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 : 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 04:08:56 EDT 2023
% Result : Theorem 8.86s 2.05s
% Output : Proof 13.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP019+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 14:22:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.68 ________ _____
% 0.21/0.68 ___ __ \_________(_)________________________________
% 0.21/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.68
% 0.21/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.68 (2023-06-19)
% 0.21/0.68
% 0.21/0.68 (c) Philipp Rümmer, 2009-2023
% 0.21/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.68 Amanda Stjerna.
% 0.21/0.68 Free software under BSD-3-Clause.
% 0.21/0.68
% 0.21/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.68
% 0.21/0.68 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.69 Running up to 7 provers in parallel.
% 0.21/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.12/1.21 Prover 4: Preprocessing ...
% 3.12/1.22 Prover 1: Preprocessing ...
% 3.12/1.25 Prover 0: Preprocessing ...
% 3.12/1.25 Prover 3: Preprocessing ...
% 3.12/1.25 Prover 2: Preprocessing ...
% 3.12/1.25 Prover 5: Preprocessing ...
% 3.12/1.25 Prover 6: Preprocessing ...
% 7.28/1.77 Prover 3: Constructing countermodel ...
% 7.28/1.77 Prover 1: Constructing countermodel ...
% 7.28/1.78 Prover 6: Proving ...
% 7.28/1.79 Prover 5: Proving ...
% 7.84/1.86 Prover 2: Proving ...
% 8.86/2.05 Prover 4: Constructing countermodel ...
% 8.86/2.05 Prover 3: proved (1352ms)
% 8.86/2.05
% 8.86/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.86/2.05
% 8.86/2.05 Prover 6: stopped
% 8.86/2.07 Prover 2: stopped
% 9.32/2.09 Prover 5: stopped
% 9.32/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.32/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.32/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.32/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.32/2.13 Prover 8: Preprocessing ...
% 10.06/2.14 Prover 7: Preprocessing ...
% 10.22/2.15 Prover 10: Preprocessing ...
% 10.22/2.15 Prover 11: Preprocessing ...
% 10.22/2.18 Prover 0: Proving ...
% 10.22/2.19 Prover 0: stopped
% 10.22/2.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.77/2.26 Prover 13: Preprocessing ...
% 10.77/2.26 Prover 7: Constructing countermodel ...
% 10.77/2.27 Prover 8: Warning: ignoring some quantifiers
% 11.15/2.27 Prover 8: Constructing countermodel ...
% 11.15/2.29 Prover 10: Constructing countermodel ...
% 11.77/2.37 Prover 13: Warning: ignoring some quantifiers
% 12.00/2.39 Prover 13: Constructing countermodel ...
% 12.37/2.43 Prover 11: Constructing countermodel ...
% 13.09/2.56 Prover 7: Found proof (size 37)
% 13.09/2.56 Prover 7: proved (494ms)
% 13.09/2.56 Prover 13: stopped
% 13.09/2.56 Prover 11: stopped
% 13.46/2.57 Prover 10: stopped
% 13.46/2.57 Prover 8: stopped
% 13.46/2.57 Prover 4: stopped
% 13.46/2.57 Prover 1: stopped
% 13.46/2.57
% 13.46/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.46/2.57
% 13.46/2.58 % SZS output start Proof for theBenchmark
% 13.46/2.58 Assumptions after simplification:
% 13.46/2.58 ---------------------------------
% 13.46/2.58
% 13.46/2.58 (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0)
% 13.46/2.61 $i(c_2Ecomplex_2Ecomplex__inv) & $i(c_2Ecomplex_2Ecomplex__of__num) &
% 13.46/2.61 $i(ty_2Erealax_2Ereal) & $i(c_2Enum_2E0) & ? [v0: $i] : ? [v1: $i] :
% 13.46/2.61 (ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = v0 &
% 13.46/2.61 ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = v1 & $i(v1) & $i(v0) & !
