TSTP Solution File: ITP019_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP019_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 10.49s 2.26s
% Output : Proof 13.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP019_2 : 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 : n010.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 14:14:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 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
% 3.52/1.22 Prover 4: Preprocessing ...
% 3.52/1.22 Prover 1: Preprocessing ...
% 3.71/1.25 Prover 6: Preprocessing ...
% 3.71/1.25 Prover 3: Preprocessing ...
% 3.71/1.25 Prover 2: Preprocessing ...
% 3.71/1.25 Prover 0: Preprocessing ...
% 3.71/1.25 Prover 5: Preprocessing ...
% 7.75/1.81 Prover 1: Warning: ignoring some quantifiers
% 7.75/1.84 Prover 3: Warning: ignoring some quantifiers
% 8.38/1.89 Prover 1: Constructing countermodel ...
% 8.38/1.89 Prover 3: Constructing countermodel ...
% 8.38/1.96 Prover 6: Proving ...
% 9.13/2.00 Prover 5: Proving ...
% 9.20/2.08 Prover 4: Warning: ignoring some quantifiers
% 9.43/2.13 Prover 4: Constructing countermodel ...
% 10.49/2.20 Prover 2: Proving ...
% 10.49/2.26 Prover 3: proved (1625ms)
% 10.49/2.26
% 10.49/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.49/2.26
% 10.49/2.27 Prover 2: stopped
% 10.49/2.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.49/2.27 Prover 5: stopped
% 10.49/2.27 Prover 6: stopped
% 10.49/2.28 Prover 0: Proving ...
% 10.49/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.49/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.49/2.28 Prover 0: stopped
% 10.49/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.49/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.28/2.37 Prover 11: Preprocessing ...
% 11.28/2.38 Prover 8: Preprocessing ...
% 11.28/2.39 Prover 7: Preprocessing ...
% 11.28/2.39 Prover 10: Preprocessing ...
% 11.28/2.40 Prover 13: Preprocessing ...
% 12.03/2.45 Prover 1: Found proof (size 32)
% 12.03/2.45 Prover 1: proved (1816ms)
% 12.03/2.45 Prover 4: stopped
% 12.03/2.46 Prover 7: stopped
% 12.03/2.48 Prover 11: stopped
% 12.03/2.49 Prover 13: stopped
% 12.72/2.50 Prover 10: Warning: ignoring some quantifiers
% 12.72/2.51 Prover 10: Constructing countermodel ...
% 12.72/2.53 Prover 10: stopped
% 12.72/2.56 Prover 8: Warning: ignoring some quantifiers
% 12.72/2.57 Prover 8: Constructing countermodel ...
% 13.20/2.59 Prover 8: stopped
% 13.20/2.59
% 13.20/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.20/2.59
% 13.24/2.60 % SZS output start Proof for theBenchmark
% 13.24/2.60 Assumptions after simplification:
% 13.24/2.60 ---------------------------------
% 13.24/2.60
% 13.24/2.60 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0)
% 13.24/2.63 tp__ty_2Enum_2Enum(fo__c_2Enum_2E0) & $i(c_2Ecomplex_2Ecomplex__inv) &
% 13.24/2.63 $i(c_2Ecomplex_2Ecomplex__of__num) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 13.24/2.63 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
% 13.24/2.63 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v1) = v2 &
% 13.24/2.63 inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = v0 &
% 13.24/2.63 ap(c_2Ecomplex_2Ecomplex__of__num, v0) = v1 &
% 13.24/2.63 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) & $i(v1) &
% 13.24/2.63 $i(v0) & ! [v3:
% 13.24/2.63 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ! [v4:
% 13.24/2.63 $i] : (v3 = v2 | ~
% 13.24/2.63 (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) = v4) |
% 13.24/2.63 ~ tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) | ?
