TSTP Solution File: SEU294+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU294+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 17:43:54 EDT 2023
% Result : Theorem 9.12s 2.21s
% Output : Proof 46.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU294+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.33 % Computer : n012.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Wed Aug 23 23:20:12 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.15/1.13 Prover 4: Preprocessing ...
% 3.15/1.13 Prover 1: Preprocessing ...
% 3.15/1.17 Prover 5: Preprocessing ...
% 3.15/1.17 Prover 0: Preprocessing ...
% 3.15/1.17 Prover 2: Preprocessing ...
% 3.15/1.17 Prover 6: Preprocessing ...
% 3.15/1.17 Prover 3: Preprocessing ...
% 6.48/1.64 Prover 2: Proving ...
% 6.48/1.64 Prover 5: Proving ...
% 6.89/1.74 Prover 1: Warning: ignoring some quantifiers
% 6.89/1.75 Prover 6: Proving ...
% 6.89/1.76 Prover 3: Warning: ignoring some quantifiers
% 7.54/1.77 Prover 1: Constructing countermodel ...
% 7.71/1.80 Prover 3: Constructing countermodel ...
% 8.10/1.90 Prover 4: Warning: ignoring some quantifiers
% 8.67/1.93 Prover 4: Constructing countermodel ...
% 9.12/1.99 Prover 0: Proving ...
% 9.12/2.20 Prover 2: proved (1588ms)
% 9.12/2.21
% 9.12/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.12/2.21
% 9.12/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.12/2.21 Prover 3: stopped
% 10.78/2.22 Prover 0: stopped
% 10.78/2.23 Prover 6: stopped
% 10.78/2.24 Prover 5: stopped
% 11.08/2.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.08/2.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.08/2.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.08/2.26 Prover 7: Preprocessing ...
% 11.08/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.38/2.29 Prover 8: Preprocessing ...
% 11.38/2.32 Prover 10: Preprocessing ...
% 11.38/2.33 Prover 11: Preprocessing ...
% 11.86/2.35 Prover 13: Preprocessing ...
% 11.86/2.39 Prover 7: Warning: ignoring some quantifiers
% 11.86/2.40 Prover 10: Warning: ignoring some quantifiers
% 11.86/2.40 Prover 10: Constructing countermodel ...
% 12.34/2.41 Prover 7: Constructing countermodel ...
% 12.34/2.45 Prover 13: Warning: ignoring some quantifiers
% 12.34/2.46 Prover 13: Constructing countermodel ...
% 12.72/2.49 Prover 8: Warning: ignoring some quantifiers
% 12.72/2.50 Prover 8: Constructing countermodel ...
% 13.41/2.56 Prover 10: gave up
% 13.41/2.57 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.70/2.60 Prover 11: Warning: ignoring some quantifiers
% 13.70/2.61 Prover 16: Preprocessing ...
% 13.70/2.61 Prover 11: Constructing countermodel ...
% 14.19/2.74 Prover 16: Warning: ignoring some quantifiers
% 14.19/2.74 Prover 16: Constructing countermodel ...
% 14.19/2.77 Prover 13: gave up
% 14.19/2.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 15.35/2.84 Prover 19: Preprocessing ...
% 15.80/2.90 Prover 7: gave up
% 16.65/3.00 Prover 19: Warning: ignoring some quantifiers
% 16.65/3.01 Prover 19: Constructing countermodel ...
