%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP001+4 : TPTP v8.1.2. Bugfixed v7.5.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 04:08:16 EDT 2023 % Result : Theorem 17.10s 3.15s % Output : Proof 23.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP001+4 : TPTP v8.1.2. Bugfixed v7.5.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n008.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 : Sun Aug 27 13:14:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.71/1.52 Prover 4: Preprocessing ... % 4.71/1.53 Prover 1: Preprocessing ... % 5.90/1.57 Prover 0: Preprocessing ... % 5.90/1.57 Prover 6: Preprocessing ... % 5.90/1.57 Prover 3: Preprocessing ... % 5.90/1.57 Prover 2: Preprocessing ... % 5.90/1.57 Prover 5: Preprocessing ... % 16.37/3.04 Prover 1: Constructing countermodel ... % 16.37/3.04 Prover 3: Constructing countermodel ... % 16.37/3.08 Prover 6: Proving ... % 17.10/3.15 Prover 3: proved (2506ms) % 17.10/3.15 % 17.10/3.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.10/3.15 % 17.10/3.16 Prover 6: stopped % 17.10/3.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.10/3.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.65/3.30 Prover 4: Constructing countermodel ... % 19.39/3.41 Prover 7: Preprocessing ... % 19.39/3.47 Prover 5: Proving ... % 19.39/3.47 Prover 5: stopped % 19.39/3.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.08/3.51 Prover 8: Preprocessing ... % 20.08/3.60 Prover 1: Found proof (size 53) % 20.08/3.60 Prover 1: proved (2970ms) % 20.08/3.60 Prover 4: stopped % 20.08/3.60 Prover 2: Proving ... % 20.08/3.60 Prover 2: stopped % 20.17/3.62 Prover 0: Proving ... % 20.17/3.62 Prover 0: stopped % 20.99/3.65 Prover 10: Preprocessing ... % 20.99/3.69 Prover 7: stopped % 21.99/3.82 Prover 10: stopped % 22.32/3.95 Prover 8: Warning: ignoring some quantifiers % 22.32/3.96 Prover 8: Constructing countermodel ... % 22.78/3.97 Prover 8: stopped % 22.78/3.97 % 22.78/3.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.78/3.97 % 22.78/3.99 % SZS output start Proof for theBenchmark % 22.92/4.00 Assumptions after simplification: % 22.92/4.00 --------------------------------- % 22.92/4.00 % 22.92/4.00 (reserved_2Eho_2Ebool__cases__ax) % 23.05/4.03 $i(c_2Ebool_2EF_2E0) & $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: % 23.05/4.03 $i] : ? [v1: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = v1 & % 23.05/4.03 s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v1) & $i(v0) & ! [v2: $i] % 23.05/4.03 : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ (s(tyop_2Emin_2Ebool, v2) = v3) | ~ % 23.05/4.03 $i(v2))) % 23.05/4.03 % 23.05/4.03 (reserved_2Eho_2Etruth) % 23.05/4.03 $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: $i] : (p(v0) = 0 & % 23.05/4.03 s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0)) % 23.05/4.03 % 23.05/4.03 (thm_2Ebool_2EBOOL__CASES__AX) % 23.05/4.04 $i(c_2Ebool_2EF_2E0) & $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: % 23.05/4.04 $i] : ? [v1: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = v1 & % 23.05/4.04 s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v1) & $i(v0) & ! [v2: $i] % 23.05/4.04 : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ (s(tyop_2Emin_2Ebool, v2) = v3) | ~ % 23.05/4.04 $i(v2))) % 23.05/4.04 % 23.05/4.04 (thm_2Ebool_2EBOUNDED__DEF) % 23.05/4.04 $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: $i] : % 23.05/4.04 (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 23.05/4.04 $i] : ( ~ (s(tyop_2Emin_2Ebool, v1) = v2) | ~ $i(v1) | ? [v3: $i] : % 23.05/4.04 (c_2Ebool_2EBOUNDED_2E1(v2) = v3 & s(tyop_2Emin_2Ebool, v3) = v0 & % 23.05/4.04 $i(v3)))) % 23.05/4.04 % 23.05/4.04 (thm_2Ebool_2ECOND__DEF) % 23.05/4.05 $i(c_2Ebool_2EF_2E0) & $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: % 23.05/4.05 $i] : ? [v1: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = v1 & % 23.05/4.05 s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v1) & $i(v0) & ! [v2: $i] % 23.05/4.05 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 23.05/4.05 [v8: $i] : ( ~ (tyop_2Emin_2Efun(v2, v5) = v6) | ~ (tyop_2Emin_2Efun(v2, % 23.05/4.05 v4) = v5) | ~ (tyop_2Emin_2Efun(v2, tyop_2Emin_2Ebool) = v4) | ~ % 23.05/4.05 (tyop_2Emin_2Efun(tyop_2Emin_2Ebool, v6) = v7) | ~ (s(v7, v3) = v8) | ~ % 23.05/4.05 $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: % 23.05/4.05 $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? % 23.05/4.05 [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? % 23.05/4.05 [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: any] : (p(v24) = v25 & % 23.05/4.05 app_2E2(v21, v22) = v23 & app_2E2(v18, v19) = v20 & app_2E2(v15, v16) = % 23.05/4.05 v17 & app_2E2(v8, v13) = v14 & s(v6, v14) = v15 & s(v5, v17) = v18 & % 23.05/4.05 s(v4, v20) = v21 & s(v2, v12) = v22 & s(v2, v11) = v19 & s(v2, v10) = % 23.05/4.05 v16 & s(tyop_2Emin_2Ebool, v23) = v24 & s(tyop_2Emin_2Ebool, v9) = v13 & % 23.05/4.05 $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 23.05/4.05 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 23.05/4.05 $i(v10) & $i(v9) & ( ~ (v25 = 0) | (v13 = v1 & ~ (v22 = v19)) | (v13 = % 23.05/4.05 v0 & ~ (v22 = v16))) & (v25 = 0 | (( ~ (v13 = v1) | v22 = v19) & ( % 23.05/4.05 ~ (v13 = v0) | v22 = v16)))) | ! [v9: $i] : ! [v10: $i] : ! % 23.05/4.05 [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! % 23.05/4.05 [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! % 23.05/4.05 [v21: $i] : ! [v22: $i] : ( ~ (c_2Emin_2E_40_2E1(v20) = v21) | ~ % 23.05/4.05 (app_2E2(v18, v14) = v19) | ~ (app_2E2(v16, v13) = v17) | ~ % 23.05/4.05 (app_2E2(v8, v12) = v15) | ~ (s(v6, v15) = v16) | ~ (s(v5, v17) = v18) % 23.05/4.05 | ~ (s(v4, v19) = v20) | ~ (s(v2, v21) = v22) | ~ (s(v2, v11) = v14) % 23.05/4.05 | ~ (s(v2, v10) = v13) | ~ (s(tyop_2Emin_2Ebool, v9) = v12) | ~ % 23.05/4.05 $i(v11) | ~ $i(v10) | ~ $i(v9) | ? [v23: $i] : % 23.05/4.05 (c_2Ebool_2ECOND_2E3(v12, v13, v14) = v23 & s(v2, v23) = v22 & $i(v23) & % 23.05/4.05 $i(v22))))) % 23.05/4.05 % 23.05/4.05 (thm_2Ebool_2EDATATYPE__TAG__DEF) % 23.05/4.05 $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: $i] : % 23.05/4.05 (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 23.05/4.05 $i] : ! [v3: $i] : ( ~ (s(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: % 23.05/4.05 $i] : (c_2Ebool_2EDATATYPE_2E1(v3) = v4 & s(tyop_2Emin_2Ebool, v4) = v0 % 23.05/4.05 & $i(v4)))) % 23.05/4.05 % 23.05/4.05 (thm_2Ebool_2EFORALL__DEF) % 23.05/4.05 $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: $i] : % 23.05/4.05 (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 23.05/4.05 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (tyop_2Emin_2Efun(v1, % 23.05/4.05 tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2) = v4) | ~ $i(v2) | ~ $i(v1) % 23.05/4.05 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v0) & % 23.05/4.05 app_2E2(v4, v6) = v7 & s(v1, v5) = v6 & s(tyop_2Emin_2Ebool, v7) = v8 & % 23.05/4.05 $i(v8) & $i(v7) & $i(v6) & $i(v5)) | ? [v5: $i] : ? [v6: $i] : % 23.05/4.06 (c_2Ebool_2E_21_2E1(v4) = v5 & p(v6) = 0 & s(tyop_2Emin_2Ebool, v5) = v6 & % 23.05/4.06 $i(v6) & $i(v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 23.05/4.06 $i] : ( ~ (tyop_2Emin_2Efun(v1, tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2) = % 23.05/4.06 v4) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : % 23.05/4.06 ( ~ (v7 = 0) & c_2Ebool_2E_21_2E1(v4) = v5 & p(v6) = v7 & % 23.05/4.06 s(tyop_2Emin_2Ebool, v5) = v6 & $i(v6) & $i(v5)) | ! [v5: $i] : ! [v6: % 23.05/4.06 $i] : ! [v7: $i] : ( ~ (app_2E2(v4, v6) = v7) | ~ (s(v1, v5) = v6) | % 23.05/4.06 ~ $i(v5) | s(tyop_2Emin_2Ebool, v7) = v0))) % 23.05/4.06 % 23.05/4.06 (thm_2Ebool_2ETRUTH) % 23.05/4.06 $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: $i] : ? [v1: int] : ( % 23.05/4.06 ~ (v1 = 0) & p(v0) = v1 & s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & % 23.05/4.06 $i(v0)) % 23.05/4.06 % 23.05/4.06 (thm_2Ebool_2ET__DEF) % 23.05/4.06 $i(c_2Ebool_2ET_2E0) & $i(tyop_2Emin_2Ebool) & ? [v0: $i] : (p(v0) = 0 & % 23.05/4.06 s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0)) % 23.05/4.06 % 23.05/4.06 (function-axioms) % 23.05/4.