TSTP Solution File: ITP019_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP019_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 04:08:55 EDT 2023
% Result : Theorem 11.55s 2.41s
% Output : Proof 15.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP019_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sun Aug 27 13:58:27 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.34/1.29 Prover 4: Preprocessing ...
% 4.34/1.29 Prover 1: Preprocessing ...
% 4.34/1.33 Prover 5: Preprocessing ...
% 4.34/1.33 Prover 6: Preprocessing ...
% 4.34/1.33 Prover 0: Preprocessing ...
% 4.34/1.33 Prover 3: Preprocessing ...
% 4.34/1.33 Prover 2: Preprocessing ...
% 9.52/2.10 Prover 1: Warning: ignoring some quantifiers
% 9.52/2.15 Prover 3: Warning: ignoring some quantifiers
% 9.52/2.15 Prover 4: Warning: ignoring some quantifiers
% 9.52/2.17 Prover 1: Constructing countermodel ...
% 9.52/2.19 Prover 3: Constructing countermodel ...
% 9.52/2.19 Prover 6: Proving ...
% 9.52/2.21 Prover 0: Proving ...
% 9.52/2.22 Prover 5: Proving ...
% 10.64/2.23 Prover 4: Constructing countermodel ...
% 11.55/2.36 Prover 2: Proving ...
% 11.55/2.40 Prover 3: proved (1796ms)
% 11.55/2.40
% 11.55/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.55/2.41
% 11.55/2.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.55/2.41 Prover 0: stopped
% 11.55/2.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.55/2.41 Prover 5: stopped
% 12.32/2.42 Prover 6: proved (1801ms)
% 12.32/2.42
% 12.32/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.32/2.42
% 12.32/2.43 Prover 2: stopped
% 12.32/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.32/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.32/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.89/2.53 Prover 8: Preprocessing ...
% 12.89/2.54 Prover 10: Preprocessing ...
% 12.89/2.55 Prover 11: Preprocessing ...
% 12.89/2.55 Prover 7: Preprocessing ...
% 12.89/2.56 Prover 13: Preprocessing ...
% 14.46/2.72 Prover 1: Found proof (size 19)
% 14.64/2.72 Prover 1: proved (2117ms)
% 14.64/2.72 Prover 4: stopped
% 14.64/2.74 Prover 10: Warning: ignoring some quantifiers
% 14.64/2.74 Prover 7: Warning: ignoring some quantifiers
% 14.64/2.75 Prover 13: stopped
% 14.64/2.76 Prover 10: Constructing countermodel ...
% 14.64/2.77 Prover 7: Constructing countermodel ...
% 14.64/2.78 Prover 10: stopped
% 14.64/2.79 Prover 7: stopped
% 14.64/2.79 Prover 8: Warning: ignoring some quantifiers
% 14.64/2.81 Prover 8: Constructing countermodel ...
% 15.31/2.82 Prover 8: stopped
% 15.31/2.85 Prover 11: Warning: ignoring some quantifiers
% 15.31/2.86 Prover 11: Constructing countermodel ...
