%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU113+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 : n026.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 17:42:33 EDT 2023 % Result : Theorem 10.11s 2.27s % Output : Proof 13.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU113+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n026.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 14:40:16 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 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 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 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 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 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 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 % 2.65/1.13 Prover 4: Preprocessing ... % 2.65/1.13 Prover 1: Preprocessing ... % 3.31/1.17 Prover 2: Preprocessing ... % 3.31/1.17 Prover 6: Preprocessing ... % 3.31/1.17 Prover 0: Preprocessing ... % 3.31/1.17 Prover 5: Preprocessing ... % 3.31/1.17 Prover 3: Preprocessing ... % 5.11/1.56 Prover 5: Proving ... % 6.30/1.59 Prover 2: Proving ... % 6.56/1.63 Prover 1: Warning: ignoring some quantifiers % 6.56/1.67 Prover 1: Constructing countermodel ... % 6.56/1.69 Prover 6: Proving ... % 6.56/1.70 Prover 3: Warning: ignoring some quantifiers % 7.11/1.71 Prover 3: Constructing countermodel ... % 7.11/1.74 Prover 4: Warning: ignoring some quantifiers % 7.11/1.76 Prover 0: Proving ... % 7.65/1.80 Prover 4: Constructing countermodel ... % 10.11/2.27 Prover 3: proved (1622ms) % 10.11/2.27 % 10.11/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.11/2.27 % 10.11/2.27 Prover 2: stopped % 10.11/2.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.11/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.11/2.27 Prover 6: stopped % 10.11/2.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.11/2.27 Prover 5: stopped % 10.11/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.11/2.28 Prover 0: stopped % 10.11/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.11/2.32 Prover 11: Preprocessing ... % 10.11/2.33 Prover 13: Preprocessing ... % 11.49/2.34 Prover 8: Preprocessing ... % 11.49/2.34 Prover 7: Preprocessing ... % 11.49/2.35 Prover 10: Preprocessing ... % 11.67/2.42 Prover 7: Warning: ignoring some quantifiers % 12.13/2.42 Prover 7: Constructing countermodel ... % 12.13/2.43 Prover 13: Warning: ignoring some quantifiers % 12.13/2.44 Prover 13: Constructing countermodel ... % 12.13/2.45 Prover 10: Warning: ignoring some quantifiers % 12.45/2.48 Prover 10: Constructing countermodel ... % 12.45/2.49 Prover 11: Warning: ignoring some quantifiers % 12.45/2.49 Prover 8: Warning: ignoring some quantifiers % 12.45/2.50 Prover 11: Constructing countermodel ... % 12.45/2.52 Prover 8: Constructing countermodel ... % 13.26/2.62 Prover 1: Found proof (size 49) % 13.26/2.62 Prover 1: proved (1979ms) % 13.26/2.63 Prover 13: stopped % 13.26/2.63 Prover 11: stopped % 13.26/2.63 Prover 8: stopped % 13.26/2.63 Prover 7: stopped % 13.26/2.63 Prover 10: stopped % 13.26/2.63 Prover 4: stopped % 13.26/2.63 % 13.26/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.26/2.63 % 13.26/2.63 % SZS output start Proof for theBenchmark % 13.71/2.63 Assumptions after simplification: % 13.71/2.63 --------------------------------- % 13.71/2.63 % 13.71/2.64 (d3_tarski) % 13.81/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 13.81/2.66 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 13.81/2.66 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.81/2.66 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 13.81/2.66 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 13.81/2.66 % 13.81/2.66 (d5_finsub_1) % 13.81/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v2) | ~ % 13.81/2.67 (preboolean(v1) = 0) | ~ $i(v1) | ~ $i(v0) | (( ~ (v2 = v1) | ( ! [v3: $i] % 13.81/2.67 : ! [v4: any] : ( ~ (subset(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] % 13.81/2.67 : ? [v6: any] : (finite(v3) = v6 & in(v3, v1) = v5 & ( ~ (v5 = 0) | % 13.81/2.67 (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (subset(v3, v0) = 0) | % 13.81/2.67 ~ $i(v3) | ? [v4: any] : ? [v5: any] : (finite(v3) = v4 & in(v3, % 13.81/2.67 v1) = v5 & ( ~ (v4 = 0) | v5 = 0))))) & (v2 = v1 | ? [v3: $i] : % 13.81/2.67 ? [v4: any] : ? [v5: any] : ? [v6: any] : (subset(v3, v0) = v5 & % 13.81/2.67 finite(v3) = v6 & in(v3, v1) = v4 & $i(v3) & ( ~ (v6 = 0) | ~ (v5 = % 13.81/2.67 0) | ~ (v4 = 0)) & (v4 = 0 | (v6 = 0 & v5 = 0)))))) % 13.81/2.67 % 13.81/2.67 (fc1_finsub_1) % 13.81/2.67 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | % 13.81/2.67 diff_closed(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | % 13.81/2.67 ~ $i(v0) | preboolean(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.81/2.67 (powerset(v0) = v1) | ~ $i(v0) | cup_closed(v1) = 0) & ! [v0: $i] : ! % 13.81/2.67 [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 13.81/2.67 empty(v1) = v2)) % 13.81/2.67 % 13.81/2.67 (fc2_finsub_1) % 13.81/2.67 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 13.81/2.67 diff_closed(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = % 13.81/2.67 v1) | ~ $i(v0) | preboolean(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.81/2.67 (finite_subsets(v0) = v1) | ~ $i(v0) | cup_closed(v1) = 0) & ! [v0: $i] : % 13.81/2.67 ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 13.81/2.67 (v2 = 0) & empty(v1) = v2)) % 13.81/2.67 % 13.81/2.67 (t26_finsub_1) % 13.81/2.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 13.81/2.67 subset(v1, v2) = v3 & finite_subsets(v0) = v1 & powerset(v0) = v2 & $i(v2) & % 13.81/2.67 $i(v1) & $i(v0)) % 13.81/2.67 % 13.81/2.67 (t2_subset) % 13.81/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 13.81/2.67 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 & % 13.81/2.67 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) % 13.81/2.67 % 13.81/2.67 (t3_subset) % 13.81/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.81/2.68 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 13.81/2.68 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 13.81/2.68 : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) % 13.81/2.68 | ~ $i(v0) | subset(v0, v1) = 0) % 13.81/2.68 % 13.81/2.68 (function-axioms) % 13.81/2.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.81/2.68 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 13.81/2.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.81/2.68 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 13.81/2.68 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.81/2.68 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 13.81/2.68 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.81/2.68 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 13.81/2.68 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 13.81/2.68 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 13.81/2.68 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 13.81/2.68 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.81/2.68 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 13.81/2.68 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.81/2.68 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 13.81/2.68 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~ % 13.81/2.68 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ % 13.81/2.68 (cap_closed(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 13.81/2.68 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0: $i] % 13.81/2.68 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 13.81/2.68 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ % 13.81/2.68 (diff_closed(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ % 13.81/2.68 (preboolean(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ % 13.81/2.68 (cup_closed(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.81/2.68 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~ % 13.81/2.68 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 13.81/2.68 : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 13.81/2.68 % 13.81/2.68 Further assumptions not needed in the proof: % 13.81/2.68 -------------------------------------------- % 13.81/2.68 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finset_1, cc2_finsub_1, % 13.81/2.68 cc3_finsub_1, dt_k5_finsub_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, % 13.81/2.68 rc1_finset_1, rc1_finsub_1, rc1_subset_1, rc1_xboole_0, rc2_finset_1, % 13.81/2.68 rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc4_finset_1, reflexivity_r1_tarski, % 13.81/2.68 t1_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 13.81/2.68 % 13.81/2.68 Those formulas are unsatisfiable: % 13.81/2.68 --------------------------------- % 13.81/2.68 % 13.81/2.68 Begin of proof % 13.81/2.69 | % 13.81/2.69 | ALPHA: (d3_tarski) implies: % 13.81/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 13.81/2.