%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU117+1 : TPTP v8.1.2. Released v3.2.0. % 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 17:42:34 EDT 2023 % Result : Theorem 9.38s 2.08s % Output : Proof 11.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU117+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n002.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 14:55:16 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.52/1.11 Prover 1: Preprocessing ... % 2.52/1.11 Prover 4: Preprocessing ... % 3.11/1.15 Prover 2: Preprocessing ... % 3.11/1.15 Prover 5: Preprocessing ... % 3.11/1.15 Prover 0: Preprocessing ... % 3.11/1.15 Prover 6: Preprocessing ... % 3.11/1.15 Prover 3: Preprocessing ... % 5.38/1.57 Prover 1: Warning: ignoring some quantifiers % 5.96/1.58 Prover 2: Proving ... % 6.04/1.59 Prover 1: Constructing countermodel ... % 6.04/1.59 Prover 5: Proving ... % 6.04/1.60 Prover 6: Proving ... % 6.04/1.60 Prover 4: Warning: ignoring some quantifiers % 6.04/1.60 Prover 3: Warning: ignoring some quantifiers % 6.22/1.62 Prover 3: Constructing countermodel ... % 6.32/1.65 Prover 4: Constructing countermodel ... % 6.93/1.77 Prover 0: Proving ... % 9.38/2.08 Prover 3: proved (1428ms) % 9.38/2.08 % 9.38/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.38/2.08 % 9.38/2.08 Prover 6: stopped % 9.38/2.08 Prover 5: stopped % 9.38/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.38/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.38/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.38/2.09 Prover 2: stopped % 9.38/2.09 Prover 0: stopped % 9.38/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.38/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.07/2.17 Prover 10: Preprocessing ... % 10.07/2.17 Prover 8: Preprocessing ... % 10.07/2.18 Prover 13: Preprocessing ... % 10.07/2.18 Prover 7: Preprocessing ... % 10.07/2.18 Prover 11: Preprocessing ... % 10.67/2.25 Prover 1: Found proof (size 39) % 10.67/2.26 Prover 1: proved (1609ms) % 10.67/2.26 Prover 13: Warning: ignoring some quantifiers % 10.67/2.26 Prover 10: Warning: ignoring some quantifiers % 10.67/2.26 Prover 4: stopped % 10.67/2.26 Prover 7: Warning: ignoring some quantifiers % 10.67/2.27 Prover 11: stopped % 10.67/2.27 Prover 10: Constructing countermodel ... % 10.97/2.27 Prover 13: Constructing countermodel ... % 10.97/2.27 Prover 7: Constructing countermodel ... % 10.97/2.28 Prover 10: stopped % 10.97/2.28 Prover 7: stopped % 10.97/2.28 Prover 13: stopped % 10.97/2.30 Prover 8: Warning: ignoring some quantifiers % 10.97/2.31 Prover 8: Constructing countermodel ... % 10.97/2.31 Prover 8: stopped % 10.97/2.31 % 10.97/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.97/2.31 % 10.97/2.32 % SZS output start Proof for theBenchmark % 10.97/2.32 Assumptions after simplification: % 10.97/2.32 --------------------------------- % 10.97/2.32 % 10.97/2.33 (d5_finsub_1) % 11.31/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v2) | ~ % 11.31/2.35 (preboolean(v1) = 0) | ~ $i(v1) | ~ $i(v0) | (( ~ (v2 = v1) | ( ! [v3: $i] % 11.31/2.35 : ! [v4: any] : ( ~ (subset(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] % 11.31/2.35 : ? [v6: any] : (in(v3, v1) = v5 & finite(v3) = v6 & ( ~ (v5 = 0) | % 11.31/2.35 (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (subset(v3, v0) = 