% 15.31/2.87 Prover 11: stopped
% 15.31/2.87
% 15.31/2.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.31/2.87
% 15.31/2.87 % SZS output start Proof for theBenchmark
% 15.31/2.88 Assumptions after simplification:
% 15.31/2.88 ---------------------------------
% 15.31/2.88
% 15.31/2.88 (thm_2Ecomplex_2ECOMPLEX__INV__EQ__0)
% 15.68/2.90 mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) & ? [v0:
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.90 : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = v0 &
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)
% 15.68/2.90 & ! [v1:
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.90 : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0) | ~
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1))
% 15.68/2.90 & ! [v1:
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.90 : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = v1)))
% 15.68/2.90
% 15.68/2.90 (thm_2Ecomplex_2ECOMPLEX__INV__NZ)
% 15.68/2.90 mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) & ? [v0:
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.90 : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = v0 &
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)
% 15.68/2.90 & ? [v1:
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.90 : ( ~ (v1 = v0) & mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0 &
% 15.68/2.90 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1)))
% 15.68/2.90
% 15.68/2.90 (function-axioms)
% 15.68/2.92 ! [v0:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v2: mono_2Etyop_2Enum_2Enum] : ! [v3:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : (v1 = v0 | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3,
% 15.68/2.92 v2) = v1) | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3,
% 15.68/2.92 v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v2:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v3:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : (v1 = v0 | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3,
% 15.68/2.92 v2) = v1) | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v3,
% 15.68/2.92 v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 15.68/2.92 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 15.68/2.92 [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 15.68/2.92 : (v1 = v0 | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3,
% 15.68/2.92 v2) = v1) | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3,
% 15.68/2.92 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1:
% 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 =
% 15.68/2.92 v0 | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 15.68/2.92 v2) = v1) | ~
% 15.68/2.92 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 15.68/2.92 v2) = v0)) & ! [v0: d] : ! [v1: d] : ! [v2: d] : ! [v3: d] : (v1 =
% 15.68/2.92 v0 | ~ (tyop_2Epair_2Eprod(v3, v2) = v1) | ~ (tyop_2Epair_2Eprod(v3, v2) =
% 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 = v0 | ~
% 15.68/2.92 (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v0)) & !
% 15.68/2.92 [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 |
% 15.68/2.92 ~ (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~
% 15.68/2.92 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 |
% 15.68/2.92 ~ (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | ~
% 15.68/2.92 (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 |
% 15.68/2.92 ~ (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | ~
% 15.68/2.92 (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: d] : ! [v1: d] : !
% 15.68/2.92 [v2: d] : ! [v3: d] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~
% 15.68/2.92 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] :
% 15.68/2.92 ! [v3: du] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = v0))
% 15.68/2.92 & ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~ (s(v3,
% 15.68/2.92 v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v2: mono_2Etyop_2Enum_2Enum] : (v1 = v0 | ~
% 15.68/2.92 (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v1) | ~
% 15.68/2.92 (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v2:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v2) = v1) | ~
% 15.68/2.92 (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~
% 15.68/2.92 (j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.92 : (v1 = v0 | ~
% 15.68/2.92 (i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v2)
% 15.68/2.92 = v0)) & ! [v0: mono_2Etyop_2Enum_2Enum] : ! [v1:
% 15.68/2.92 mono_2Etyop_2Enum_2Enum] : ! [v2: du] : (v1 = v0 | ~
% 15.68/2.92 (j_mono_2Etyop_2Enum_2Enum(v2) = v1) | ~ (j_mono_2Etyop_2Enum_2Enum(v2) =
% 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Enum_2Enum] : (v1 =
% 15.68/2.92 v0 | ~ (i_mono_2Etyop_2Enum_2Enum(v2) = v1) | ~
% 15.68/2.92 (i_mono_2Etyop_2Enum_2Enum(v2) = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : (v1 = v0 | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29]
% 15.68/2.92 : (v1 = v0 | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29(v2)
% 15.68/2.92 = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 15.68/2.92 : ! [v1:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 15.68/2.92 : ! [v2: du] : (v1 = v0 | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 15.68/2.92 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 15.68/2.92 : (v1 = v0 | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 15.68/2.92 = v1) | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 15.68/2.92 = v0)) & ! [v0:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 15.68/2.92 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 15.68/2.92 [v2: du] : (v1 = v0 | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 15.68/2.92 v1) | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 15.68/2.92 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 =
% 15.68/2.92 v0 | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 15.68/2.92 v1) | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 15.68/2.92 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 =
% 15.68/2.92 v0 | ~ (i_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~
% 15.68/2.92 (i_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 15.68/2.92 du] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = v1) | ~
% 15.68/2.92 (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1
% 15.68/2.92 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_21_2E1(v2) = v0))
% 15.68/2.92 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : !
% 15.68/2.92 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~
% 15.68/2.92 (j_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] :
% 15.68/2.92 ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 =
% 15.68/2.92 v0 | ~ (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~
% 15.68/2.92 (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.68/2.92 MultipleValueBool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~
% 15.68/2.92 (p(v2) = v1) | ~ (p(v2) = v0))
% 15.68/2.92
% 15.68/2.92 Further assumptions not needed in the proof:
% 15.68/2.92 --------------------------------------------
% 15.68/2.92 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,
% 15.68/2.92 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1,
% 15.68/2.92 arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1,
% 15.68/2.92 arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,
% 15.68/2.92 arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,
% 15.68/2.92 arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, ij_2Emono_2Etyop_2Emin_2Ebool,
% 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,
% 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,
% 15.68/2.92 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,
% 15.68/2.92 ij_2Emono_2Etyop_2Enum_2Enum,
% 15.68/2.92 ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,
% 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Ebool,
% 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,
% 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,
% 15.68/2.92 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,
% 15.68/2.92 ji_2Emono_2Etyop_2Enum_2Enum,
% 15.68/2.92 ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,
% 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,
% 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,
% 15.68/2.92 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,
% 15.68/2.92 reserved_2Eho_2Ebool__cases__ax, reserved_2Eho_2Eboolext,
% 15.68/2.92 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ei__thm, reserved_2Eho_2Ek__thm,
% 15.68/2.92 reserved_2Eho_2Enotfalse, reserved_2Eho_2Es__thm, reserved_2Eho_2Etruth,
% 15.68/2.92 reserved_2Elogic_2E_2F_5C, reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E,
% 15.68/2.92 reserved_2Elogic_2E_5C_2F, reserved_2Elogic_2E_7E, reserved_2Equant_2E_21,
% 15.68/2.92 reserved_2Equant_2E_3F, thm_2Ebool_2EFORALL__SIMP, thm_2Ebool_2EIMP__CLAUSES,
% 15.68/2.92 thm_2Ebool_2ETRUTH
% 15.68/2.92
% 15.68/2.92 Those formulas are unsatisfiable:
% 15.68/2.92 ---------------------------------
% 15.68/2.92
% 15.68/2.92 Begin of proof
% 15.68/2.93 |
% 15.68/2.93 | ALPHA: (thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) implies:
% 15.68/2.93 | (1) ? [v0:
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.93 | : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) =
% 15.68/2.93 | v0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)
% 15.68/2.93 | & ! [v1:
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.93 | : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0) | ~
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1))
% 15.68/2.93 | & ! [v1:
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.93 | : (v1 = v0 | ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = v1)))
% 15.68/2.93 |
% 15.68/2.93 | ALPHA: (thm_2Ecomplex_2ECOMPLEX__INV__NZ) implies:
% 15.68/2.93 | (2) ? [v0:
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.93 | : (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) =
% 15.68/2.93 | v0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0)
% 15.68/2.93 | & ? [v1:
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.93 | : ( ~ (v1 = v0) & mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v1) = v0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v1)))
% 15.68/2.93 |
% 15.68/2.93 | ALPHA: (function-axioms) implies:
% 15.68/2.93 | (3) ! [v0:
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.93 | : ! [v1:
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29]
% 15.68/2.93 | : ! [v2: mono_2Etyop_2Enum_2Enum] : (v1 = v0 | ~
% 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v1) | ~
% 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(v2) = v0))
% 15.68/2.93 |
% 15.68/2.93 | DELTA: instantiating (2) with fresh symbol all_52_0 gives:
% 15.68/2.93 | (4) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) =
% 15.68/2.93 | all_52_0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_52_0)
% 15.68/2.93 | & ? [v0: any] : ( ~ (v0 = all_52_0) &
% 15.68/2.93 | mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_52_0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0))
% 15.68/2.93 |
% 15.68/2.93 | ALPHA: (4) implies:
% 15.68/2.93 | (5) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) =
% 15.68/2.93 | all_52_0
% 15.68/2.93 | (6) ? [v0: any] : ( ~ (v0 = all_52_0) &
% 15.68/2.93 | mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_52_0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0))
% 15.68/2.93 |
% 15.68/2.93 | DELTA: instantiating (1) with fresh symbol all_62_0 gives:
% 15.68/2.93 | (7) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) =
% 15.68/2.93 | all_62_0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_62_0)
% 15.68/2.93 | & ! [v0: any] : (v0 = all_62_0 | ~
% 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_62_0) | ~
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0))
% 15.68/2.93 | & ! [v0: int] : (v0 = all_62_0 | ~
% 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_62_0) = v0))
% 15.68/2.93 |
% 15.68/2.93 | ALPHA: (7) implies:
% 15.68/2.93 | (8) mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) =
% 15.68/2.93 | all_62_0
% 15.68/2.93 | (9) ! [v0: any] : (v0 = all_62_0 | ~
% 15.68/2.93 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(v0) = all_62_0) | ~
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(v0))
% 15.68/2.93 |
% 15.68/2.93 | DELTA: instantiating (6) with fresh symbol all_104_0 gives:
% 15.68/2.93 | (10) ~ (all_104_0 = all_52_0) &
% 15.68/2.93 | mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_52_0 &
% 15.68/2.93 | mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_104_0)
% 15.68/2.93 |
% 15.68/2.93 | ALPHA: (10) implies:
% 15.68/2.93 | (11) ~ (all_104_0 = all_52_0)
% 15.68/2.93 | (12) mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(all_104_0)
% 15.68/2.93 | (13) mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_52_0
% 15.68/2.93 |
% 15.68/2.94 | GROUND_INST: instantiating (3) with all_52_0, all_62_0,
% 15.68/2.94 | mono_2Ec_2Enum_2E0_2E0, simplifying with (5), (8) gives:
% 15.68/2.94 | (14) all_62_0 = all_52_0
% 15.68/2.94 |
% 15.68/2.94 | GROUND_INST: instantiating (9) with all_104_0, simplifying with (12) gives:
% 15.68/2.94 | (15) all_104_0 = all_62_0 | ~
% 15.68/2.94 | (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_62_0)
% 15.68/2.94 |
% 15.68/2.94 | BETA: splitting (15) gives:
% 15.68/2.94 |
% 15.68/2.94 | Case 1:
% 15.68/2.94 | |
% 15.68/2.94 | | (16) ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_62_0)
% 15.68/2.94 | |
% 15.68/2.94 | | REDUCE: (14), (16) imply:
% 15.68/2.94 | | (17) ~ (mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1(all_104_0) = all_52_0)
% 15.68/2.94 | |
% 15.68/2.94 | | PRED_UNIFY: (13), (17) imply:
% 15.68/2.94 | | (18) $false
% 15.68/2.94 | |
% 15.68/2.94 | | CLOSE: (18) is inconsistent.
% 15.68/2.94 | |
% 15.68/2.94 | Case 2:
% 15.68/2.94 | |
% 15.68/2.94 | | (19) all_104_0 = all_62_0
% 15.68/2.94 | |
% 15.68/2.94 | | COMBINE_EQS: (14), (19) imply:
% 15.68/2.94 | | (20) all_104_0 = all_52_0
% 15.68/2.94 | |
% 15.68/2.94 | | REDUCE: (11), (20) imply:
% 15.68/2.94 | | (21) $false
% 15.68/2.94 | |
% 15.68/2.94 | | CLOSE: (21) is inconsistent.
% 15.68/2.94 | |
% 15.68/2.94 | End of split
% 15.68/2.94 |
% 15.68/2.94 End of proof
% 15.68/2.94 % SZS output end Proof for theBenchmark
% 15.68/2.94
% 15.68/2.94 2357ms
%------------------------------------------------------------------------------