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 13.81/2.69 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 13.81/2.69 | % 13.81/2.69 | ALPHA: (fc1_finsub_1) implies: % 13.81/2.69 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? % 13.81/2.69 | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 13.81/2.69 | % 13.81/2.69 | ALPHA: (fc2_finsub_1) implies: % 13.81/2.69 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 13.81/2.69 | preboolean(v1) = 0) % 13.81/2.69 | % 13.81/2.69 | ALPHA: (t3_subset) implies: % 13.81/2.69 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.81/2.69 | (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ % 13.81/2.69 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 13.81/2.69 | % 13.81/2.69 | ALPHA: (function-axioms) implies: % 13.81/2.69 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.81/2.69 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 13.81/2.69 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.81/2.69 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 13.81/2.69 | % 13.81/2.69 | DELTA: instantiating (t26_finsub_1) with fresh symbols all_40_0, all_40_1, % 13.81/2.69 | all_40_2, all_40_3 gives: % 13.81/2.69 | (7) ~ (all_40_0 = 0) & subset(all_40_2, all_40_1) = all_40_0 & % 13.81/2.69 | finite_subsets(all_40_3) = all_40_2 & powerset(all_40_3) = all_40_1 & % 13.81/2.69 | $i(all_40_1) & $i(all_40_2) & $i(all_40_3) % 13.81/2.69 | % 13.81/2.69 | ALPHA: (7) implies: % 13.81/2.69 | (8) ~ (all_40_0 = 0) % 13.81/2.69 | (9) $i(all_40_3) % 13.81/2.69 | (10) $i(all_40_2) % 13.81/2.69 | (11) $i(all_40_1) % 13.81/2.69 | (12) powerset(all_40_3) = all_40_1 % 13.81/2.69 | (13) finite_subsets(all_40_3) = all_40_2 % 13.81/2.69 | (14) subset(all_40_2, all_40_1) = all_40_0 % 13.81/2.69 | % 13.81/2.69 | GROUND_INST: instantiating (2) with all_40_3, all_40_1, simplifying with (9), % 13.81/2.69 | (12) gives: % 13.81/2.69 | (15) ? [v0: int] : ( ~ (v0 = 0) & empty(all_40_1) = v0) % 13.81/2.69 | % 13.81/2.69 | GROUND_INST: instantiating (3) with all_40_3, all_40_2, simplifying with (9), % 13.81/2.69 | (13) gives: % 13.81/2.69 | (16) preboolean(all_40_2) = 0 % 13.81/2.69 | % 13.81/2.69 | GROUND_INST: instantiating (1) with all_40_2, all_40_1, all_40_0, simplifying % 13.81/2.69 | with (10), (11), (14) gives: % 13.81/2.70 | (17) all_40_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 13.81/2.70 | all_40_1) = v1 & in(v0, all_40_2) = 0 & $i(v0)) % 13.81/2.70 | % 13.81/2.70 | DELTA: instantiating (15) with fresh symbol all_48_0 gives: % 13.81/2.70 | (18) ~ (all_48_0 = 0) & empty(all_40_1) = all_48_0 % 13.81/2.70 | % 13.81/2.70 | ALPHA: (18) implies: % 13.81/2.70 | (19) ~ (all_48_0 = 0) % 13.81/2.70 | (20) empty(all_40_1) = all_48_0 % 13.81/2.70 | % 13.81/2.70 | BETA: splitting (17) gives: % 13.81/2.70 | % 13.81/2.70 | Case 1: % 13.81/2.70 | | % 13.81/2.70 | | (21) all_40_0 = 0 % 13.81/2.70 | | % 13.81/2.70 | | REDUCE: (8), (21) imply: % 13.81/2.70 | | (22) $false % 13.81/2.70 | | % 13.81/2.70 | | CLOSE: (22) is inconsistent. % 13.81/2.70 | | % 13.81/2.70 | Case 2: % 13.81/2.70 | | % 13.81/2.70 | | (23) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_40_1) = v1 & % 13.81/2.70 | | in(v0, all_40_2) = 0 & $i(v0)) % 13.81/2.70 | | % 13.81/2.70 | | DELTA: instantiating (23) with fresh symbols all_63_0, all_63_1 gives: % 13.81/2.70 | | (24) ~ (all_63_0 = 0) & in(all_63_1, all_40_1) = all_63_0 & in(all_63_1, % 13.81/2.70 | | all_40_2) = 0 & $i(all_63_1) % 13.81/2.70 | | % 13.81/2.70 | | ALPHA: (24) implies: % 13.81/2.70 | | (25) ~ (all_63_0 = 0) % 13.81/2.70 | | (26) $i(all_63_1) % 13.81/2.70 | | (27) in(all_63_1, all_40_2) = 0 % 13.81/2.70 | | (28) in(all_63_1, all_40_1) = all_63_0 % 13.81/2.70 | | % 13.81/2.70 | | GROUND_INST: instantiating (t2_subset) with all_63_1, all_40_1, all_63_0, % 13.81/2.70 | | simplifying with (11), (26), (28) gives: % 13.81/2.70 | | (29) all_63_0 = 0 | ? [v0: any] : ? [v1: any] : (element(all_63_1, % 13.81/2.70 | | all_40_1) = v0 & empty(all_40_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 13.81/2.70 | | % 13.81/2.70 | | GROUND_INST: instantiating (d5_finsub_1) with