TSTP Solution File: SWW469+5 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 : Fri Sep 1 00:50:09 EDT 2023
% Result : Theorem 15.52s 2.88s
% Output : Proof 20.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 19:06:10 EDT 2023
% 0.12/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.02/1.47 Prover 4: Preprocessing ...
% 5.02/1.47 Prover 1: Preprocessing ...
% 5.38/1.52 Prover 0: Preprocessing ...
% 5.38/1.52 Prover 5: Preprocessing ...
% 5.38/1.52 Prover 2: Preprocessing ...
% 5.38/1.52 Prover 3: Preprocessing ...
% 5.38/1.52 Prover 6: Preprocessing ...
% 12.37/2.49 Prover 1: Warning: ignoring some quantifiers
% 12.37/2.54 Prover 3: Warning: ignoring some quantifiers
% 13.11/2.59 Prover 1: Constructing countermodel ...
% 13.11/2.59 Prover 3: Constructing countermodel ...
% 13.11/2.60 Prover 6: Proving ...
% 14.83/2.81 Prover 4: Warning: ignoring some quantifiers
% 14.83/2.84 Prover 5: Proving ...
% 15.52/2.87 Prover 3: proved (2242ms)
% 15.52/2.87
% 15.52/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.52/2.88
% 15.81/2.89 Prover 5: stopped
% 15.81/2.89 Prover 6: stopped
% 15.81/2.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.81/2.91 Prover 4: Constructing countermodel ...
% 15.81/2.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.81/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.29/2.97 Prover 0: Proving ...
% 16.29/3.00 Prover 0: stopped
% 16.29/3.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.72/3.06 Prover 1: Found proof (size 20)
% 16.72/3.06 Prover 1: proved (2427ms)
% 16.72/3.06 Prover 4: stopped
% 17.11/3.12 Prover 8: Preprocessing ...
% 17.11/3.13 Prover 7: Preprocessing ...
% 17.11/3.14 Prover 10: Preprocessing ...
% 17.11/3.18 Prover 11: Preprocessing ...
% 17.11/3.19 Prover 2: Proving ...
% 17.11/3.20 Prover 2: stopped
% 18.61/3.28 Prover 10: stopped
% 18.96/3.31 Prover 7: stopped
% 18.96/3.33 Prover 11: stopped
% 19.14/3.41 Prover 8: Warning: ignoring some quantifiers
% 19.53/3.45 Prover 8: Constructing countermodel ...
% 19.53/3.47 Prover 8: stopped
% 19.53/3.47
% 19.53/3.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.53/3.47
% 19.53/3.48 % SZS output start Proof for theBenchmark
% 19.77/3.48 Assumptions after simplification:
% 19.77/3.48 ---------------------------------
% 19.77/3.48
% 19.77/3.48 (conj_0)
% 19.77/3.50 hBOOL(hoare_1883395792gleton) = 0 & $i(hoare_1883395792gleton)
% 19.77/3.50
% 19.77/3.50 (conj_1)
% 19.77/3.51 $i(state) & ? [v0: $i] : ? [v1: $i] : (ti(state, v0) = v1 & $i(v1) & $i(v0)
% 19.77/3.51 & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (ti(state, v2) = v3) | ~
% 19.77/3.51 $i(v2)))
% 19.77/3.51
% 19.77/3.51 (fact_0_state__not__singleton__def)
% 19.77/3.51 $i(hoare_1883395792gleton) & $i(state) & ? [v0: any] :
% 19.77/3.51 (hBOOL(hoare_1883395792gleton) = v0 & ((v0 = 0 & ? [v1: $i] : ? [v2: $i] :
% 19.77/3.51 ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & ti(state, v2) = v4 &
% 19.77/3.51 ti(state, v1) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1))) | ( ~ (v0 =
% 19.77/3.51 0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 19.77/3.51 | ~ (ti(state, v2) = v4) | ~ (ti(state, v1) = v3) | ~ $i(v2) | ~
% 19.77/3.51 $i(v1)))))
% 19.77/3.51
% 19.77/3.51 (function-axioms)
% 19.77/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.77/3.52 $i] : (v1 = v0 | ~ (hAPP(v5, v4, v3, v2) = v1) | ~ (hAPP(v5, v4, v3, v2) =
% 19.77/3.52 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 19.77/3.52 ~ (type_definition(v3, v2) = v1) | ~ (type_definition(v3, v2) = v0)) & !