% 13.24/2.63 [v5: $i] : ? [v6:
% 13.24/2.63 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( ~ (v6
% 13.24/2.63 = v2) &
% 13.24/2.64 surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v5) = v6
% 13.24/2.64 & ap(c_2Ecomplex_2Ecomplex__inv, v4) = v5 &
% 13.24/2.64 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v6) &
% 13.24/2.64 $i(v5))) & ! [v3: $i] : ( ~
% 13.24/2.64 (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) = v3) |
% 13.24/2.64 ? [v4: $i] :
% 13.24/2.64 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v4) = v2 &
% 13.24/2.64 ap(c_2Ecomplex_2Ecomplex__inv, v3) = v4 & $i(v4))))
% 13.24/2.64
% 13.24/2.64 (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ)
% 13.24/2.64 tp__ty_2Enum_2Enum(fo__c_2Enum_2E0) & $i(c_2Ecomplex_2Ecomplex__inv) &
% 13.24/2.64 $i(c_2Ecomplex_2Ecomplex__of__num) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 13.24/2.64 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
% 13.24/2.64 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v1) = v2 &
% 13.24/2.64 inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = v0 &
% 13.24/2.64 ap(c_2Ecomplex_2Ecomplex__of__num, v0) = v1 &
% 13.24/2.64 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) & $i(v1) &
% 13.24/2.64 $i(v0) & ? [v3:
% 13.24/2.64 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ? [v4:
% 13.24/2.64 $i] : ? [v5: $i] : ( ~ (v3 = v2) &
% 13.24/2.64 inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) = v4 &
% 13.24/2.64 surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v5) = v2 &
% 13.24/2.64 ap(c_2Ecomplex_2Ecomplex__inv, v4) = v5 &
% 13.24/2.64 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) & $i(v5)
% 13.24/2.64 & $i(v4)))
% 13.24/2.64
% 13.24/2.64 (stp_eq_fo_c_2Enum_2E0)
% 13.24/2.64 inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = c_2Enum_2E0 &
% 13.24/2.64 tp__ty_2Enum_2Enum(fo__c_2Enum_2E0) & $i(c_2Enum_2E0)
% 13.24/2.64
% 13.24/2.64 (function-axioms)
% 13.24/2.65 ! [v0: del] : ! [v1: del] : ! [v2: del] : ! [v3: del] : (v1 = v0 | ~
% 13.24/2.65 (ty_2Epair_2Eprod(v3, v2) = v1) | ~ (ty_2Epair_2Eprod(v3, v2) = v0)) & !
% 13.24/2.65 [v0: tp__o] : ! [v1: tp__o] : ! [v2: tp__o] : ! [v3: tp__o] : (v1 = v0 | ~
% 13.24/2.65 (fo__c_2Ebool_2E_2F_5C(v3, v2) = v1) | ~ (fo__c_2Ebool_2E_2F_5C(v3, v2) =
% 13.24/2.65 v0)) & ! [v0: tp__o] : ! [v1: tp__o] : ! [v2: tp__o] : ! [v3: tp__o] :
% 13.24/2.65 (v1 = v0 | ~ (fo__c_2Emin_2E_3D_3D_3E(v3, v2) = v1) | ~
% 13.24/2.65 (fo__c_2Emin_2E_3D_3D_3E(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.24/2.65 [v2: $i] : ! [v3: del] : (v1 = v0 | ~ (k(v3, v2) = v1) | ~ (k(v3, v2) =
% 13.24/2.65 v0)) & ! [v0: del] : ! [v1: del] : ! [v2: del] : ! [v3: del] : (v1 =
% 13.24/2.65 v0 | ~ (arr(v3, v2) = v1) | ~ (arr(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 13.24/2.65 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ap(v3, v2) = v1) | ~
% 13.24/2.65 (ap(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 13.24/2.65 : ! [v2: del] : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3,
% 13.24/2.65 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: del] : (v1 = v0 | ~
% 13.24/2.65 (c_2Ebool_2E_21(v2) = v1) | ~ (c_2Ebool_2E_21(v2) = v0)) & ! [v0: $i] : !