% 19.09/3.36 Prover 16: gave up
% 45.22/6.90 Prover 11: Found proof (size 32)
% 45.22/6.90 Prover 11: proved (4652ms)
% 45.22/6.90 Prover 4: stopped
% 45.22/6.90 Prover 8: stopped
% 45.22/6.90 Prover 1: stopped
% 45.22/6.90 Prover 19: stopped
% 45.22/6.90
% 45.22/6.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.22/6.90
% 45.22/6.90 % SZS output start Proof for theBenchmark
% 45.22/6.91 Assumptions after simplification:
% 45.22/6.91 ---------------------------------
% 45.22/6.91
% 45.22/6.91 (cc2_finset_1)
% 45.22/6.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 45.22/6.93 (powerset(v0) = v1) | ~ (finite(v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4:
% 45.22/6.93 int] : (( ~ (v4 = 0) & finite(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) =
% 45.22/6.93 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) =
% 45.22/6.94 v1) | ~ (element(v2, v1) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] :
% 45.22/6.94 ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3))) & ! [v0: $i]
% 45.22/6.94 : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (powerset(v0) = v1 & $i(v1)
% 45.22/6.94 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (finite(v2) = v3) | ~ $i(v2)
% 45.22/6.94 | ? [v4: int] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2: $i] : (
% 45.22/6.94 ~ (element(v2, v1) = 0) | ~ $i(v2) | finite(v2) = 0)))
% 45.22/6.94
% 45.22/6.94 (rc1_subset_1)
% 45.22/6.94 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 45.22/6.94 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v0) = v2 &
% 45.22/6.94 empty(v3) = v4 & element(v3, v2) = 0 & $i(v3) & $i(v2))) & ! [v0: $i] :
% 45.22/6.94 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i]
% 45.22/6.94 : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & empty(v3)
% 45.22/6.94 = v5 & element(v3, v1) = 0) | (v2 = 0 & empty(v0) = 0))))
% 45.22/6.94
% 45.22/6.94 (rc3_ordinal1)
% 45.22/6.94 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 &
% 45.22/6.94 epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0 &
% 45.22/6.94 $i(v0))
% 45.22/6.94
% 45.22/6.94 (t13_finset_1)
% 45.22/6.94 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = 0 &
% 45.22/6.94 finite(v1) = 0 & finite(v0) = v2 & $i(v1) & $i(v0))
% 45.22/6.94
% 45.22/6.94 (t3_subset)
% 45.22/6.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 45.22/6.95 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 45.22/6.95 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 45.22/6.95 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 45.22/6.95 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0,
% 45.22/6.95 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 45.22/6.95 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 45.22/6.95 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 45.22/6.95 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) =
% 45.22/6.95 0 & $i(v2)))
% 45.22/6.95
% 45.22/6.95 (function-axioms)
% 45.22/6.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 45.22/6.95 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 45.22/6.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 45.22/6.95 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 45.22/6.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 45.22/6.96 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 45.22/6.96 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 45.22/6.96 ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & !
% 45.22/6.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 45.22/6.96 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0)) &
% 45.22/6.96 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 45.22/6.96 v0 | ~ (ordinal_yielding(v2) = v1) | ~ (ordinal_yielding(v2) = v0)) & !
% 45.22/6.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 45.22/6.96 | ~ (being_limit_ordinal(v2) = v1) | ~ (being_limit_ordinal(v2) = v0)) &
% 45.22/6.96 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 45.22/6.96 v0 | ~ (function_yielding(v2) = v1) | ~ (function_yielding(v2) = v0)) & !
% 45.22/6.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 45.22/6.96 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) =
% 45.22/6.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 45.22/6.96 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 45.22/6.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 45.22/6.96 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.22/6.96 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~