% 13.46/2.61 [v2: $i] : (v2 = v1 | ~ (ap(c_2Ecomplex_2Ecomplex__inv, v2) = v1) | ~
% 13.46/2.61 $i(v2) | ~ mem(v2, v0)) & ! [v2: $i] : (v2 = v1 | ~
% 13.46/2.61 (ap(c_2Ecomplex_2Ecomplex__inv, v1) = v2) | ~ mem(v1, v0)))
% 13.46/2.61
% 13.46/2.61 (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ)
% 13.46/2.61 $i(c_2Ecomplex_2Ecomplex__inv) & $i(c_2Ecomplex_2Ecomplex__of__num) &
% 13.46/2.61 $i(ty_2Erealax_2Ereal) & $i(c_2Enum_2E0) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 13.46/2.61 $i] : ( ~ (v2 = v1) & ty_2Epair_2Eprod(ty_2Erealax_2Ereal,
% 13.46/2.61 ty_2Erealax_2Ereal) = v0 & ap(c_2Ecomplex_2Ecomplex__inv, v2) = v1 &
% 13.46/2.61 ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = v1 & $i(v2) & $i(v1) &
% 13.46/2.61 $i(v0) & mem(v2, v0))
% 13.46/2.61
% 13.46/2.61 (mem_c_2Ecomplex_2Ecomplex__inv)
% 13.46/2.61 $i(c_2Ecomplex_2Ecomplex__inv) & $i(ty_2Erealax_2Ereal) & ? [v0: $i] : ?
% 13.46/2.61 [v1: $i] : (ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = v0 &
% 13.46/2.61 arr(v0, v0) = v1 & $i(v1) & $i(v0) & mem(c_2Ecomplex_2Ecomplex__inv, v1))
% 13.46/2.61
% 13.46/2.61 (mem_c_2Ecomplex_2Ecomplex__of__num)
% 13.46/2.61 $i(c_2Ecomplex_2Ecomplex__of__num) & $i(ty_2Erealax_2Ereal) &
% 13.46/2.61 $i(ty_2Enum_2Enum) & ? [v0: $i] : ? [v1: $i] :
% 13.46/2.61 (ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = v0 &
% 13.46/2.61 arr(ty_2Enum_2Enum, v0) = v1 & $i(v1) & $i(v0) &
% 13.46/2.61 mem(c_2Ecomplex_2Ecomplex__of__num, v1))
% 13.46/2.61
% 13.46/2.61 (function-axioms)
% 13.46/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.46/2.62 (ty_2Epair_2Eprod(v3, v2) = v1) | ~ (ty_2Epair_2Eprod(v3, v2) = v0)) & !
% 13.46/2.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k(v3, v2)
% 13.46/2.62 = v1) | ~ (k(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.46/2.62 ! [v3: $i] : (v1 = v0 | ~ (ap(v3, v2) = v1) | ~ (ap(v3, v2) = v0)) & ! [v0:
% 13.46/2.62 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (arr(v3, v2) =
% 13.46/2.62 v1) | ~ (arr(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.46/2.62 (v1 = v0 | ~ (c_2Ebool_2E_21(v2) = v1) | ~ (c_2Ebool_2E_21(v2) = v0)) & !
% 13.46/2.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_2Emin_2E_3D(v2) = v1)
% 13.46/2.62 | ~ (c_2Emin_2E_3D(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.46/2.62 (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0))
% 13.46/2.62
% 13.46/2.62 Further assumptions not needed in the proof:
% 13.46/2.62 --------------------------------------------
% 13.46/2.62 ap_tp, arr_ne, ax_all_p, ax_and_p, ax_eq_p, ax_false_p, ax_imp_p, ax_neg_p,
% 13.46/2.62 ax_true_p, bool_ne, boolext, conj_thm_2Ebool_2EFORALL__SIMP,
% 13.46/2.62 conj_thm_2Ebool_2EIMP__CLAUSES, conj_thm_2Ebool_2ETRUTH, funcext, ibeta, ind_ne,
% 13.46/2.62 kbeta, mem_c_2Ebool_2EF, mem_c_2Ebool_2ET, mem_c_2Ebool_2E_21,