% 19.77/3.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.77/3.52 (sum_sum(v3, v2) = v1) | ~ (sum_sum(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 19.77/3.52 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (node(v3, v2) = v1) | ~
% 19.77/3.52 (node(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 19.77/3.52 : (v1 = v0 | ~ (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0)) & ! [v0: $i] : !
% 19.77/3.52 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ti(v3, v2) = v1) | ~
% 19.77/3.52 (ti(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 19.77/3.52 : ! [v2: $i] : (v1 = v0 | ~ (enum(v2) = v1) | ~ (enum(v2) = v0)) & ! [v0:
% 19.77/3.52 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member(v2) = v1) | ~
% 19.77/3.52 (member(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 19.77/3.52 : ! [v2: $i] : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0)) & !
% 19.77/3.52 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (fequal(v2) = v1) | ~
% 19.77/3.52 (fequal(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.77/3.52 (collect(v2) = v1) | ~ (collect(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.77/3.52 [v2: $i] : (v1 = v0 | ~ (hoare_1580379338ep_set(v2) = v1) | ~
% 19.77/3.52 (hoare_1580379338ep_set(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 19.77/3.52 : (v1 = v0 | ~ (hoare_2037801986triple(v2) = v1) | ~
% 19.77/3.52 (hoare_2037801986triple(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 19.77/3.52 : (v1 = v0 | ~ (hoare_509422987triple(v2) = v1) | ~
% 19.77/3.52 (hoare_509422987triple(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 19.77/3.52 : (v1 = v0 | ~ (hoare_244953527triple(v2) = v1) | ~
% 19.77/3.52 (hoare_244953527triple(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 19.77/3.52 : (v1 = v0 | ~ (undefined(v2) = v1) | ~ (undefined(v2) = v0)) & ! [v0: $i]
% 19.77/3.52 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (induct_equal(v2) = v1) | ~
% 19.77/3.52 (induct_equal(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 19.77/3.52 v0 | ~ (equal_equal(v2) = v1) | ~ (equal_equal(v2) = v0)) & ! [v0:
% 19.77/3.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 19.77/3.52 ~ (cl_HOL_Oequal(v2) = v1) | ~ (cl_HOL_Oequal(v2) = v0))
% 19.77/3.52
% 19.77/3.52 Further assumptions not needed in the proof:
% 19.77/3.52 --------------------------------------------
% 19.77/3.53 arity_Com_Ocom___HOL_Oequal, arity_Com_Ostate___HOL_Oequal,
% 19.77/3.53 arity_HOL_Obool___Enum_Oenum, arity_HOL_Obool___HOL_Oequal,
% 19.77/3.53 arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal, arity_fun___Enum_Oenum,
% 19.77/3.53 arity_fun___HOL_Oequal, arity_sum___Enum_Oenum, arity_sum___HOL_Oequal,
% 19.77/3.53 fact_10_Rep__triple__cases, fact_11_Abs__triple__inverse,
% 19.77/3.53 fact_12_type__definition__triple, fact_13_Abs__triple__inject,
% 19.77/3.53 fact_14_Abs__triple__induct, fact_15_Abs__triple__cases,
% 19.77/3.53 fact_16_type__definition_OAbs__inject, fact_17_type__definition_OAbs__inverse,
% 19.77/3.53 fact_18_type__definition_ORep__inject, fact_19_type__definition_ORep__inverse,
% 19.77/3.53 fact_1_equal__triple__def, fact_20_type__definition_ORep,
% 19.77/3.53 fact_21_induct__false__def, fact_22_type__definition_ORep__cases,
% 19.77/3.53 fact_23_type__definition_OAbs__cases, fact_24_type__definition_OAbs__induct,
% 19.77/3.53 fact_25_type__definition_ORep__induct, fact_26_induct__trueI,
% 19.77/3.53 fact_27_induct__true__def, fact_28_induct__equal__def, fact_29_ext,
% 19.77/3.53 fact_2_Rep__triple__inject, fact_30_mem__def, fact_31_Collect__def,