% 45.22/6.96 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.22/6.96 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 45.22/6.96 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.22/6.96 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 45.22/6.96 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.22/6.96 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~
% 45.22/6.96 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 45.22/6.96 : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & !
% 45.22/6.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 45.22/6.96 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & !
% 45.22/6.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 45.22/6.96 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & !
% 45.22/6.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 45.22/6.96 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 45.22/6.96
% 45.22/6.96 Further assumptions not needed in the proof:
% 45.22/6.96 --------------------------------------------
% 45.22/6.96 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 45.22/6.96 cc1_relat_1, cc2_arytm_3, cc2_funct_1, cc2_ordinal1, cc3_ordinal1, cc4_arytm_3,
% 45.22/6.96 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc2_ordinal1,
% 45.22/6.96 fc4_relat_1, fc8_arytm_3, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1,
% 45.22/6.96 rc1_ordinal1, rc1_ordinal2, rc1_relat_1, rc1_xboole_0, rc2_arytm_3,
% 45.22/6.96 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1,
% 45.22/6.96 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1, rc3_relat_1,
% 45.22/6.96 rc4_funct_1, rc4_ordinal1, rc5_funct_1, reflexivity_r1_tarski, t1_subset,
% 45.22/6.96 t2_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 45.22/6.96
% 45.22/6.96 Those formulas are unsatisfiable:
% 45.22/6.96 ---------------------------------
% 45.22/6.96
% 45.22/6.96 Begin of proof
% 45.22/6.96 |
% 45.22/6.96 | ALPHA: (cc2_finset_1) implies:
% 46.33/6.96 | (1) ! [v0: $i] : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 46.33/6.96 | (powerset(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: int] : (v3 = 0 |
% 46.33/6.96 | ~ (finite(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 46.33/6.96 | element(v2, v1) = v4)) & ! [v2: $i] : ( ~ (element(v2, v1) =
% 46.33/6.96 | 0) | ~ $i(v2) | finite(v2) = 0)))
% 46.33/6.96 |
% 46.33/6.96 | ALPHA: (rc1_subset_1) implies:
% 46.33/6.96 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0)
% 46.33/6.96 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 46.33/6.96 | powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0 & $i(v3) &
% 46.33/6.96 | $i(v2)))
% 46.33/6.96 |
% 46.33/6.96 | ALPHA: (t3_subset) implies:
% 46.33/6.96 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 46.33/6.96 | $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 46.33/6.96 | $i(v2)))
% 46.33/6.96 |
% 46.33/6.96 | ALPHA: (function-axioms) implies:
% 46.33/6.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 46.33/6.96 | v1) | ~ (powerset(v2) = v0))
% 46.33/6.96 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 46.33/6.96 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 46.33/6.96 | v2) = v0))
% 46.33/6.96 |
% 46.33/6.96 | DELTA: instantiating (rc3_ordinal1) with fresh symbols all_65_0, all_65_1
% 46.33/6.96 | gives:
% 46.33/6.96 | (6) ~ (all_65_0 = 0) & empty(all_65_1) = all_65_0 &
% 46.33/6.96 | epsilon_connected(all_65_1) = 0 & epsilon_transitive(all_65_1) = 0 &
% 46.33/6.96 | ordinal(all_65_1) = 0 & $i(all_65_1)
% 46.33/6.96 |
% 46.33/6.96 | ALPHA: (6) implies:
% 46.33/6.96 | (7) ~ (all_65_0 = 0)
% 46.33/6.96 | (8) $i(all_65_1)
% 46.33/6.97 | (9) empty(all_65_1) = all_65_0
% 46.33/6.97 |
% 46.33/6.97 | DELTA: instantiating (t13_finset_1) with fresh symbols all_67_0, all_67_1,
% 46.33/6.97 | all_67_2 gives:
% 46.33/6.97 | (10) ~ (all_67_0 = 0) & subset(all_67_2, all_67_1) = 0 & finite(all_67_1)
% 46.33/6.97 | = 0 & finite(all_67_2) = all_67_0 & $i(all_67_1) & $i(all_67_2)
% 46.33/6.97 |
% 46.33/6.97 | ALPHA: (10) implies:
% 46.33/6.97 | (11) ~ (all_67_0 = 0)
% 46.33/6.97 | (12) $i(all_67_2)
% 46.33/6.97 | (13) $i(all_67_1)
% 46.33/6.97 | (14) finite(all_67_2) = all_67_0
% 46.33/6.97 | (15) finite(all_67_1) = 0
% 46.33/6.97 | (16) subset(all_67_2, all_67_1) = 0
% 46.33/6.97 |
% 46.33/6.97 | GROUND_INST: instantiating (2) with all_65_1, all_65_0, simplifying with (8),