% 13.24/2.65 [v1: $i] : ! [v2: del] : (v1 = v0 | ~ (c_2Emin_2E_3D(v2) = v1) | ~
% 13.24/2.65 (c_2Emin_2E_3D(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.24/2.65 tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (v1 = v0 |
% 13.24/2.65 ~ (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) = v1) |
% 13.24/2.65 ~ (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) = v0))
% 13.24/2.65 & ! [v0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : !
% 13.24/2.65 [v1: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ! [v2:
% 13.24/2.65 $i] : (v1 = v0 | ~
% 13.24/2.65 (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) = v1) |
% 13.24/2.65 ~ (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) = v0))
% 13.24/2.65 & ! [v0: $i] : ! [v1: $i] : ! [v2: tp__ty_2Erealax_2Ereal] : (v1 = v0 | ~
% 13.24/2.65 (inj__ty_2Erealax_2Ereal(v2) = v1) | ~ (inj__ty_2Erealax_2Ereal(v2) = v0))
% 13.24/2.65 & ! [v0: tp__ty_2Erealax_2Ereal] : ! [v1: tp__ty_2Erealax_2Ereal] : ! [v2:
% 13.24/2.65 $i] : (v1 = v0 | ~ (surj__ty_2Erealax_2Ereal(v2) = v1) | ~
% 13.24/2.65 (surj__ty_2Erealax_2Ereal(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.24/2.65 tp__ty_2Enum_2Enum] : (v1 = v0 | ~ (inj__ty_2Enum_2Enum(v2) = v1) | ~
% 13.24/2.65 (inj__ty_2Enum_2Enum(v2) = v0)) & ! [v0: tp__ty_2Enum_2Enum] : ! [v1:
% 13.24/2.65 tp__ty_2Enum_2Enum] : ! [v2: $i] : (v1 = v0 | ~ (surj__ty_2Enum_2Enum(v2)
% 13.24/2.65 = v1) | ~ (surj__ty_2Enum_2Enum(v2) = v0)) & ! [v0: tp__o] : ! [v1:
% 13.24/2.65 tp__o] : ! [v2: tp__o] : (v1 = v0 | ~ (fo__c_2Ebool_2E_7E(v2) = v1) | ~
% 13.24/2.65 (fo__c_2Ebool_2E_7E(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: tp__o]
% 13.24/2.65 : (v1 = v0 | ~ (inj__o(v2) = v1) | ~ (inj__o(v2) = v0)) & ! [v0: tp__o] :
% 13.24/2.65 ! [v1: tp__o] : ! [v2: $i] : (v1 = v0 | ~ (surj__o(v2) = v1) | ~
% 13.24/2.65 (surj__o(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: del] : (v1 = v0 |
% 13.24/2.65 ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.24/2.65 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) =
% 13.24/2.65 v0))
% 13.24/2.65
% 13.24/2.65 Further assumptions not needed in the proof:
% 13.24/2.65 --------------------------------------------
% 13.24/2.65 ap_tp, ax_all_p, ax_and_p, ax_eq_p, ax_false_p, ax_imp_p, ax_neg_p, ax_true_p,
% 13.24/2.65 boolext, conj_thm_2Ebool_2EFORALL__SIMP, conj_thm_2Ebool_2EIMP__CLAUSES,
% 13.24/2.65 conj_thm_2Ebool_2ETRUTH, funcext, ibeta, kbeta, mem_c_2Ebool_2EF,
% 13.24/2.65 mem_c_2Ebool_2ET, mem_c_2Ebool_2E_21, mem_c_2Ebool_2E_2F_5C, mem_c_2Ebool_2E_7E,
% 13.24/2.65 mem_c_2Ecomplex_2Ecomplex__inv, mem_c_2Ecomplex_2Ecomplex__of__num,
% 13.24/2.65 mem_c_2Emin_2E_3D, mem_c_2Emin_2E_3D_3D_3E, mem_c_2Enum_2E0,
% 13.24/2.65 stp_eq_fo_c_2Ebool_2EF, stp_eq_fo_c_2Ebool_2ET, stp_eq_fo_c_2Ebool_2E_2F_5C,