% 19.77/3.53 fact_3_equal, fact_4_equal__refl, fact_5_equal__eq, fact_6_eq__equal,
% 19.77/3.53 fact_7_Rep__triple__inverse, fact_8_Rep__triple, fact_9_Rep__triple__induct,
% 19.77/3.53 help_fequal_1_1_T, help_fequal_2_1_T, help_ti_idem,
% 19.77/3.53 tsy_c_HOL_Oequal__class_Oequal_res, tsy_c_HOL_Oinduct__equal_res,
% 19.77/3.53 tsy_c_HOL_Oinduct__false_res, tsy_c_HOL_Oinduct__true_res,
% 19.77/3.53 tsy_c_HOL_Oundefined_res, tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res,
% 19.77/3.53 tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res,
% 19.77/3.53 tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res,
% 19.77/3.53 tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res,
% 19.77/3.53 tsy_c_Set_OCollect_res, tsy_c_Typedef_Otype__definition_res, tsy_c_fequal_res,
% 19.77/3.53 tsy_c_hAPP_arg1, tsy_c_hAPP_arg2, tsy_c_hAPP_res, tsy_c_hBOOL_arg1,
% 19.77/3.53 tsy_c_member_res
% 19.77/3.53
% 19.77/3.53 Those formulas are unsatisfiable:
% 19.77/3.53 ---------------------------------
% 19.77/3.53
% 19.77/3.53 Begin of proof
% 19.77/3.53 |
% 19.77/3.53 | ALPHA: (fact_0_state__not__singleton__def) implies:
% 19.77/3.53 | (1) ? [v0: any] : (hBOOL(hoare_1883395792gleton) = v0 & ((v0 = 0 & ? [v1:
% 19.77/3.53 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) &
% 19.77/3.53 | ti(state, v2) = v4 & ti(state, v1) = v3 & $i(v4) & $i(v3) &
% 19.77/3.53 | $i(v2) & $i(v1))) | ( ~ (v0 = 0) & ! [v1: $i] : ! [v2: $i] :
% 19.77/3.53 | ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (ti(state, v2) = v4) |
% 19.77/3.53 | ~ (ti(state, v1) = v3) | ~ $i(v2) | ~ $i(v1)))))
% 19.77/3.53 |
% 19.77/3.53 | ALPHA: (conj_0) implies:
% 19.77/3.53 | (2) hBOOL(hoare_1883395792gleton) = 0
% 19.77/3.53 |
% 19.77/3.53 | ALPHA: (conj_1) implies:
% 19.77/3.53 | (3) ? [v0: $i] : ? [v1: $i] : (ti(state, v0) = v1 & $i(v1) & $i(v0) & !
% 19.77/3.53 | [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (ti(state, v2) = v3) | ~
% 19.77/3.53 | $i(v2)))
% 19.77/3.53 |
% 19.77/3.53 | ALPHA: (function-axioms) implies:
% 19.77/3.53 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.77/3.53 | (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0))
% 19.77/3.53 |
% 19.77/3.53 | DELTA: instantiating (3) with fresh symbols all_43_0, all_43_1 gives:
% 19.77/3.53 | (5) ti(state, all_43_1) = all_43_0 & $i(all_43_0) & $i(all_43_1) & ! [v0:
% 19.77/3.53 | $i] : ! [v1: int] : (v1 = all_43_0 | ~ (ti(state, v0) = v1) | ~
% 19.77/3.53 | $i(v0))
% 19.77/3.53 |
% 19.77/3.53 | ALPHA: (5) implies:
% 19.77/3.53 | (6) ! [v0: $i] : ! [v1: int] : (v1 = all_43_0 | ~ (ti(state, v0) = v1) |
% 19.77/3.53 | ~ $i(v0))
% 19.77/3.53 |
% 19.77/3.53 | DELTA: instantiating (1) with fresh symbol all_55_0 gives:
% 19.77/3.54 | (7) hBOOL(hoare_1883395792gleton) = all_55_0 & ((all_55_0 = 0 & ? [v0: $i]
% 19.77/3.54 | : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 19.77/3.54 | ti(state, v1) = v3 & ti(state, v0) = v2 & $i(v3) & $i(v2) &
% 19.77/3.54 | $i(v1) & $i(v0))) | ( ~ (all_55_0 = 0) & ! [v0: $i] : ! [v1:
% 19.77/3.54 | $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (ti(state, v1) =
% 19.77/3.54 | v3) | ~ (ti(state, v0) = v2) | ~ $i(v1) | ~ $i(v0))))
% 19.77/3.54 |
% 19.77/3.54 | ALPHA: (7) implies:
% 19.77/3.54 | (8) hBOOL(hoare_1883395792gleton) = all_55_0
% 19.77/3.54 | (9) (all_55_0 = 0 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 19.77/3.54 | ( ~ (v3 = v2) & ti(state, v1) = v3 & ti(state, v0) = v2 & $i(v3) &
% 19.77/3.54 | $i(v2) & $i(v1) & $i(v0))) | ( ~ (all_55_0 = 0) & ! [v0: $i] : !