% 46.33/6.97 | (9) gives:
% 46.33/6.97 | (17) all_65_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 46.33/6.97 | & powerset(all_65_1) = v0 & empty(v1) = v2 & element(v1, v0) = 0 &
% 46.33/6.97 | $i(v1) & $i(v0))
% 46.33/6.97 |
% 46.33/6.97 | GROUND_INST: instantiating (1) with all_67_1, simplifying with (13), (15)
% 46.33/6.97 | gives:
% 46.33/6.97 | (18) ? [v0: $i] : (powerset(all_67_1) = v0 & $i(v0) & ! [v1: $i] : !
% 46.33/6.97 | [v2: int] : (v2 = 0 | ~ (finite(v1) = v2) | ~ $i(v1) | ? [v3:
% 46.33/6.97 | int] : ( ~ (v3 = 0) & element(v1, v0) = v3)) & ! [v1: $i] : ( ~
% 46.33/6.97 | (element(v1, v0) = 0) | ~ $i(v1) | finite(v1) = 0))
% 46.33/6.97 |
% 46.33/6.97 | GROUND_INST: instantiating (3) with all_67_2, all_67_1, simplifying with (12),
% 46.33/6.97 | (13), (16) gives:
% 46.33/6.97 | (19) ? [v0: $i] : (powerset(all_67_1) = v0 & element(all_67_2, v0) = 0 &
% 46.33/6.97 | $i(v0))
% 46.33/6.97 |
% 46.33/6.97 | DELTA: instantiating (19) with fresh symbol all_83_0 gives:
% 46.33/6.97 | (20) powerset(all_67_1) = all_83_0 & element(all_67_2, all_83_0) = 0 &
% 46.33/6.97 | $i(all_83_0)
% 46.33/6.97 |
% 46.33/6.97 | ALPHA: (20) implies:
% 46.33/6.97 | (21) element(all_67_2, all_83_0) = 0
% 46.33/6.97 | (22) powerset(all_67_1) = all_83_0
% 46.33/6.97 |
% 46.33/6.97 | DELTA: instantiating (18) with fresh symbol all_339_0 gives:
% 46.33/6.97 | (23) powerset(all_67_1) = all_339_0 & $i(all_339_0) & ! [v0: $i] : ! [v1:
% 46.33/6.97 | int] : (v1 = 0 | ~ (finite(v0) = v1) | ~ $i(v0) | ? [v2: int] : (
% 46.33/6.97 | ~ (v2 = 0) & element(v0, all_339_0) = v2)) & ! [v0: $i] : ( ~
% 46.33/6.97 | (element(v0, all_339_0) = 0) | ~ $i(v0) | finite(v0) = 0)
% 46.33/6.97 |
% 46.33/6.97 | ALPHA: (23) implies:
% 46.33/6.97 | (24) powerset(all_67_1) = all_339_0
% 46.33/6.97 | (25) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (finite(v0) = v1) | ~
% 46.33/6.97 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0, all_339_0) = v2))
% 46.33/6.97 |
% 46.33/6.97 | GROUND_INST: instantiating (25) with all_67_2, all_67_0, simplifying with
% 46.33/6.97 | (12), (14) gives:
% 46.33/6.97 | (26) all_67_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & element(all_67_2,
% 46.33/6.97 | all_339_0) = v0)
% 46.33/6.97 |
% 46.33/6.97 | BETA: splitting (26) gives:
% 46.33/6.97 |
% 46.33/6.97 | Case 1:
% 46.33/6.97 | |
% 46.33/6.97 | | (27) all_67_0 = 0
% 46.33/6.97 | |
% 46.33/6.97 | | REDUCE: (11), (27) imply:
% 46.33/6.97 | | (28) $false
% 46.33/6.98 | |
% 46.33/6.98 | | CLOSE: (28) is inconsistent.
% 46.33/6.98 | |
% 46.33/6.98 | Case 2:
% 46.33/6.98 | |
% 46.33/6.98 | | (29) ? [v0: int] : ( ~ (v0 = 0) & element(all_67_2, all_339_0) = v0)
% 46.33/6.98 | |
% 46.33/6.98 | | DELTA: instantiating (29) with fresh symbol all_480_0 gives:
% 46.33/6.98 | | (30) ~ (all_480_0 = 0) & element(all_67_2, all_339_0) = all_480_0
% 46.33/6.98 | |
% 46.33/6.98 | | ALPHA: (30) implies:
% 46.33/6.98 | | (31) ~ (all_480_0 = 0)
% 46.33/6.98 | | (32) element(all_67_2, all_339_0) = all_480_0
% 46.33/6.98 | |
% 46.33/6.98 | | BETA: splitting (17) gives:
% 46.33/6.98 | |
% 46.33/6.98 | | Case 1:
% 46.33/6.98 | | |
% 46.33/6.98 | | | (33) all_65_0 = 0
% 46.33/6.98 | | |
% 46.33/6.98 | | | REDUCE: (7), (33) imply:
% 46.33/6.98 | | | (34) $false
% 46.33/6.98 | | |
% 46.33/6.98 | | | CLOSE: (34) is inconsistent.
% 46.33/6.98 | | |
% 46.33/6.98 | | Case 2:
% 46.33/6.98 | | |
% 46.33/6.98 | | |
% 46.33/6.98 | | | GROUND_INST: instantiating (4) with all_83_0, all_339_0, all_67_1,
% 46.33/6.98 | | | simplifying with (22), (24) gives:
% 46.33/6.98 | | | (35) all_339_0 = all_83_0
% 46.33/6.98 | | |
% 46.33/6.98 | | | REDUCE: (32), (35) imply:
% 46.33/6.98 | | | (36) element(all_67_2, all_83_0) = all_480_0
% 46.33/6.98 | | |
% 46.33/6.98 | | | GROUND_INST: instantiating (5) with 0, all_480_0, all_83_0, all_67_2,
% 46.33/6.98 | | | simplifying with (21), (36) gives:
% 46.33/6.98 | | | (37) all_480_0 = 0
% 46.33/6.98 | | |
% 46.33/6.98 | | | REDUCE: (31), (37) imply:
% 46.33/6.98 | | | (38) $false
% 46.33/6.98 | | |
% 46.33/6.98 | | | CLOSE: (38) is inconsistent.
% 46.33/6.98 | | |
% 46.33/6.98 | | End of split
% 46.33/6.98 | |
% 46.33/6.98 | End of split
% 46.33/6.98 |
% 46.33/6.98 End of proof
% 46.33/6.98 % SZS output end Proof for theBenchmark
% 46.33/6.98
% 46.33/6.98 6384ms
%------------------------------------------------------------------------------