%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------