% 13.24/2.65 stp_eq_fo_c_2Ebool_2E_7E, stp_eq_fo_c_2Emin_2E_3D_3D_3E,
% 13.24/2.65 stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,
% 13.24/2.65 stp_inj_mem_o, stp_inj_mem_ty_2Enum_2Enum, stp_inj_mem_ty_2Erealax_2Ereal,
% 13.24/2.65 stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,
% 13.24/2.65 stp_inj_surj_o, stp_inj_surj_ty_2Enum_2Enum, stp_inj_surj_ty_2Erealax_2Ereal,
% 13.24/2.65 stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,
% 13.24/2.65 stp_iso_mem_o, stp_iso_mem_ty_2Enum_2Enum, stp_iso_mem_ty_2Erealax_2Ereal
% 13.24/2.65
% 13.24/2.65 Those formulas are unsatisfiable:
% 13.24/2.65 ---------------------------------
% 13.24/2.65
% 13.24/2.65 Begin of proof
% 13.24/2.66 |
% 13.24/2.66 | ALPHA: (stp_eq_fo_c_2Enum_2E0) implies:
% 13.24/2.66 | (1) inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = c_2Enum_2E0
% 13.24/2.66 |
% 13.24/2.66 | ALPHA: (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) implies:
% 13.24/2.66 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2:
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
% 13.24/2.66 | (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v1) =
% 13.24/2.66 | v2 & inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = v0 &
% 13.24/2.66 | ap(c_2Ecomplex_2Ecomplex__of__num, v0) = v1 &
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) &
% 13.24/2.66 | $i(v1) & $i(v0) & ! [v3:
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : !
% 13.24/2.66 | [v4: $i] : (v3 = v2 | ~
% 13.24/2.66 | (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3)
% 13.24/2.66 | = v4) | ~
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) |
% 13.24/2.66 | ? [v5: $i] : ? [v6:
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : (
% 13.24/2.66 | ~ (v6 = v2) &
% 13.24/2.66 | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v5)
% 13.24/2.66 | = v6 & ap(c_2Ecomplex_2Ecomplex__inv, v4) = v5 &
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v6)
% 13.24/2.66 | & $i(v5))) & ! [v3: $i] : ( ~
% 13.24/2.66 | (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2)
% 13.24/2.66 | = v3) | ? [v4: $i] :
% 13.24/2.66 | (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v4)
% 13.24/2.66 | = v2 & ap(c_2Ecomplex_2Ecomplex__inv, v3) = v4 & $i(v4))))
% 13.24/2.66 |
% 13.24/2.66 | ALPHA: (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) implies:
% 13.24/2.66 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2:
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
% 13.24/2.66 | (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v1) =
% 13.24/2.66 | v2 & inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = v0 &
% 13.24/2.66 | ap(c_2Ecomplex_2Ecomplex__of__num, v0) = v1 &
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) &
% 13.24/2.66 | $i(v1) & $i(v0) & ? [v3:
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ?