% 19.77/3.54 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (ti(state, v1) =
% 19.77/3.54 | v3) | ~ (ti(state, v0) = v2) | ~ $i(v1) | ~ $i(v0)))
% 19.77/3.54 |
% 19.77/3.54 | GROUND_INST: instantiating (4) with 0, all_55_0, hoare_1883395792gleton,
% 19.77/3.54 | simplifying with (2), (8) gives:
% 19.77/3.54 | (10) all_55_0 = 0
% 19.77/3.54 |
% 19.77/3.54 | BETA: splitting (9) gives:
% 19.77/3.54 |
% 19.77/3.54 | Case 1:
% 19.77/3.54 | |
% 19.77/3.54 | | (11) all_55_0 = 0 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 19.77/3.54 | | : ( ~ (v3 = v2) & ti(state, v1) = v3 & ti(state, v0) = v2 & $i(v3) &
% 19.77/3.54 | | $i(v2) & $i(v1) & $i(v0))
% 19.77/3.54 | |
% 19.77/3.54 | | ALPHA: (11) implies:
% 19.77/3.54 | | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 19.77/3.54 | | v2) & ti(state, v1) = v3 & ti(state, v0) = v2 & $i(v3) & $i(v2)
% 19.77/3.54 | | & $i(v1) & $i(v0))
% 19.77/3.54 | |
% 19.77/3.54 | | DELTA: instantiating (12) with fresh symbols all_96_0, all_96_1, all_96_2,
% 19.77/3.54 | | all_96_3 gives:
% 19.77/3.54 | | (13) ~ (all_96_0 = all_96_1) & ti(state, all_96_2) = all_96_0 &
% 19.77/3.54 | | ti(state, all_96_3) = all_96_1 & $i(all_96_0) & $i(all_96_1) &
% 19.77/3.54 | | $i(all_96_2) & $i(all_96_3)
% 19.77/3.54 | |
% 19.77/3.54 | | ALPHA: (13) implies:
% 19.77/3.54 | | (14) ~ (all_96_0 = all_96_1)
% 19.77/3.54 | | (15) $i(all_96_3)
% 19.77/3.54 | | (16) $i(all_96_2)
% 19.77/3.54 | | (17) ti(state, all_96_3) = all_96_1
% 19.77/3.54 | | (18) ti(state, all_96_2) = all_96_0
% 19.77/3.54 | |
% 19.77/3.54 | | GROUND_INST: instantiating (6) with all_96_3, all_96_1, simplifying with
% 19.77/3.54 | | (15), (17) gives:
% 19.77/3.54 | | (19) all_96_1 = all_43_0
% 19.77/3.54 | |
% 19.77/3.55 | | GROUND_INST: instantiating (6) with all_96_2, all_96_0, simplifying with
% 19.77/3.55 | | (16), (18) gives:
% 19.77/3.55 | | (20) all_96_0 = all_43_0
% 19.77/3.55 | |
% 20.08/3.55 | | REDUCE: (14), (19), (20) imply:
% 20.08/3.55 | | (21) $false
% 20.08/3.55 | |
% 20.08/3.55 | | CLOSE: (21) is inconsistent.
% 20.08/3.55 | |
% 20.08/3.55 | Case 2:
% 20.08/3.55 | |
% 20.08/3.55 | | (22) ~ (all_55_0 = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.08/3.55 | | [v3: $i] : (v3 = v2 | ~ (ti(state, v1) = v3) | ~ (ti(state, v0) =
% 20.08/3.55 | | v2) | ~ $i(v1) | ~ $i(v0))
% 20.08/3.55 | |
% 20.08/3.55 | | ALPHA: (22) implies:
% 20.08/3.55 | | (23) ~ (all_55_0 = 0)
% 20.08/3.55 | |
% 20.08/3.55 | | REDUCE: (10), (23) imply:
% 20.08/3.55 | | (24) $false
% 20.08/3.55 | |
% 20.08/3.55 | | CLOSE: (24) is inconsistent.
% 20.08/3.55 | |
% 20.08/3.55 | End of split
% 20.08/3.55 |
% 20.08/3.55 End of proof
% 20.08/3.55 % SZS output end Proof for theBenchmark
% 20.08/3.55
% 20.08/3.55 2939ms
%------------------------------------------------------------------------------