TSTP Solution File: SEU294+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU294+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.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 8.32s 1.87s
% Output : Proof 22.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU294+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 20:58:46 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.82/1.08 Prover 4: Preprocessing ...
% 2.82/1.08 Prover 1: Preprocessing ...
% 3.25/1.12 Prover 2: Preprocessing ...
% 3.25/1.12 Prover 5: Preprocessing ...
% 3.25/1.12 Prover 6: Preprocessing ...
% 3.25/1.12 Prover 3: Preprocessing ...
% 3.25/1.12 Prover 0: Preprocessing ...
% 5.91/1.51 Prover 2: Proving ...
% 5.91/1.51 Prover 5: Proving ...
% 6.36/1.57 Prover 1: Warning: ignoring some quantifiers
% 6.36/1.60 Prover 1: Constructing countermodel ...
% 6.36/1.60 Prover 6: Proving ...
% 6.36/1.64 Prover 3: Warning: ignoring some quantifiers
% 7.06/1.66 Prover 3: Constructing countermodel ...
% 7.31/1.71 Prover 4: Warning: ignoring some quantifiers
% 7.31/1.72 Prover 4: Constructing countermodel ...
% 7.55/1.79 Prover 0: Proving ...
% 8.32/1.87 Prover 2: proved (1242ms)
% 8.32/1.87
% 8.32/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.32/1.87
% 8.32/1.88 Prover 3: stopped
% 8.32/1.88 Prover 6: stopped
% 8.32/1.89 Prover 5: stopped
% 8.77/1.91 Prover 0: stopped
% 8.77/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.77/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.77/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.77/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.77/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.23/1.99 Prover 10: Preprocessing ...
% 9.23/2.00 Prover 11: Preprocessing ...
% 9.23/2.00 Prover 7: Preprocessing ...
% 9.23/2.01 Prover 13: Preprocessing ...
% 9.23/2.04 Prover 8: Preprocessing ...
% 9.23/2.06 Prover 7: Warning: ignoring some quantifiers
% 9.97/2.06 Prover 10: Warning: ignoring some quantifiers
% 9.97/2.07 Prover 7: Constructing countermodel ...
% 9.97/2.07 Prover 10: Constructing countermodel ...
% 9.97/2.08 Prover 13: Warning: ignoring some quantifiers
% 9.97/2.09 Prover 13: Constructing countermodel ...
% 10.24/2.14 Prover 8: Warning: ignoring some quantifiers
% 10.24/2.15 Prover 8: Constructing countermodel ...
% 10.24/2.21 Prover 10: gave up
% 10.24/2.22 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.24/2.23 Prover 11: Warning: ignoring some quantifiers
% 10.24/2.24 Prover 7: gave up
% 10.24/2.25 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.40/2.27 Prover 11: Constructing countermodel ...
% 11.40/2.30 Prover 19: Preprocessing ...
% 11.40/2.30 Prover 16: Preprocessing ...
% 12.12/2.42 Prover 16: Warning: ignoring some quantifiers
% 12.12/2.43 Prover 13: gave up
% 12.59/2.43 Prover 16: Constructing countermodel ...
% 12.83/2.48 Prover 19: Warning: ignoring some quantifiers
% 12.83/2.51 Prover 19: Constructing countermodel ...
% 14.85/2.84 Prover 16: gave up
% 22.00/3.70 Prover 11: Found proof (size 24)
% 22.00/3.70 Prover 11: proved (1788ms)
% 22.00/3.70 Prover 4: stopped
% 22.00/3.70 Prover 8: stopped
% 22.16/3.71 Prover 19: stopped
% 22.21/3.73 Prover 1: stopped
% 22.21/3.73
% 22.21/3.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.21/3.73
% 22.21/3.73 % SZS output start Proof for theBenchmark
% 22.21/3.73 Assumptions after simplification:
% 22.21/3.73 ---------------------------------
% 22.21/3.73
% 22.21/3.73 (cc2_finset_1)
% 22.21/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 22.21/3.76 (powerset(v0) = v1) | ~ (finite(v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4:
% 22.21/3.76 int] : (( ~ (v4 = 0) & finite(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) =
% 22.21/3.76 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) =
% 22.21/3.76 v1) | ~ (element(v2, v1) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] :
% 22.21/3.76 ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3))) & ! [v0: $i]
% 22.21/3.76 : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (powerset(v0) = v1 & $i(v1)
% 22.21/3.76 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (finite(v2) = v3) | ~ $i(v2)
% 22.21/3.76 | ? [v4: int] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2: $i] : (
% 22.21/3.76 ~ (element(v2, v1) = 0) | ~ $i(v2) | finite(v2) = 0)))
% 22.21/3.76
% 22.21/3.76 (t13_finset_1)
% 22.21/3.76 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = 0 &
% 22.21/3.76 finite(v1) = 0 & finite(v0) = v2 & $i(v1) & $i(v0))
% 22.21/3.76
% 22.21/3.76 (t3_subset)
% 22.21/3.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 22.21/3.77 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 22.21/3.77 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 22.21/3.77 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 22.21/3.77 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0,
% 22.21/3.77 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 22.21/3.77 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 22.21/3.77 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 22.21/3.77 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) =
% 22.21/3.77 0 & $i(v2)))
% 22.21/3.77
% 22.21/3.77 (function-axioms)
% 22.21/3.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 22.21/3.77 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 22.21/3.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 22.21/3.77 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 22.21/3.77 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 22.21/3.77 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 22.21/3.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 22.21/3.77 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) =
% 22.21/3.77 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 22.21/3.77 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 22.21/3.77 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 22.21/3.77 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.21/3.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~
% 22.21/3.77 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.21/3.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 22.21/3.77 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.21/3.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 22.21/3.77 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.21/3.77 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~
% 22.21/3.77 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 22.21/3.77 : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & !
% 22.21/3.77 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 22.21/3.77 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & !
% 22.21/3.77 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 22.21/3.77 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & !
% 22.21/3.77 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 22.21/3.77 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 22.21/3.77
% 22.21/3.77 Further assumptions not needed in the proof:
% 22.21/3.77 --------------------------------------------
% 22.21/3.77 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 22.21/3.77 cc1_relat_1, cc2_arytm_3, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 22.21/3.77 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_m1_subset_1, existence_m1_subset_1,
% 22.21/3.77 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc2_ordinal1, fc4_relat_1,
% 22.21/3.77 rc1_arytm_3, rc1_finset_1, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_subset_1,
% 22.21/3.77 rc1_xboole_0, rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_relat_1,
% 22.21/3.77 rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc3_funct_1, rc3_ordinal1,
% 22.21/3.77 rc3_relat_1, rc4_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 22.21/3.77 t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 22.21/3.77
% 22.21/3.77 Those formulas are unsatisfiable:
% 22.21/3.77 ---------------------------------
% 22.21/3.77
% 22.21/3.77 Begin of proof
% 22.21/3.77 |
% 22.21/3.77 | ALPHA: (cc2_finset_1) implies:
% 22.21/3.78 | (1) ! [v0: $i] : ( ~ (finite(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 22.21/3.78 | (powerset(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: int] : (v3 = 0 |
% 22.21/3.78 | ~ (finite(v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 22.21/3.78 | element(v2, v1) = v4)) & ! [v2: $i] : ( ~ (element(v2, v1) =
% 22.21/3.78 | 0) | ~ $i(v2) | finite(v2) = 0)))
% 22.21/3.78 |
% 22.21/3.78 | ALPHA: (t3_subset) implies:
% 22.21/3.78 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 22.21/3.78 | $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 22.21/3.78 | $i(v2)))
% 22.21/3.78 |
% 22.21/3.78 | ALPHA: (function-axioms) implies:
% 22.21/3.78 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 22.21/3.78 | v1) | ~ (powerset(v2) = v0))
% 22.21/3.78 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.21/3.78 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 22.21/3.78 | v2) = v0))
% 22.21/3.78 |
% 22.21/3.78 | DELTA: instantiating (t13_finset_1) with fresh symbols all_54_0, all_54_1,
% 22.21/3.78 | all_54_2 gives:
% 22.21/3.78 | (5) ~ (all_54_0 = 0) & subset(all_54_2, all_54_1) = 0 & finite(all_54_1) =
% 22.21/3.78 | 0 & finite(all_54_2) = all_54_0 & $i(all_54_1) & $i(all_54_2)
% 22.21/3.78 |
% 22.21/3.78 | ALPHA: (5) implies:
% 22.21/3.78 | (6) ~ (all_54_0 = 0)
% 22.21/3.78 | (7) $i(all_54_2)
% 22.21/3.78 | (8) $i(all_54_1)
% 22.21/3.78 | (9) finite(all_54_2) = all_54_0
% 22.21/3.78 | (10) finite(all_54_1) = 0
% 22.21/3.78 | (11) subset(all_54_2, all_54_1) = 0
% 22.21/3.78 |
% 22.21/3.78 | GROUND_INST: instantiating (1) with all_54_1, simplifying with (8), (10)
% 22.21/3.78 | gives:
% 22.21/3.78 | (12) ? [v0: $i] : (powerset(all_54_1) = v0 & $i(v0) & ! [v1: $i] : !