% 13.46/2.62 mem_c_2Ebool_2E_2F_5C, mem_c_2Ebool_2E_7E, mem_c_2Emin_2E_3D,
% 13.46/2.62 mem_c_2Emin_2E_3D_3D_3E, mem_c_2Enum_2E0, ne_ty_2Enum_2Enum,
% 13.46/2.62 ne_ty_2Epair_2Eprod, ne_ty_2Erealax_2Ereal
% 13.46/2.62
% 13.46/2.62 Those formulas are unsatisfiable:
% 13.46/2.62 ---------------------------------
% 13.46/2.62
% 13.46/2.62 Begin of proof
% 13.46/2.62 |
% 13.46/2.62 | ALPHA: (mem_c_2Ecomplex_2Ecomplex__of__num) implies:
% 13.46/2.62 | (1) ? [v0: $i] : ? [v1: $i] : (ty_2Epair_2Eprod(ty_2Erealax_2Ereal,
% 13.46/2.62 | ty_2Erealax_2Ereal) = v0 & arr(ty_2Enum_2Enum, v0) = v1 & $i(v1) &
% 13.46/2.62 | $i(v0) & mem(c_2Ecomplex_2Ecomplex__of__num, v1))
% 13.46/2.62 |
% 13.46/2.62 | ALPHA: (mem_c_2Ecomplex_2Ecomplex__inv) implies:
% 13.46/2.62 | (2) ? [v0: $i] : ? [v1: $i] : (ty_2Epair_2Eprod(ty_2Erealax_2Ereal,
% 13.46/2.62 | ty_2Erealax_2Ereal) = v0 & arr(v0, v0) = v1 & $i(v1) & $i(v0) &
% 13.46/2.62 | mem(c_2Ecomplex_2Ecomplex__inv, v1))
% 13.46/2.62 |
% 13.46/2.62 | ALPHA: (conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) implies:
% 13.46/2.62 | (3) ? [v0: $i] : ? [v1: $i] : (ty_2Epair_2Eprod(ty_2Erealax_2Ereal,
% 13.46/2.62 | ty_2Erealax_2Ereal) = v0 & ap(c_2Ecomplex_2Ecomplex__of__num,
% 13.46/2.62 | c_2Enum_2E0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : (v2 = v1 | ~
% 13.46/2.62 | (ap(c_2Ecomplex_2Ecomplex__inv, v2) = v1) | ~ $i(v2) | ~ mem(v2,
% 13.46/2.62 | v0)) & ! [v2: $i] : (v2 = v1 | ~
% 13.46/2.62 | (ap(c_2Ecomplex_2Ecomplex__inv, v1) = v2) | ~ mem(v1, v0)))
% 13.46/2.62 |
% 13.46/2.62 | ALPHA: (conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) implies:
% 13.46/2.62 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 13.46/2.62 | ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = v0 &
% 13.46/2.62 | ap(c_2Ecomplex_2Ecomplex__inv, v2) = v1 &
% 13.46/2.62 | ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = v1 & $i(v2) &
% 13.46/2.62 | $i(v1) & $i(v0) & mem(v2, v0))
% 13.46/2.62 |
% 13.46/2.62 | ALPHA: (function-axioms) implies:
% 13.46/2.62 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.46/2.62 | (ap(v3, v2) = v1) | ~ (ap(v3, v2) = v0))
% 13.46/2.62 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.46/2.62 | (ty_2Epair_2Eprod(v3, v2) = v1) | ~ (ty_2Epair_2Eprod(v3, v2) = v0))
% 13.46/2.62 |
% 13.46/2.62 | DELTA: instantiating (2) with fresh symbols all_21_0, all_21_1 gives:
% 13.46/2.62 | (7) ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = all_21_1 &
% 13.46/2.62 | arr(all_21_1, all_21_1) = all_21_0 & $i(all_21_0) & $i(all_21_1) &
% 13.46/2.63 | mem(c_2Ecomplex_2Ecomplex__inv, all_21_0)
% 13.46/2.63 |
% 13.46/2.63 | ALPHA: (7) implies:
% 13.46/2.63 | (8) ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = all_21_1
% 13.46/2.63 |
% 13.46/2.63 | DELTA: instantiating (1) with fresh symbols all_25_0, all_25_1 gives:
% 13.46/2.63 | (9) ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = all_25_1 &
% 13.46/2.63 | arr(ty_2Enum_2Enum, all_25_1) = all_25_0 & $i(all_25_0) & $i(all_25_1)
% 13.46/2.63 | & mem(c_2Ecomplex_2Ecomplex__of__num, all_25_0)
% 13.46/2.63 |
% 13.46/2.63 | ALPHA: (9) implies:
% 13.46/2.63 | (10) ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = all_25_1
% 13.46/2.63 |
% 13.46/2.63 | DELTA: instantiating (4) with fresh symbols all_29_0, all_29_1, all_29_2
% 13.46/2.63 | gives:
% 13.46/2.63 | (11) ~ (all_29_0 = all_29_1) & ty_2Epair_2Eprod(ty_2Erealax_2Ereal,
% 13.46/2.63 | ty_2Erealax_2Ereal) = all_29_2 & ap(c_2Ecomplex_2Ecomplex__inv,
% 13.46/2.63 | all_29_0) = all_29_1 & ap(c_2Ecomplex_2Ecomplex__of__num,
% 13.46/2.63 | c_2Enum_2E0) = all_29_1 & $i(all_29_0) & $i(all_29_1) & $i(all_29_2)
% 13.46/2.63 | & mem(all_29_0, all_29_2)
% 13.46/2.63 |
% 13.46/2.63 | ALPHA: (11) implies:
% 13.46/2.63 | (12) ~ (all_29_0 = all_29_1)
% 13.46/2.63 | (13) mem(all_29_0, all_29_2)
% 13.46/2.63 | (14) $i(all_29_0)
% 13.46/2.63 | (15) ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = all_29_1
% 13.46/2.63 | (16) ap(c_2Ecomplex_2Ecomplex__inv, all_29_0) = all_29_1
% 13.46/2.63 | (17) ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = all_29_2
% 13.46/2.63 |
% 13.46/2.63 | DELTA: instantiating (3) with fresh symbols all_31_0, all_31_1 gives:
% 13.46/2.63 | (18) ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = all_31_1 &
% 13.46/2.63 | ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = all_31_0 &
% 13.46/2.63 | $i(all_31_0) & $i(all_31_1) & ! [v0: any] : (v0 = all_31_0 | ~
% 13.46/2.63 | (ap(c_2Ecomplex_2Ecomplex__inv, v0) = all_31_0) | ~ $i(v0) | ~
% 13.46/2.63 | mem(v0, all_31_1)) & ! [v0: int] : (v0 = all_31_0 | ~
% 13.46/2.63 | (ap(c_2Ecomplex_2Ecomplex__inv, all_31_0) = v0) | ~ mem(all_31_0,
% 13.46/2.63 | all_31_1))
% 13.46/2.63 |
% 13.46/2.63 | ALPHA: (18) implies:
% 13.46/2.63 | (19) ap(c_2Ecomplex_2Ecomplex__of__num, c_2Enum_2E0) = all_31_0
% 13.46/2.63 | (20) ty_2Epair_2Eprod(ty_2Erealax_2Ereal, ty_2Erealax_2Ereal) = all_31_1
% 13.46/2.63 | (21) ! [v0: any] : (v0 = all_31_0 | ~ (ap(c_2Ecomplex_2Ecomplex__inv, v0)
% 13.46/2.63 | = all_31_0) | ~ $i(v0) | ~ mem(v0, all_31_1))
% 13.46/2.63 |
% 13.46/2.63 | GROUND_INST: instantiating (5) with all_29_1, all_31_0, c_2Enum_2E0,
% 13.46/2.63 | c_2Ecomplex_2Ecomplex__of__num, simplifying with (15), (19)
% 13.46/2.63 | gives:
% 13.46/2.63 | (22) all_31_0 = all_29_1
% 13.46/2.63 |
% 13.46/2.63 | GROUND_INST: instantiating (6) with all_29_2, all_31_1, ty_2Erealax_2Ereal,
% 13.46/2.63 | ty_2Erealax_2Ereal, simplifying with (17), (20) gives:
% 13.46/2.63 | (23) all_31_1 = all_29_2
% 13.46/2.63 |
% 13.46/2.63 | GROUND_INST: instantiating (6) with all_25_1, all_31_1, ty_2Erealax_2Ereal,