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 23.05/4.07 | ~ (c_2Ebool_2ECOND_2E3(v4, v3, v2) = v1) | ~ (c_2Ebool_2ECOND_2E3(v4, % 23.05/4.07 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 23.05/4.07 (v1 = v0 | ~ (c_2Ebool_2Eliteral__case_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2Eliteral__case_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 23.05/4.07 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_2Ebool_2ETYPE__DEFINITION_2E2(v3, % 23.05/4.07 v2) = v1) | ~ (c_2Ebool_2ETYPE__DEFINITION_2E2(v3, v2) = v0)) & ! [v0: % 23.05/4.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.05/4.07 (c_2Ebool_2ERES__SELECT_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2ERES__SELECT_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.05/4.07 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_2Ebool_2ERES__FORALL_2E2(v3, v2) = % 23.05/4.07 v1) | ~ (c_2Ebool_2ERES__FORALL_2E2(v3, v2) = v0)) & ! [v0: $i] : ! % 23.05/4.07 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.05/4.07 (c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 23.05/4.07 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.05/4.07 (c_2Ebool_2ERES__EXISTS_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2ERES__EXISTS_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.05/4.07 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_2Ebool_2ELET_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2ELET_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 23.05/4.07 : ! [v3: $i] : (v1 = v0 | ~ (c_2Ebool_2EIN_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2EIN_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 23.05/4.07 : ! [v3: $i] : (v1 = v0 | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Emin_2E_3D_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 23.05/4.07 : ! [v3: $i] : (v1 = v0 | ~ (c_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~ % 23.05/4.07 (c_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.05/4.07 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | % 23.05/4.07 ~ (c_2Ebool_2E_5C_2F_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.05/4.07 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | % 23.05/4.07 ~ (c_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.05/4.07 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~ % 23.05/4.07 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.05/4.07 ! [v3: $i] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = % 23.05/4.07 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.05/4.07 ~ (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.05/4.07 [v2: $i] : (v1 = v0 | ~ (c_2Ebool_2EONTO_2E1(v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2EONTO_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.05/4.07 (v1 = v0 | ~ (c_2Ebool_2EONE__ONE_2E1(v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2EONE__ONE_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.05/4.07 $i] : (v1 = v0 | ~ (c_2Ebool_2EDATATYPE_2E1(v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2EDATATYPE_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.05/4.07 $i] : (v1 = v0 | ~ (c_2Ebool_2EBOUNDED_2E1(v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2EBOUNDED_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 23.05/4.07 : (v1 = v0 | ~ (c_2Emin_2E_40_2E1(v2) = v1) | ~ (c_2Emin_2E_40_2E1(v2) = % 23.05/4.07 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.05/4.07 (c_2Ebool_2E_3F_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_3F_21_2E1(v2) = v0)) & ! % 23.05/4.07 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = % 23.05/4.07 v1) | ~ (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.05/4.07 [v2: $i] : (v1 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ % 23.05/4.07 (c_2Ebool_2E_21_2E1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.05/4.07 (v1 = v0 | ~ (c_2Ebool_2E_7E_2E1(v2) = v1) | ~ (c_2Ebool_2E_7E_2E1(v2) = % 23.05/4.07 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 23.05/4.07 $i] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 23.05/4.07 % 23.05/4.07 Further assumptions not needed in the proof: % 23.05/4.07 -------------------------------------------- % 23.05/4.07 arityeq1_2Ec_2Ebool_2EBOUNDED_2E1, % 23.05/4.07 arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27a, % 23.05/4.07 arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2EA_27a_20mono_2EA_27b, % 23.05/4.07 arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind, % 23.05/4.07 arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2EA_27a_20mono_2EA_27b, % 23.05/4.07 arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind, % 23.05/4.07 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, % 23.05/4.07 arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a, % 23.05/4.07 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1, % 23.05/4.07 arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a, % 23.05/4.07 arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a, % 23.05/4.07 arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2EA_27b, % 23.05/4.07 arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27a, % 23.05/4.07 arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27a, % 23.05/4.07 arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a, % 23.05/4.07 arityeq2_2Ec_2Ebool_2ERES__SELECT_2E2_2Emono_2EA_27a, % 23.05/4.07 arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2EA_27b, % 23.05/4.07 arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, % 23.05/4.07 arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27b, % 23.05/4.07 arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, % 23.05/4.07 arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, reserved_2Eho_2Eboolext, % 23.05/4.07 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ei__thm, reserved_2Eho_2Ek__thm, % 23.05/4.07 reserved_2Eho_2Enotfalse, reserved_2Eho_2Es__thm, reserved_2Elogic_2E_2F_5C, % 23.05/4.07 reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E, reserved_2Elogic_2E_5C_2F, % 23.05/4.07 reserved_2Elogic_2E_7E, reserved_2Equant_2E_21, reserved_2Equant_2E_3F, % 23.05/4.07 thm_2Ebool_2EAND__DEF, thm_2Ebool_2EETA__AX, thm_2Ebool_2EEXISTS__DEF, % 23.05/4.07 thm_2Ebool_2EEXISTS__UNIQUE__DEF, thm_2Ebool_2EF__DEF, % 23.05/4.07 thm_2Ebool_2EINFINITY__AX, thm_2Ebool_2EIN__DEF, thm_2Ebool_2ELET__DEF, % 23.05/4.07 thm_2Ebool_2ENOT__DEF, thm_2Ebool_2EONE__ONE__DEF, thm_2Ebool_2EONTO__DEF, % 23.05/4.07 thm_2Ebool_2EOR__DEF, thm_2Ebool_2ERES__EXISTS__DEF, % 23.05/4.07 thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF, thm_2Ebool_2ERES__FORALL__DEF, % 23.05/4.07 thm_2Ebool_2ERES__SELECT__DEF, thm_2Ebool_2ESELECT__AX, % 23.05/4.07 thm_2Ebool_2ETYPE__DEFINITION, thm_2Ebool_2Eliteral__case__DEF % 23.05/4.07 % 23.05/4.07 Those formulas are unsatisfiable: % 23.05/4.07 --------------------------------- % 23.05/4.07 % 23.05/4.07 Begin of proof % 23.05/4.07 | % 23.05/4.07 | ALPHA: (thm_2Ebool_2EBOOL__CASES__AX) implies: % 23.05/4.08 | (1) ? [v0: $i] : ? [v1: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = % 23.05/4.08 | v1 & s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v1) & $i(v0) & % 23.05/4.08 | ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 23.05/4.08 | (s(tyop_2Emin_2Ebool, v2) = v3) | ~ $i(v2))) % 23.05/4.08 | % 23.05/4.08 | ALPHA: (thm_2Ebool_2ET__DEF) implies: % 23.05/4.08 | (2) ? [v0: $i] : (p(v0) = 0 & s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 % 23.05/4.08 | & $i(v0)) % 23.05/4.08 | % 23.05/4.08 | ALPHA: (thm_2Ebool_2EFORALL__DEF) implies: % 23.05/4.08 | (3) ? [v0: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0) & % 23.05/4.08 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 23.05/4.08 | (tyop_2Emin_2Efun(v1, tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2) = % 23.05/4.08 | v4) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 23.05/4.08 | $i] : ? [v8: $i] : ( ~ (v8 = v0) & app_2E2(v4, v6) = v7 & s(v1, % 23.05/4.08 | v5) = v6 & s(tyop_2Emin_2Ebool, v7) = v8 & $i(v8) & $i(v7) & % 23.05/4.08 | $i(v6) & $i(v5)) | ? [v5: $i] : ? [v6: $i] : % 23.05/4.08 | (c_2Ebool_2E_21_2E1(v4) = v5 & p(v6) = 0 & s(tyop_2Emin_2Ebool, v5) % 23.05/4.08 | = v6 & $i(v6) & $i(v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.05/4.08 | $i] : ! [v4: $i] : ( ~ (tyop_2Emin_2Efun(v1, tyop_2Emin_2Ebool) = % 23.05/4.08 | v3) | ~ (s(v3, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : % 23.05/4.08 | ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & c_2Ebool_2E_21_2E1(v4) % 23.05/4.08 | = v5 & p(v6) = v7 & s(tyop_2Emin_2Ebool, v5) = v6 & $i(v6) & % 23.05/4.08 | $i(v5)) | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 23.05/4.08 | (app_2E2(v4, v6) = v7) | ~ (s(v1, v5) = v6) | ~ $i(v5) | % 23.05/4.08 | s(tyop_2Emin_2Ebool, v7) = v0))) % 23.05/4.08 | % 23.05/4.08 | ALPHA: (thm_2Ebool_2ECOND__DEF) implies: % 23.05/4.09 | (4) ? [v0: $i] : ? [v1: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = % 23.05/4.09 | v1 & s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v1) & $i(v0) & % 23.05/4.09 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 23.05/4.09 | ! [v7: $i] : ! [v8: $i] : ( ~ (tyop_2Emin_2Efun(v2, v5) = v6) | ~ % 23.05/4.09 | (tyop_2Emin_2Efun(v2, v4) = v5) | ~ (tyop_2Emin_2Efun(v2, % 23.05/4.09 | tyop_2Emin_2Ebool) = v4) | ~ % 23.05/4.09 | (tyop_2Emin_2Efun(tyop_2Emin_2Ebool, v6) = v7) | ~ (s(v7, v3) = % 23.05/4.09 | v8) | ~ $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : ? % 23.05/4.09 | [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 23.05/4.09 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : % 23.05/4.09 | ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 23.05/4.09 | [v24: $i] : ? [v25: any] : (p(v24) = v25 & app_2E2(v21, v22) = v23 % 23.05/4.09 | & app_2E2(v18, v19) = v20 & app_2E2(v15, v16) = v17 & app_2E2(v8, % 23.05/4.09 | v13) = v14 & s(v6, v14) = v15 & s(v5, v17) = v18 & s(v4, v20) = % 23.05/4.09 | v21 & s(v2, v12) = v22 & s(v2, v11) = v19 & s(v2, v10) = v16 & % 23.05/4.09 | s(tyop_2Emin_2Ebool, v23) = v24 & s(tyop_2Emin_2Ebool, v9) = v13 % 23.05/4.09 | & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & % 23.05/4.09 | $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 23.05/4.09 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & ( ~ (v25 = 0) | (v13 = v1 % 23.05/4.09 | & ~ (v22 = v19)) | (v13 = v0 & ~ (v22 = v16))) & (v25 = 0 | % 23.05/4.09 | (( ~ (v13 = v1) | v22 = v19) & ( ~ (v13 = v0) | v22 = v16)))) | % 23.05/4.09 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: % 23.05/4.09 | $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : % 23.05/4.09 | ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! % 23.05/4.09 | [v22: $i] : ( ~ (c_2Emin_2E_40_2E1(v20) = v21) | ~ (app_2E2(v18, % 23.05/4.09 | v14) = v19) | ~ (app_2E2(v16, v13) = v17) | ~ (app_2E2(v8, % 23.05/4.09 | v12) = v15) | ~ (s(v6, v15) = v16) | ~ (s(v5, v17) = v18) | % 23.05/4.09 | ~ (s(v4, v19) = v20) | ~ (s(v2, v21) = v22) | ~ (s(v2, v11) = % 23.05/4.09 | v14) | ~ (s(v2, v10) = v13) | ~ (s(tyop_2Emin_2Ebool, v9) = % 23.05/4.09 | v12) | ~ $i(v11) | ~ $i(v10) | ~ $i(v9) | ? [v23: $i] : % 23.05/4.09 | (c_2Ebool_2ECOND_2E3(v12, v13, v14) = v23 & s(v2, v23) = v22 & % 23.05/4.09 | $i(v23) & $i(v22))))) % 23.05/4.09 | % 23.05/4.09 | ALPHA: (thm_2Ebool_2EBOUNDED__DEF) implies: % 23.05/4.09 | (5) ? [v0: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0) & % 23.05/4.09 | ! [v1: $i] : ! [v2: $i] : ( ~ (s(tyop_2Emin_2Ebool, v1) = v2) | ~ % 23.05/4.09 | $i(v1) | ? [v3: $i] : (c_2Ebool_2EBOUNDED_2E1(v2) = v3 & % 23.05/4.09 | s(tyop_2Emin_2Ebool, v3) = v0 & $i(v3)))) % 23.05/4.09 | % 23.05/4.09 | ALPHA: (thm_2Ebool_2EDATATYPE__TAG__DEF) implies: % 