0) | % 11.31/2.35 ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & % 11.31/2.35 finite(v3) = v4 & ( ~ (v4 = 0) | v5 = 0))))) & (v2 = v1 | ? [v3: % 11.31/2.35 $i] : ? [v4: any] : ? [v5: any] : ? [v6: any] : (subset(v3, v0) = % 11.31/2.35 v5 & in(v3, v1) = v4 & finite(v3) = v6 & $i(v3) & ( ~ (v6 = 0) | ~ % 11.31/2.35 (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 0)))))) % 11.31/2.35 % 11.31/2.35 (fc2_finsub_1) % 11.31/2.36 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 11.31/2.36 diff_closed(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = % 11.31/2.36 v1) | ~ $i(v0) | cup_closed(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 11.31/2.36 (finite_subsets(v0) = v1) | ~ $i(v0) | preboolean(v1) = 0) & ! [v0: $i] : % 11.31/2.36 ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 11.31/2.36 (v2 = 0) & empty(v1) = v2)) % 11.31/2.36 % 11.31/2.36 (t2_subset) % 11.31/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 11.31/2.36 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 & % 11.31/2.36 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 11.31/2.36 % 11.31/2.36 (t32_finsub_1) % 11.31/2.36 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 11.31/2.36 = 0) & finite_subsets(v0) = v2 & powerset(v0) = v3 & element(v1, v3) = v4 % 11.31/2.36 & element(v1, v2) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.31/2.36 % 11.31/2.36 (t3_subset) % 11.31/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.31/2.36 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 11.31/2.36 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 11.31/2.36 : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) % 11.31/2.36 | ~ $i(v0) | subset(v0, v1) = 0) % 11.31/2.36 % 11.31/2.36 (function-axioms) % 11.43/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.43/2.37 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 11.43/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.43/2.37 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 11.43/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.43/2.37 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: % 11.43/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.43/2.37 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 11.43/2.37 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 11.43/2.37 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 11.43/2.37 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 11.43/2.37 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.43/2.37 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 11.43/2.37 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.43/2.37 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 11.43/2.37 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~ % 11.43/2.37 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ % 11.43/2.37 (cap_closed(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 11.43/2.37 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0: $i] % 11.43/2.37 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 11.43/2.37 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.43/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~ % 11.43/2.37 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 11.43/2.37 : ! [v2: $i] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = % 11.43/2.37 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.43/2.37 $i] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! % 11.43/2.37 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 11.43/2.37 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0: % 11.43/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.43/2.37 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 11.43/2.37 % 11.43/2.37 Further assumptions not needed in the proof: % 11.43/2.37 -------------------------------------------- % 11.43/2.37 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finset_1, cc2_finsub_1, % 11.43/2.37 cc3_finsub_1, dt_k5_finsub_1, existence_m1_subset_1, fc1_finsub_1, fc1_subset_1, % 11.43/2.37 fc1_xboole_0, rc1_finset_1, rc1_finsub_1, rc1_subset_1, rc1_xboole_0, % 11.43/2.37 rc2_finset_1, rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc4_finset_1, % 11.43/2.37 reflexivity_r1_tarski, t1_subset, t4_subset, t5_subset, t6_boole, t7_boole, % 11.43/2.37 t8_boole % 11.43/2.37 % 11.43/2.37 Those formulas are unsatisfiable: % 11.43/2.37 --------------------------------- % 11.43/2.37 % 11.43/2.37 Begin of proof % 11.43/2.37 | % 11.43/2.37 | ALPHA: (fc2_finsub_1) implies: % 11.43/2.37 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 11.43/2.37 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 11.43/2.37 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 11.43/2.37 | preboolean(v1) = 0) % 11.43/2.38 | % 11.43/2.38 | ALPHA: (t3_subset) implies: % 11.43/2.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.43/2.38 | (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ % 11.43/2.38 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 11.43/2.38 | % 11.43/2.38 | ALPHA: (function-axioms) implies: % 11.43/2.38 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.43/2.38 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 11.43/2.38 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.43/2.38 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 11.43/2.38 | v2) = v0)) % 11.43/2.38 | % 11.43/2.38 | DELTA: instantiating (t32_finsub_1) with fresh symbols all_39_0, all_39_1, % 11.43/2.38 | all_39_2, all_39_3, all_39_4 gives: % 11.43/2.38 | (6) ~ (all_39_0 = 0) & finite_subsets(all_39_4) = all_39_2 & % 11.43/2.38 | powerset(all_39_4) = all_39_1 & element(all_39_3, all_39_1) = all_39_0 % 11.43/2.38 | & element(all_39_3, all_39_2) = 0 & $i(all_39_1) & $i(all_39_2) & % 11.43/2.38 | $i(all_39_3) & $i(all_39_4) % 11.43/2.38 | % 11.43/2.38 | ALPHA: (6) implies: % 11.43/2.38 | (7) ~ (all_39_0 = 0) % 11.43/2.38 | (8) $i(all_39_4) % 11.43/2.38 | (9) $i(all_39_3) % 11.43/2.38 | (10) $i(all_39_2) % 11.43/2.38 | (11) element(all_39_3, all_39_2) = 0 % 11.43/2.38 | (12) element(all_39_3, all_39_1) = all_39_0 % 11.43/2.38 | (13) powerset(all_39_4) = all_39_1 % 11.43/2.38 | (14) finite_subsets(all_39_4) = all_39_2 % 11.43/2.38 | % 11.43/2.38 | GROUND_INST: instantiating (3) with all_39_3, all_39_4, all_39_1, all_39_0, % 11.43/2.38 | simplifying with (8), (9), (12), (13) gives: % 11.43/2.38 | (15) all_39_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_39_3, % 11.43/2.38 | all_39_4) = v0) % 11.43/2.38 | % 11.43/2.38 | GROUND_INST: instantiating (2) with all_39_4, all_39_2, simplifying with (8), % 11.43/2.38 | (14) gives: % 