% 13.24/2.66 | [v4: $i] : ? [v5: $i] : ( ~ (v3 = v2) &
% 13.24/2.66 | inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) =
% 13.24/2.66 | v4 &
% 13.24/2.66 | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v5)
% 13.24/2.66 | = v2 & ap(c_2Ecomplex_2Ecomplex__inv, v4) = v5 &
% 13.24/2.66 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) &
% 13.24/2.66 | $i(v5) & $i(v4)))
% 13.24/2.66 |
% 13.24/2.66 | ALPHA: (function-axioms) implies:
% 13.24/2.66 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: tp__ty_2Enum_2Enum] : (v1 = v0 | ~
% 13.24/2.66 | (inj__ty_2Enum_2Enum(v2) = v1) | ~ (inj__ty_2Enum_2Enum(v2) = v0))
% 13.24/2.66 | (5) ! [v0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
% 13.24/2.66 | ! [v1: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
% 13.24/2.66 | ! [v2: $i] : (v1 = v0 | ~
% 13.24/2.66 | (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) =
% 13.24/2.66 | v1) | ~
% 13.24/2.66 | (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) =
% 13.24/2.66 | v0))
% 13.24/2.66 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.24/2.66 | (ap(v3, v2) = v1) | ~ (ap(v3, v2) = v0))
% 13.24/2.67 |
% 13.24/2.67 | DELTA: instantiating (3) with fresh symbols all_62_0, all_62_1, all_62_2
% 13.24/2.67 | gives:
% 13.24/2.67 | (7) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_62_1)
% 13.24/2.67 | = all_62_0 & inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = all_62_2 &
% 13.24/2.67 | ap(c_2Ecomplex_2Ecomplex__of__num, all_62_2) = all_62_1 &
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_62_0)
% 13.24/2.67 | & $i(all_62_1) & $i(all_62_2) & ? [v0: any] : ? [v1: $i] : ? [v2:
% 13.24/2.67 | $i] : ( ~ (v0 = all_62_0) &
% 13.24/2.67 | inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) =
% 13.24/2.67 | v1 &
% 13.24/2.67 | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) =
% 13.24/2.67 | all_62_0 & ap(c_2Ecomplex_2Ecomplex__inv, v1) = v2 &
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) &
% 13.24/2.67 | $i(v2) & $i(v1))
% 13.24/2.67 |
% 13.24/2.67 | ALPHA: (7) implies:
% 13.24/2.67 | (8) ap(c_2Ecomplex_2Ecomplex__of__num, all_62_2) = all_62_1
% 13.24/2.67 | (9) inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = all_62_2
% 13.24/2.67 | (10) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_62_1)
% 13.24/2.67 | = all_62_0
% 13.24/2.67 | (11) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = all_62_0) &
% 13.24/2.67 | inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) =
% 13.24/2.67 | v1 &
% 13.24/2.67 | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2) =
% 13.24/2.67 | all_62_0 & ap(c_2Ecomplex_2Ecomplex__inv, v1) = v2 &
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) &
% 13.24/2.67 | $i(v2) & $i(v1))
% 13.24/2.67 |
% 13.24/2.67 | DELTA: instantiating (2) with fresh symbols all_64_0, all_64_1, all_64_2
% 13.24/2.67 | gives:
% 13.24/2.67 | (12) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_64_1)
% 13.24/2.67 | = all_64_0 & inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = all_64_2 &
% 13.24/2.67 | ap(c_2Ecomplex_2Ecomplex__of__num, all_64_2) = all_64_1 &
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_64_0)
% 13.24/2.67 | & $i(all_64_1) & $i(all_64_2) & ! [v0: any] : ! [v1: $i] : (v0 =
% 13.24/2.67 | all_64_0 | ~
% 13.24/2.67 | (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) =
% 13.24/2.67 | v1) | ~
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) |
% 13.24/2.67 | ? [v2: $i] : ? [v3: any] : ( ~ (v3 = all_64_0) &
% 13.24/2.67 | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2)
% 13.24/2.67 | = v3 & ap(c_2Ecomplex_2Ecomplex__inv, v1) = v2 &
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) &
% 13.24/2.67 | $i(v2))) & ! [v0: $i] : ( ~
% 13.24/2.67 | (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_64_0)
% 13.24/2.67 | = v0) | ? [v1: $i] :
% 13.24/2.67 | (surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v1)
% 13.24/2.67 | = all_64_0 & ap(c_2Ecomplex_2Ecomplex__inv, v0) = v1 & $i(v1)))
% 13.24/2.67 |
% 13.24/2.67 | ALPHA: (12) implies:
% 13.24/2.67 | (13) ap(c_2Ecomplex_2Ecomplex__of__num, all_64_2) = all_64_1
% 13.24/2.67 | (14) inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = all_64_2
% 13.24/2.67 | (15) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_64_1)
% 13.24/2.67 | = all_64_0
% 13.24/2.67 | (16) ! [v0: any] : ! [v1: $i] : (v0 = all_64_0 | ~
% 13.24/2.67 | (inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) =
% 13.24/2.67 | v1) | ~
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0) |
% 13.24/2.67 | ? [v2: $i] : ? [v3: any] : ( ~ (v3 = all_64_0) &
% 13.24/2.67 | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v2)
% 13.24/2.67 | = v3 & ap(c_2Ecomplex_2Ecomplex__inv, v1) = v2 &
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v3) &
% 13.24/2.67 | $i(v2)))
% 13.24/2.67 |
% 13.24/2.67 | DELTA: instantiating (11) with fresh symbols all_67_0, all_67_1, all_67_2
% 13.24/2.67 | gives:
% 13.24/2.67 | (17) ~ (all_67_2 = all_62_0) &
% 13.24/2.67 | inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_67_2)
% 13.24/2.67 | = all_67_1 &
% 13.24/2.67 | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_67_0)
% 13.24/2.67 | = all_62_0 & ap(c_2Ecomplex_2Ecomplex__inv, all_67_1) = all_67_0 &
% 13.24/2.67 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_67_2)
% 13.24/2.67 | & $i(all_67_0) & $i(all_67_1)
% 13.24/2.67 |
% 13.24/2.67 | ALPHA: (17) implies:
% 13.24/2.67 | (18) ~ (all_67_2 = all_62_0)
% 13.24/2.67 | (19) tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_67_2)
% 13.24/2.68 | (20) ap(c_2Ecomplex_2Ecomplex__inv, all_67_1) = all_67_0
% 13.24/2.68 | (21) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_67_0)
% 13.24/2.68 | = all_62_0
% 13.24/2.68 | (22) inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_67_2)
% 13.24/2.68 | = all_67_1
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (4) with all_62_2, all_64_2, fo__c_2Enum_2E0,
% 13.24/2.68 | simplifying with (9), (14) gives:
% 13.24/2.68 | (23) all_64_2 = all_62_2
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (4) with c_2Enum_2E0, all_64_2, fo__c_2Enum_2E0,
% 13.24/2.68 | simplifying with (1), (14) gives:
% 13.24/2.68 | (24) all_64_2 = c_2Enum_2E0
% 13.24/2.68 |
% 13.24/2.68 | COMBINE_EQS: (23), (24) imply:
% 13.24/2.68 | (25) all_62_2 = c_2Enum_2E0
% 13.24/2.68 |
% 13.24/2.68 | REDUCE: (13), (24) imply:
% 13.24/2.68 | (26) ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = all_64_1
% 13.24/2.68 |
% 13.24/2.68 | REDUCE: (8), (25) imply:
% 13.24/2.68 | (27) ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = all_62_1
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (6) with all_62_1, all_64_1, c_2Enum_2E0,
% 13.24/2.68 | c_2Ecomplex_2Ecomplex__of__num, simplifying with (26), (27)
% 13.24/2.68 | gives:
% 13.24/2.68 | (28) all_64_1 = all_62_1
% 13.24/2.68 |
% 13.24/2.68 | REDUCE: (15), (28) imply:
% 13.24/2.68 | (29) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_62_1)
% 13.24/2.68 | = all_64_0
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (5) with all_62_0, all_64_0, all_62_1, simplifying
% 13.24/2.68 | with (10), (29) gives:
% 13.24/2.68 | (30) all_64_0 = all_62_0
% 13.24/2.68 |
% 13.24/2.68 | GROUND_INST: instantiating (16) with all_67_2, all_67_1, simplifying with
% 13.24/2.68 | (19), (22) gives:
% 13.24/2.68 | (31) all_67_2 = all_64_0 | ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_64_0)
% 13.24/2.68 | & surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0)
% 13.24/2.68 | = v1 & ap(c_2Ecomplex_2Ecomplex__inv, all_67_1) = v0 &
% 13.24/2.68 | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v1) &
% 13.24/2.68 | $i(v0))
% 13.24/2.68 |
% 13.24/2.68 | BETA: splitting (31) gives:
% 13.24/2.68 |
% 13.24/2.68 | Case 1:
% 13.24/2.68 | |
% 13.24/2.68 | | (32) all_67_2 = all_64_0
% 13.24/2.68 | |
% 13.24/2.68 | | COMBINE_EQS: (30), (32) imply:
% 13.24/2.68 | | (33) all_67_2 = all_62_0
% 13.24/2.68 | |
% 13.24/2.68 | | REDUCE: (18), (33) imply:
% 13.24/2.68 | | (34) $false
% 13.24/2.68 | |
% 13.24/2.68 | | CLOSE: (34) is inconsistent.