23.05/4.09 | (6) ? [v0: $i] : (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0) & % 23.05/4.09 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1, v2) = v3) | ~ % 23.05/4.09 | $i(v2) | ~ $i(v1) | ? [v4: $i] : (c_2Ebool_2EDATATYPE_2E1(v3) = % 23.05/4.09 | v4 & s(tyop_2Emin_2Ebool, v4) = v0 & $i(v4)))) % 23.05/4.09 | % 23.05/4.09 | ALPHA: (thm_2Ebool_2ETRUTH) implies: % 23.05/4.09 | (7) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & p(v0) = v1 & % 23.05/4.09 | s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = v0 & $i(v0)) % 23.05/4.09 | % 23.05/4.09 | ALPHA: (function-axioms) implies: % 23.05/4.09 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 23.05/4.09 | (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 23.05/4.10 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.05/4.10 | (s(v3, v2) = v1) | ~ (s(v3, v2) = v0)) % 23.05/4.10 | % 23.05/4.10 | DELTA: instantiating (2) with fresh symbol all_48_0 gives: % 23.39/4.10 | (10) p(all_48_0) = 0 & s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_48_0 & % 23.39/4.10 | $i(all_48_0) % 23.39/4.10 | % 23.39/4.10 | ALPHA: (10) implies: % 23.39/4.10 | (11) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_48_0 % 23.39/4.10 | % 23.39/4.10 | DELTA: instantiating (2) with fresh symbol all_50_0 gives: % 23.39/4.10 | (12) p(all_50_0) = 0 & s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_50_0 & % 23.39/4.10 | $i(all_50_0) % 23.39/4.10 | % 23.39/4.10 | ALPHA: (12) implies: % 23.39/4.10 | (13) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_50_0 % 23.39/4.10 | (14) p(all_50_0) = 0 % 23.39/4.10 | % 23.39/4.10 | DELTA: instantiating (7) with fresh symbols all_54_0, all_54_1 gives: % 23.39/4.10 | (15) ~ (all_54_0 = 0) & p(all_54_1) = all_54_0 & s(tyop_2Emin_2Ebool, % 23.39/4.10 | c_2Ebool_2ET_2E0) = all_54_1 & $i(all_54_1) % 23.39/4.10 | % 23.39/4.10 | ALPHA: (15) implies: % 23.39/4.10 | (16) ~ (all_54_0 = 0) % 23.39/4.10 | (17) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_54_1 % 23.39/4.10 | (18) p(all_54_1) = all_54_0 % 23.39/4.10 | % 23.39/4.10 | DELTA: instantiating (5) with fresh symbol all_56_0 gives: % 23.39/4.10 | (19) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_56_0 & $i(all_56_0) & ! % 23.39/4.10 | [v0: $i] : ! [v1: $i] : ( ~ (s(tyop_2Emin_2Ebool, v0) = v1) | ~ % 23.39/4.10 | $i(v0) | ? [v2: $i] : (c_2Ebool_2EBOUNDED_2E1(v1) = v2 & % 23.39/4.10 | s(tyop_2Emin_2Ebool, v2) = all_56_0 & $i(v2))) % 23.39/4.10 | % 23.39/4.10 | ALPHA: (19) implies: % 23.39/4.10 | (20) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_56_0 % 23.39/4.10 | % 23.39/4.10 | DELTA: instantiating (6) with fresh symbol all_59_0 gives: % 23.39/4.10 | (21) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_59_0 & $i(all_59_0) & ! % 23.39/4.10 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (s(v0, v1) = v2) | ~ % 23.39/4.10 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (c_2Ebool_2EDATATYPE_2E1(v2) = v3 % 23.39/4.10 | & s(tyop_2Emin_2Ebool, v3) = all_59_0 & $i(v3))) % 23.39/4.10 | % 23.39/4.10 | ALPHA: (21) implies: % 23.39/4.10 | (22) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_59_0 % 23.39/4.10 | % 23.39/4.10 | DELTA: instantiating (1) with fresh symbols all_62_0, all_62_1 gives: % 23.39/4.10 | (23) s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = all_62_0 & % 23.39/4.10 | s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_62_1 & $i(all_62_0) & % 23.39/4.10 | $i(all_62_1) & ! [v0: $i] : ! [v1: int] : (v1 = all_62_0 | v1 = % 23.39/4.10 | all_62_1 | ~ (s(tyop_2Emin_2Ebool, v0) = v1) | ~ $i(v0)) % 23.39/4.10 | % 23.39/4.10 | ALPHA: (23) implies: % 23.39/4.10 | (24) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_62_1 % 23.39/4.10 | % 23.39/4.10 | DELTA: instantiating (1) with fresh symbols all_65_0, all_65_1 gives: % 23.39/4.11 | (25) s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = all_65_0 & % 23.39/4.11 | s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_65_1 & $i(all_65_0) & % 