11.43/2.38 | (16) preboolean(all_39_2) = 0 % 11.43/2.38 | % 11.43/2.38 | GROUND_INST: instantiating (1) with all_39_4, all_39_2, simplifying with (8), % 11.43/2.38 | (14) gives: % 11.43/2.38 | (17) ? [v0: int] : ( ~ (v0 = 0) & empty(all_39_2) = v0) % 11.43/2.38 | % 11.43/2.38 | DELTA: instantiating (17) with fresh symbol all_49_0 gives: % 11.43/2.38 | (18) ~ (all_49_0 = 0) & empty(all_39_2) = all_49_0 % 11.43/2.38 | % 11.43/2.38 | ALPHA: (18) implies: % 11.43/2.38 | (19) ~ (all_49_0 = 0) % 11.43/2.38 | (20) empty(all_39_2) = all_49_0 % 11.43/2.38 | % 11.43/2.38 | BETA: splitting (15) gives: % 11.43/2.38 | % 11.43/2.38 | Case 1: % 11.43/2.38 | | % 11.43/2.38 | | (21) all_39_0 = 0 % 11.43/2.38 | | % 11.43/2.38 | | REDUCE: (7), (21) imply: % 11.43/2.38 | | (22) $false % 11.43/2.38 | | % 11.43/2.38 | | CLOSE: (22) is inconsistent. % 11.43/2.38 | | % 11.43/2.38 | Case 2: % 11.43/2.38 | | % 11.43/2.39 | | (23) ? [v0: int] : ( ~ (v0 = 0) & subset(all_39_3, all_39_4) = v0) % 11.43/2.39 | | % 11.43/2.39 | | DELTA: instantiating (23) with fresh symbol all_62_0 gives: % 11.43/2.39 | | (24) ~ (all_62_0 = 0) & subset(all_39_3, all_39_4) = all_62_0 % 11.43/2.39 | | % 11.43/2.39 | | ALPHA: (24) implies: % 11.43/2.39 | | (25) ~ (all_62_0 = 0) % 11.43/2.39 | | (26) subset(all_39_3, all_39_4) = all_62_0 % 11.43/2.39 | | % 11.43/2.39 | | GROUND_INST: instantiating (d5_finsub_1) with all_39_4, all_39_2, all_39_2, % 11.43/2.39 | | simplifying with (8), (10), (14), (16) gives: % 11.43/2.39 | | (27) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_39_4) = v1) | ~ % 11.43/2.39 | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, all_39_2) = v2 & % 11.43/2.39 | | finite(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 11.43/2.39 | | $i] : ( ~ (subset(v0, all_39_4) = 0) | ~ $i(v0) | ? [v1: any] : % 11.43/2.39 | | ? [v2: any] : (in(v0, all_39_2) = v2 & finite(v0) = v1 & ( ~ (v1 = % 11.43/2.39 | | 0) | v2 = 0))) % 11.43/2.39 | | % 11.43/2.39 | | ALPHA: (27) implies: % 11.43/2.39 | | (28) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_39_4) = v1) | ~ % 11.43/2.39 | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, all_39_2) = v2 & % 11.43/2.39 | | finite(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 11.43/2.39 | | % 11.43/2.39 | | GROUND_INST: instantiating (28) with all_39_3, all_62_0, simplifying with % 11.43/2.39 | | (9), (26) gives: % 11.43/2.39 | | (29) ? [v0: any] : ? [v1: any] : (in(all_39_3, all_39_2) = v0 & % 11.43/2.39 | | finite(all_39_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_62_0 = 0))) % 11.43/2.39 | | % 11.43/2.39 | | DELTA: instantiating (29) with fresh symbols all_81_0, all_81_1 gives: % 11.43/2.39 | | (30) in(all_39_3, all_39_2) = all_81_1 & finite(all_39_3) = all_81_0 & ( % 11.43/2.39 | | ~ (all_81_1 = 0) | (all_81_0 = 0 & all_62_0 = 0)) % 11.43/2.39 | | % 11.43/2.39 | | ALPHA: (30) implies: % 11.43/2.39 | | (31) in(all_39_3, all_39_2) = all_81_1 % 11.43/2.39 | | (32) ~ (all_81_1 = 0) | (all_81_0 = 0 & all_62_0 = 0) % 11.43/2.39 | | % 11.43/2.39 | | BETA: splitting (32) gives: % 11.43/2.39 | | % 11.43/2.39 | | Case 1: % 11.43/2.39 | | | % 11.43/2.39 | | | (33) ~ (all_81_1 = 0) % 11.43/2.39 | | | % 11.43/2.39 | | | GROUND_INST: instantiating (t2_subset) with all_39_3, all_39_2, all_81_1, % 11.43/2.39 | | | simplifying