1) = v0 & s(all_40_3, % 25.27/4.21 | | | | | v0) = v1 & $i(v1) & $i(v0)) % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | DELTA: instantiating (61) with fresh symbols all_161_0, all_161_1 % 25.27/4.21 | | | | | gives: % 25.27/4.21 | | | | | (62) ~ (all_161_0 = all_40_0) & % 25.27/4.21 | | | | | c_2Ecomplex_2Ecomplex__inv_2E1(all_35_1) = all_161_1 & % 25.27/4.21 | | | | | s(all_40_3, all_161_1) = all_161_0 & $i(all_161_0) & % 25.27/4.21 | | | | | $i(all_161_1) % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | ALPHA: (62) implies: % 25.27/4.21 | | | | | (63) ~ (all_161_0 = all_40_0) % 25.27/4.21 | | | | | (64) s(all_40_3, all_161_1) = all_161_0 % 25.27/4.21 | | | | | (65) c_2Ecomplex_2Ecomplex__inv_2E1(all_35_1) = all_161_1 % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | REDUCE: (50), (63) imply: % 25.27/4.21 | | | | | (66) ~ (all_161_0 = all_35_3) % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | REDUCE: (38), (64) imply: % 25.27/4.21 | | | | | (67) s(all_29_2, all_161_1) = all_161_0 % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | GROUND_INST: instantiating (7) with all_35_3, all_161_0, all_35_0, % 25.27/4.21 | | | | | all_29_2, simplifying with (41) gives: % 25.27/4.21 | | | | | (68) all_161_0 = all_35_3 | ~ (s(all_29_2, all_35_0) = all_161_0) % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | GROUND_INST: instantiating (5) with all_35_0, all_161_1, all_35_1, % 25.27/4.21 | | | | | simplifying with (20), (65) gives: % 25.27/4.21 | | | | | (69) all_161_1 = all_35_0 % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | REDUCE: (67), (69) imply: % 25.27/4.21 | | | | | (70) s(all_29_2, all_35_0) = all_161_0 % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | BETA: splitting (68) gives: % 25.27/4.21 | | | | | % 25.27/4.21 | | | | | Case 1: % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | | (71) ~ (s(all_29_2, all_35_0) = all_161_0) % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | | PRED_UNIFY: (70), (71) imply: % 25.27/4.21 | | | | | | (72) $false % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | | CLOSE: (72) is inconsistent. % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | Case 2: % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | | (73) all_161_0 = all_35_3 % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | | REDUCE: (66), (73) imply: % 25.27/4.21 | | | | | | (74) $false % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | | CLOSE: (74) is inconsistent. % 25.27/4.21 | | | | | | % 25.27/4.21 | | | | | End of split % 25.27/4.21 | | | | | % 25.27/4.21 | | | | End of split % 25.27/4.21 | | | | % 25.27/4.21 | | | End of split % 25.27/4.21 | | | % 25.27/4.21 | | Case 2: % 25.27/4.21 | | | % 25.27/4.21 | | | (75) all_35_1 = all_35_3 % 25.27/4.21 | | | % 25.27/4.21 | | | REDUCE: (14), (75) imply: % 25.27/4.21 | | | (76) $false % 25.27/4.21 | | | % 25.27/4.21 | | | CLOSE: (76) is inconsistent. % 25.27/4.21 | | | % 25.27/4.21 | | End of split % 25.27/4.21 | | % 25.27/4.21 | End of split % 25.27/4.21 | % 25.27/4.21 End of proof % 25.27/4.21 % SZS output end Proof for theBenchmark % 25.27/4.21 % 25.27/4.21 3617ms %------------------------------------------------------------------------------