23.39/4.11 | $i(all_65_1) & ! [v0: $i] : ! [v1: int] : (v1 = all_65_0 | v1 = % 23.39/4.11 | all_65_1 | ~ (s(tyop_2Emin_2Ebool, v0) = v1) | ~ $i(v0)) % 23.39/4.11 | % 23.39/4.11 | ALPHA: (25) implies: % 23.39/4.11 | (26) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_65_1 % 23.39/4.11 | % 23.39/4.11 | DELTA: instantiating (3) with fresh symbol all_87_0 gives: % 23.39/4.11 | (27) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_87_0 & $i(all_87_0) & ! % 23.39/4.11 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.39/4.11 | (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2) | ~ (s(v2, v1) = v3) % 23.39/4.11 | | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 23.39/4.11 | ? [v7: any] : ( ~ (v7 = all_87_0) & app_2E2(v3, v5) = v6 & s(v0, v4) % 23.39/4.11 | = v5 & s(tyop_2Emin_2Ebool, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & % 23.39/4.11 | $i(v4)) | ? [v4: $i] : ? [v5: $i] : (c_2Ebool_2E_21_2E1(v3) = v4 % 23.39/4.11 | & p(v5) = 0 & s(tyop_2Emin_2Ebool, v4) = v5 & $i(v5) & $i(v4))) & % 23.39/4.11 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.39/4.11 | (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2) | ~ (s(v2, v1) = v3) % 23.39/4.11 | | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : % 23.39/4.11 | ( ~ (v6 = 0) & c_2Ebool_2E_21_2E1(v3) = v4 & p(v5) = v6 & % 23.39/4.11 | s(tyop_2Emin_2Ebool, v4) = v5 & $i(v5) & $i(v4)) | ! [v4: $i] : % 23.39/4.11 | ! [v5: $i] : ! [v6: $i] : ( ~ (app_2E2(v3, v5) = v6) | ~ (s(v0, % 23.39/4.11 | v4) = v5) | ~ $i(v4) | s(tyop_2Emin_2Ebool, v6) = all_87_0)) % 23.39/4.11 | % 23.39/4.11 | ALPHA: (27) implies: % 23.39/4.11 | (28) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_87_0 % 23.39/4.11 | % 23.39/4.11 | DELTA: instantiating (4) with fresh symbols all_99_0, all_99_1 gives: % 23.39/4.11 | (29) s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) = all_99_0 & % 23.39/4.11 | s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_99_1 & $i(all_99_0) & % 23.39/4.11 | $i(all_99_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 23.39/4.11 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (tyop_2Emin_2Efun(v0, % 23.39/4.11 | v3) = v4) | ~ (tyop_2Emin_2Efun(v0, v2) = v3) | ~ % 23.39/4.11 | (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2) | ~ % 23.39/4.11 | (tyop_2Emin_2Efun(tyop_2Emin_2Ebool, v4) = v5) | ~ (s(v5, v1) = v6) % 23.39/4.11 | | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 23.39/4.11 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 23.39/4.11 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : % 23.39/4.11 | ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: % 23.39/4.11 | any] : (p(v22) = v23 & app_2E2(v19, v20) = v21 & app_2E2(v16, v17) % 23.39/4.11 | = v18 & app_2E2(v13, v14) = v15 & app_2E2(v6, v11) = v12 & s(v4, % 23.39/4.11 | v12) = v13 & s(v3, v15) = v16 & s(v2, v18) = v19 & s(v0, v10) = % 23.39/4.11 | v20 & s(v0, v9) = v17 & s(v0, v8) = v14 & s(tyop_2Emin_2Ebool, % 23.39/4.11 | v21) = v22 & s(tyop_2Emin_2Ebool, v7) = v11 & $i(v22) & $i(v21) % 23.39/4.11 | & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & % 23.39/4.11 | $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) % 23.39/4.11 | & $i(v7) & ( ~ (v23 = 0) | (v11 = all_99_0 & ~ (v20 = v17)) | % 23.39/4.11 | (v11 = all_99_1 & ~ (v20 = v14))) & (v23 = 0 | (( ~ (v11 = % 23.39/4.11 | all_99_0) | v20 = v17) & ( ~ (v11 = all_99_1) | v20 = % 23.39/4.11 | v14)))) | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 23.39/4.11 | $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : % 23.39/4.11 | ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: % 23.39/4.11 | $i] : ! [v20: $i] : ( ~ (c_2Emin_2E_40_2E1(v18) = v19) | ~ % 23.39/4.11 | (app_2E2(v16, v12) = v17) | ~ (app_2E2(v14, v11) = v15) | ~ % 23.39/4.11 | (app_2E2(v6, v10) = v13) | ~ (s(v4, v13) = v14) | ~ (s(v3, v15) % 23.39/4.11 | = v16) | ~ (s(v2, v17) = v18) | ~ (s(v0, v19) = v20) | ~ % 23.39/4.11 | (s(v0, v9) = v12) | ~ (s(v0, v8) = v11) | ~ % 23.39/4.11 | (s(tyop_2Emin_2Ebool, v7) = v10) | ~ $i(v9) | ~ $i(v8) | ~ % 23.39/4.11 | $i(v7) | ? [v21: $i] : (c_2Ebool_2ECOND_2E3(v10, v11, v12) = v21 % 23.39/4.12 | & s(v0, v21) = v20 & $i(v21) & $i(v20)))) % 23.39/4.12 | % 23.39/4.12 | ALPHA: (29) implies: % 23.39/4.12 | (30) s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) = all_99_1 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_48_0, all_54_1, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (11), (17) gives: % 23.39/4.12 | (31) all_54_1 = all_48_0 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_54_1, all_59_0, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (17), (22) gives: % 23.39/4.12 | (32) all_59_0 = all_54_1 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_59_0, all_62_1, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (22), (24) gives: % 23.39/4.12 | (33) all_62_1 = all_59_0 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_59_0, all_87_0, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (22), (28) gives: % 23.39/4.12 | (34) all_87_0 = all_59_0 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_56_0, all_87_0, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (20), (28) gives: % 23.39/4.12 | (35) all_87_0 = all_56_0 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_65_1, all_99_1, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (26), (30) gives: % 23.39/4.12 | (36) all_99_1 = all_65_1 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_62_1, all_99_1, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (24), (30) gives: % 23.39/4.12 | (37) all_99_1 = all_62_1 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (9) with all_50_0, all_99_1, c_2Ebool_2ET_2E0, % 23.39/4.12 | tyop_2Emin_2Ebool, simplifying with (13), (30) gives: % 23.39/4.12 | (38) all_99_1 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (36), (38) imply: % 23.39/4.12 | (39) all_65_1 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (36), (37) imply: % 23.39/4.12 | (40) all_65_1 = all_62_1 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (34), (35) imply: % 23.39/4.12 | (41) all_59_0 = all_56_0 % 23.39/4.12 | % 23.39/4.12 | SIMP: (41) implies: % 23.39/4.12 | (42) all_59_0 = all_56_0 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (39), (40) imply: % 23.39/4.12 | (43) all_62_1 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | SIMP: (43) implies: % 23.39/4.12 | (44) all_62_1 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (33), (44) imply: % 23.39/4.12 | (45) all_59_0 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | SIMP: (45) implies: % 23.39/4.12 | (46) all_59_0 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (32), (42) imply: % 23.39/4.12 | (47) all_56_0 = all_54_1 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (42), (46) imply: % 23.39/4.12 | (48) all_56_0 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (47), (48) imply: % 23.39/4.12 | (49) all_54_1 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | SIMP: (49) implies: % 23.39/4.12 | (50) all_54_1 = all_50_0 % 23.39/4.12 | % 23.39/4.12 | COMBINE_EQS: (31), (50) imply: % 23.39/4.12 | (51) all_50_0 = all_48_0 % 23.39/4.12 | % 23.39/4.12 | SIMP: (51) implies: % 23.39/4.12 | (52) all_50_0 = all_48_0 % 23.39/4.12 | % 23.39/4.12 | REDUCE: (18), (31) imply: % 23.39/4.12 | (53) p(all_48_0) = all_54_0 % 23.39/4.12 | % 23.39/4.12 | REDUCE: (14), (52) imply: % 23.39/4.12 | (54) p(all_48_0) = 0 % 23.39/4.12 | % 23.39/4.12 | GROUND_INST: instantiating (8) with 0, all_54_0, all_48_0, simplifying with % 23.39/4.12 | (53), (54) gives: % 23.39/4.12 | (55) all_54_0 = 0 % 23.39/4.12 | % 23.39/4.12 | REDUCE: (16), (55) imply: % 23.39/4.12 | (56) $false % 23.39/4.13 | % 23.39/4.13 | CLOSE: (56) is inconsistent. % 23.39/4.13 | % 23.39/4.13 End of proof % 23.39/4.13 % SZS output end Proof for theBenchmark % 23.39/4.13 % 23.39/4.13 3515ms %------------------------------------------------------------------------------