with (9), (10), (31) gives: % 11.43/2.39 | | | (34) all_81_1 = 0 | ? [v0: any] : ? [v1: any] : (element(all_39_3, % 11.43/2.39 | | | all_39_2) = v0 & empty(all_39_2) = v1 & ( ~ (v0 = 0) | v1 = % 11.43/2.39 | | | 0)) % 11.43/2.39 | | | % 11.43/2.39 | | | BETA: splitting (34) gives: % 11.43/2.39 | | | % 11.43/2.39 | | | Case 1: % 11.43/2.39 | | | | % 11.43/2.39 | | | | (35) all_81_1 = 0 % 11.43/2.39 | | | | % 11.43/2.39 | | | | REDUCE: (33), (35) imply: % 11.43/2.39 | | | | (36) $false % 11.43/2.39 | | | | % 11.43/2.39 | | | | CLOSE: (36) is inconsistent. % 11.43/2.39 | | | | % 11.43/2.39 | | | Case 2: % 11.43/2.39 | | | | % 11.43/2.39 | | | | (37) ? [v0: any] : ? [v1: any] : (element(all_39_3, all_39_2) = v0 % 11.43/2.39 | | | | & empty(all_39_2) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 11.43/2.39 | | | | % 11.43/2.39 | | | | DELTA: instantiating (37) with fresh symbols all_138_0, all_138_1 gives: % 11.43/2.39 | | | | (38) element(all_39_3, all_39_2) = all_138_1 & empty(all_39_2) = % 11.43/2.39 | | | | all_138_0 & ( ~ (all_138_1 = 0) | all_138_0 = 0) % 11.43/2.39 | | | | % 11.43/2.39 | | | | ALPHA: (38) implies: % 11.43/2.39 | | | | (39) empty(all_39_2) = all_138_0 % 11.43/2.39 | | | | (40) element(all_39_3, all_39_2) = all_138_1 % 11.43/2.39 | | | | (41) ~ (all_138_1 = 0) | all_138_0 = 0 % 11.43/2.39 | | | | % 11.43/2.39 | | | | GROUND_INST: instantiating (4) with all_49_0, all_138_0, all_39_2, % 11.43/2.39 | | | | simplifying with (20), (39) gives: % 11.43/2.39 | | | | (42) all_138_0 = all_49_0 % 11.43/2.39 | | | | % 11.43/2.39 | | | | GROUND_INST: instantiating (5) with 0, all_138_1, all_39_2, all_39_3, % 11.43/2.39 | | | | simplifying with (11), (40) gives: % 11.43/2.39 | | | | (43) all_138_1 = 0 % 11.43/2.39 | | | | % 11.43/2.39 | | | | BETA: splitting (41) gives: % 11.43/2.39 | | | | % 11.43/2.39 | | | | Case 1: % 11.43/2.40 | | | | | % 11.43/2.40 | | | | | (44) ~ (all_138_1 = 0) % 11.43/2.40 | | | | | % 11.43/2.40 | | | | | REDUCE: (43), (44) imply: % 11.43/2.40 | | | | | (45) $false % 11.43/2.40 | | | | | % 11.43/2.40 | | | | | CLOSE: (45) is inconsistent. % 11.43/2.40 | | | | | % 11.43/2.40 | | | | Case 2: % 11.43/2.40 | | | | | % 11.43/2.40 | | | | | (46) all_138_0 = 0 % 11.43/2.40 | | | | | % 11.43/2.40 | | | | | COMBINE_EQS: (42), (46) imply: % 11.43/2.40 | | | | | (47) all_49_0 = 0 % 11.43/2.40 | | | | | % 11.43/2.40 | | | | | REDUCE: (19), (47) imply: % 11.43/2.40 | | | | | (48) $false % 11.43/2.40 | | | | | % 11.43/2.40 | | | | | CLOSE: (48) is inconsistent. % 11.43/2.40 | | | | | % 11.43/2.40 | | | | End of split % 11.43/2.40 | | | | % 11.43/2.40 | | | End of split % 11.43/2.40 | | | % 11.43/2.40 | | Case 2: % 11.43/2.40 | | | % 11.43/2.40 | | | (49) all_81_0 = 0 & all_62_0 = 0 % 11.43/2.40 | | | % 11.43/2.40 | | | ALPHA: (49) implies: % 11.43/2.40 | | | (50) all_62_0 = 0 % 11.43/2.40 | | | % 11.43/2.40 | | | REDUCE: (25), (50) imply: % 11.43/2.40 | | | (51) $false % 11.43/2.40 | | | % 11.43/2.40 | | | CLOSE: (51) is inconsistent. % 11.43/2.40 | | | % 11.43/2.40 | | End of split % 11.43/2.40 | | % 11.43/2.40 | End of split % 11.43/2.40 | % 11.43/2.40 End of proof % 11.43/2.40 % SZS output end Proof for theBenchmark % 11.43/2.40 % 11.43/2.40 1776ms %------------------------------------------------------------------------------