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