% 13.24/2.68 | |
% 13.24/2.68 | Case 2:
% 13.24/2.68 | |
% 13.24/2.68 | | (35) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_64_0) &
% 13.24/2.68 | | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v0)
% 13.24/2.68 | | = v1 & ap(c_2Ecomplex_2Ecomplex__inv, all_67_1) = v0 &
% 13.24/2.68 | | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(v1) &
% 13.24/2.68 | | $i(v0))
% 13.24/2.68 | |
% 13.24/2.68 | | DELTA: instantiating (35) with fresh symbols all_115_0, all_115_1 gives:
% 13.24/2.68 | | (36) ~ (all_115_0 = all_64_0) &
% 13.24/2.68 | | surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_115_1)
% 13.24/2.68 | | = all_115_0 & ap(c_2Ecomplex_2Ecomplex__inv, all_67_1) = all_115_1 &
% 13.24/2.68 | | tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_115_0)
% 13.24/2.68 | | & $i(all_115_1)
% 13.24/2.68 | |
% 13.24/2.68 | | ALPHA: (36) implies:
% 13.24/2.68 | | (37) ~ (all_115_0 = all_64_0)
% 13.24/2.68 | | (38) ap(c_2Ecomplex_2Ecomplex__inv, all_67_1) = all_115_1
% 13.24/2.68 | | (39) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_115_1)
% 13.24/2.68 | | = all_115_0
% 13.24/2.68 | |
% 13.24/2.68 | | REDUCE: (30), (37) imply:
% 13.24/2.68 | | (40) ~ (all_115_0 = all_62_0)
% 13.24/2.68 | |
% 13.24/2.69 | | GROUND_INST: instantiating (6) with all_67_0, all_115_1, all_67_1,
% 13.24/2.69 | | c_2Ecomplex_2Ecomplex__inv, simplifying with (20), (38) gives:
% 13.24/2.69 | | (41) all_115_1 = all_67_0
% 13.24/2.69 | |
% 13.24/2.69 | | REDUCE: (39), (41) imply:
% 13.24/2.69 | | (42) surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal(all_67_0)
% 13.24/2.69 | | = all_115_0
% 13.24/2.69 | |
% 13.24/2.69 | | GROUND_INST: instantiating (5) with all_62_0, all_115_0, all_67_0,
% 13.24/2.69 | | simplifying with (21), (42) gives:
% 13.24/2.69 | | (43) all_115_0 = all_62_0
% 13.24/2.69 | |
% 13.24/2.69 | | REDUCE: (40), (43) imply:
% 13.24/2.69 | | (44) $false
% 13.24/2.69 | |
% 13.24/2.69 | | CLOSE: (44) is inconsistent.
% 13.24/2.69 | |
% 13.24/2.69 | End of split
% 13.24/2.69 |
% 13.24/2.69 End of proof
% 13.24/2.69 % SZS output end Proof for theBenchmark
% 13.24/2.69
% 13.24/2.69 2072ms
%------------------------------------------------------------------------------