% 13.46/2.63 | ty_2Erealax_2Ereal, simplifying with (10), (20) gives:
% 13.46/2.63 | (24) all_31_1 = all_25_1
% 13.46/2.63 |
% 13.46/2.63 | GROUND_INST: instantiating (6) with all_21_1, all_31_1, ty_2Erealax_2Ereal,
% 13.46/2.63 | ty_2Erealax_2Ereal, simplifying with (8), (20) gives:
% 13.46/2.63 | (25) all_31_1 = all_21_1
% 13.46/2.63 |
% 13.46/2.63 | COMBINE_EQS: (23), (24) imply:
% 13.46/2.63 | (26) all_29_2 = all_25_1
% 13.46/2.63 |
% 13.46/2.63 | COMBINE_EQS: (23), (25) imply:
% 13.46/2.63 | (27) all_29_2 = all_21_1
% 13.46/2.63 |
% 13.46/2.63 | COMBINE_EQS: (26), (27) imply:
% 13.46/2.63 | (28) all_25_1 = all_21_1
% 13.46/2.63 |
% 13.46/2.63 | REDUCE: (13), (27) imply:
% 13.46/2.63 | (29) mem(all_29_0, all_21_1)
% 13.46/2.63 |
% 13.46/2.63 | GROUND_INST: instantiating (21) with all_29_0, simplifying with (14) gives:
% 13.46/2.63 | (30) all_31_0 = all_29_0 | ~ (ap(c_2Ecomplex_2Ecomplex__inv, all_29_0) =
% 13.46/2.63 | all_31_0) | ~ mem(all_29_0, all_31_1)
% 13.46/2.63 |
% 13.46/2.63 | BETA: splitting (30) gives:
% 13.46/2.63 |
% 13.46/2.63 | Case 1:
% 13.46/2.63 | |
% 13.46/2.63 | | (31) ~ (ap(c_2Ecomplex_2Ecomplex__inv, all_29_0) = all_31_0)
% 13.46/2.63 | |
% 13.46/2.64 | | REDUCE: (22), (31) imply:
% 13.46/2.64 | | (32) ~ (ap(c_2Ecomplex_2Ecomplex__inv, all_29_0) = all_29_1)
% 13.46/2.64 | |
% 13.46/2.64 | | PRED_UNIFY: (16), (32) imply:
% 13.46/2.64 | | (33) $false
% 13.46/2.64 | |
% 13.46/2.64 | | CLOSE: (33) is inconsistent.
% 13.46/2.64 | |
% 13.46/2.64 | Case 2:
% 13.46/2.64 | |
% 13.46/2.64 | | (34) all_31_0 = all_29_0 | ~ mem(all_29_0, all_31_1)
% 13.46/2.64 | |
% 13.46/2.64 | | BETA: splitting (34) gives:
% 13.46/2.64 | |
% 13.46/2.64 | | Case 1:
% 13.46/2.64 | | |
% 13.46/2.64 | | | (35) ~ mem(all_29_0, all_31_1)
% 13.46/2.64 | | |
% 13.46/2.64 | | | REDUCE: (25), (35) imply:
% 13.46/2.64 | | | (36) ~ mem(all_29_0, all_21_1)
% 13.46/2.64 | | |
% 13.46/2.64 | | | PRED_UNIFY: (29), (36) imply:
% 13.46/2.64 | | | (37) $false
% 13.46/2.64 | | |
% 13.46/2.64 | | | CLOSE: (37) is inconsistent.
% 13.46/2.64 | | |
% 13.46/2.64 | | Case 2:
% 13.46/2.64 | | |
% 13.46/2.64 | | | (38) all_31_0 = all_29_0
% 13.46/2.64 | | |
% 13.46/2.64 | | | COMBINE_EQS: (22), (38) imply:
% 13.46/2.64 | | | (39) all_29_0 = all_29_1
% 13.46/2.64 | | |
% 13.46/2.64 | | | SIMP: (39) implies:
% 13.46/2.64 | | | (40) all_29_0 = all_29_1
% 13.46/2.64 | | |
% 13.46/2.64 | | | REDUCE: (12), (40) imply:
% 13.46/2.64 | | | (41) $false
% 13.46/2.64 | | |
% 13.46/2.64 | | | CLOSE: (41) is inconsistent.
% 13.46/2.64 | | |
% 13.46/2.64 | | End of split
% 13.46/2.64 | |
% 13.46/2.64 | End of split
% 13.46/2.64 |
% 13.46/2.64 End of proof
% 13.46/2.64 % SZS output end Proof for theBenchmark
% 13.46/2.64
% 13.46/2.64 1961ms
%------------------------------------------------------------------------------