% 22.21/3.78 | [v2: int] : (v2 = 0 | ~ (finite(v1) = v2) | ~ $i(v1) | ? [v3:
% 22.21/3.78 | int] : ( ~ (v3 = 0) & element(v1, v0) = v3)) & ! [v1: $i] : ( ~
% 22.21/3.78 | (element(v1, v0) = 0) | ~ $i(v1) | finite(v1) = 0))
% 22.21/3.78 |
% 22.21/3.78 | GROUND_INST: instantiating (2) with all_54_2, all_54_1, simplifying with (7),
% 22.21/3.78 | (8), (11) gives:
% 22.21/3.78 | (13) ? [v0: $i] : (powerset(all_54_1) = v0 & element(all_54_2, v0) = 0 &
% 22.21/3.78 | $i(v0))
% 22.21/3.78 |
% 22.21/3.78 | DELTA: instantiating (13) with fresh symbol all_66_0 gives:
% 22.21/3.78 | (14) powerset(all_54_1) = all_66_0 & element(all_54_2, all_66_0) = 0 &
% 22.21/3.78 | $i(all_66_0)
% 22.21/3.78 |
% 22.21/3.78 | ALPHA: (14) implies:
% 22.21/3.78 | (15) element(all_54_2, all_66_0) = 0
% 22.21/3.78 | (16) powerset(all_54_1) = all_66_0
% 22.21/3.78 |
% 22.21/3.78 | DELTA: instantiating (12) with fresh symbol all_191_0 gives:
% 22.21/3.79 | (17) powerset(all_54_1) = all_191_0 & $i(all_191_0) & ! [v0: $i] : ! [v1:
% 22.21/3.79 | int] : (v1 = 0 | ~ (finite(v0) = v1) | ~ $i(v0) | ? [v2: int] : (
% 22.21/3.79 | ~ (v2 = 0) & element(v0, all_191_0) = v2)) & ! [v0: $i] : ( ~
% 22.21/3.79 | (element(v0, all_191_0) = 0) | ~ $i(v0) | finite(v0) = 0)
% 22.21/3.79 |
% 22.21/3.79 | ALPHA: (17) implies:
% 22.21/3.79 | (18) powerset(all_54_1) = all_191_0
% 22.21/3.79 | (19) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (finite(v0) = v1) | ~
% 22.21/3.79 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & element(v0, all_191_0) = v2))
% 22.21/3.79 |
% 22.21/3.79 | GROUND_INST: instantiating (19) with all_54_2, all_54_0, simplifying with (7),
% 22.21/3.79 | (9) gives:
% 22.21/3.79 | (20) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & element(all_54_2,
% 22.21/3.79 | all_191_0) = v0)
% 22.21/3.79 |
% 22.21/3.79 | BETA: splitting (20) gives:
% 22.21/3.79 |
% 22.21/3.79 | Case 1:
% 22.21/3.79 | |
% 22.21/3.79 | | (21) all_54_0 = 0
% 22.21/3.79 | |
% 22.21/3.79 | | REDUCE: (6), (21) imply:
% 22.21/3.79 | | (22) $false
% 22.21/3.79 | |
% 22.21/3.79 | | CLOSE: (22) is inconsistent.
% 22.21/3.79 | |
% 22.21/3.79 | Case 2:
% 22.21/3.79 | |
% 22.21/3.79 | | (23) ? [v0: int] : ( ~ (v0 = 0) & element(all_54_2, all_191_0) = v0)
% 22.21/3.79 | |
% 22.21/3.79 | | DELTA: instantiating (23) with fresh symbol all_290_0 gives:
% 22.21/3.79 | | (24) ~ (all_290_0 = 0) & element(all_54_2, all_191_0) = all_290_0
% 22.21/3.79 | |
% 22.21/3.79 | | ALPHA: (24) implies:
% 22.21/3.79 | | (25) ~ (all_290_0 = 0)
% 22.21/3.79 | | (26) element(all_54_2, all_191_0) = all_290_0
% 22.21/3.79 | |
% 22.21/3.79 | | GROUND_INST: instantiating (3) with all_66_0, all_191_0, all_54_1,
% 22.21/3.79 | | simplifying with (16), (18) gives:
% 22.21/3.79 | | (27) all_191_0 = all_66_0
% 22.21/3.79 | |
% 22.21/3.79 | | REDUCE: (26), (27) imply:
% 22.21/3.79 | | (28) element(all_54_2, all_66_0) = all_290_0
% 22.21/3.79 | |
% 22.21/3.79 | | GROUND_INST: instantiating (4) with 0, all_290_0, all_66_0, all_54_2,
% 22.21/3.79 | | simplifying with (15), (28) gives:
% 22.21/3.79 | | (29) all_290_0 = 0
% 22.21/3.79 | |
% 22.21/3.79 | | REDUCE: (25), (29) imply:
% 22.21/3.79 | | (30) $false
% 22.21/3.79 | |
% 22.21/3.79 | | CLOSE: (30) is inconsistent.
% 22.21/3.79 | |
% 22.21/3.79 | End of split
% 22.21/3.79 |
% 22.21/3.79 End of proof
% 22.21/3.79 % SZS output end Proof for theBenchmark
% 22.21/3.79
% 22.21/3.79 3184ms
%------------------------------------------------------------------------------