all_40_3, all_40_2, all_40_2, % 13.81/2.70 | | simplifying with (9), (10), (13), (16) gives: % 13.81/2.70 | | (30) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_40_3) = v1) | ~ % 13.81/2.70 | | $i(v0) | ? [v2: any] : ? [v3: any] : (finite(v0) = v3 & in(v0, % 13.81/2.70 | | all_40_2) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 13.81/2.70 | | $i] : ( ~ (subset(v0, all_40_3) = 0) | ~ $i(v0) | ? [v1: any] : % 13.81/2.70 | | ? [v2: any] : (finite(v0) = v1 & in(v0, all_40_2) = v2 & ( ~ (v1 = % 13.81/2.70 | | 0) | v2 = 0))) % 13.81/2.70 | | % 13.81/2.70 | | ALPHA: (30) implies: % 13.81/2.70 | | (31) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_40_3) = v1) | ~ % 13.81/2.70 | | $i(v0) | ? [v2: any] : ? [v3: any] : (finite(v0) = v3 & in(v0, % 13.81/2.70 | | all_40_2) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 13.81/2.70 | | % 13.81/2.70 | | BETA: splitting (29) gives: % 13.81/2.70 | | % 13.81/2.70 | | Case 1: % 13.81/2.70 | | | % 13.81/2.70 | | | (32) all_63_0 = 0 % 13.81/2.70 | | | % 13.81/2.70 | | | REDUCE: (25), (32) imply: % 13.81/2.70 | | | (33) $false % 13.81/2.70 | | | % 13.81/2.70 | | | CLOSE: (33) is inconsistent. % 13.81/2.70 | | | % 13.81/2.70 | | Case 2: % 13.81/2.70 | | | % 13.81/2.70 | | | (34) ? [v0: any] : ? [v1: any] : (element(all_63_1, all_40_1) = v0 & % 13.81/2.70 | | | empty(all_40_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 13.81/2.70 | | | % 13.81/2.70 | | | DELTA: instantiating (34) with fresh symbols all_97_0, all_97_1 gives: % 13.81/2.70 | | | (35) element(all_63_1, all_40_1) = all_97_1 & empty(all_40_1) = % 13.81/2.70 | | | all_97_0 & ( ~ (all_97_1 = 0) | all_97_0 = 0) % 13.81/2.70 | | | % 13.81/2.70 | | | ALPHA: (35) implies: % 13.81/2.70 | | | (36) empty(all_40_1) = all_97_0 % 13.81/2.70 | | | (37) element(all_63_1, all_40_1) = all_97_1 % 13.81/2.70 | | | (38) ~ (all_97_1 = 0) | all_97_0 = 0 % 13.81/2.70 | | | % 13.81/2.71 | | | GROUND_INST: instantiating (5) with all_48_0, all_97_0, all_40_1, % 13.81/2.71 | | | simplifying with (20), (36) gives: % 13.81/2.71 | | | (39) all_97_0 = all_48_0 % 13.81/2.71 | | | % 13.81/2.71 | | | BETA: splitting (38) gives: % 13.81/2.71 | | | % 13.81/2.71 | | | Case 1: % 13.81/2.71 | | | | % 13.81/2.71 | | | | (40) ~ (all_97_1 = 0) % 13.81/2.71 | | | | % 13.81/2.71 | | | | GROUND_INST: instantiating (4) with all_63_1, all_40_3, all_40_1, % 13.81/2.71 | | | | all_97_1, simplifying with (9), (12), (26), (37) gives: % 13.81/2.71 | | | | (41) all_97_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_63_1, % 13.81/2.71 | | | | all_40_3) = v0) % 13.81/2.71 | | | | % 13.81/2.71 | | | | BETA: splitting (41) gives: % 13.81/2.71 | | | | % 13.81/2.71 | | | | Case 1: % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | (42) all_97_1 = 0 % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | REDUCE: (40), (42) imply: % 13.81/2.71 | | | | | (43) $false % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | CLOSE: (43) is inconsistent. % 13.81/2.71 | | | | | % 13.81/2.71 | | | | Case 2: % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & subset(all_63_1, all_40_3) = v0) % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | DELTA: instantiating (44) with fresh symbol all_137_0 gives: % 13.81/2.71 | | | | | (45) ~ (all_137_0 = 0) & subset(all_63_1, all_40_3) = all_137_0 % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | ALPHA: (45) implies: % 13.81/2.71 | | | | | (46) ~ (all_137_0 = 0) % 13.81/2.71 | | | | | (47) subset(all_63_1, all_40_3) = all_137_0 % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | GROUND_INST: instantiating (31) with all_63_1, all_137_0, simplifying % 13.81/2.71 | | | | | with (26), (47) gives: % 13.81/2.71 | | | | | (48) ? [v0: any] : ? [v1: any] : (finite(all_63_1) = v1 & % 13.81/2.71 | | | | | in(all_63_1, all_40_2) = v0 & ( ~ (v0 = 0) | (v1 = 0 & % 13.81/2.71 | | | | | all_137_0 = 0))) % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | DELTA: instantiating (48) with fresh symbols all_176_0, all_176_1 % 13.81/2.71 | | | | | gives: % 13.81/2.71 | | | | | (49) finite(all_63_1) = all_176_0 & in(all_63_1, all_40_2) = % 13.81/2.71 | | | | | all_176_1 & ( ~ (all_176_1 = 0) | (all_176_0 = 0 & all_137_0 = % 13.81/2.71 | | | | | 0)) % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | ALPHA: (49) implies: % 13.81/2.71 | | | | | (50) in(all_63_1, all_40_2) = all_176_1 % 13.81/2.71 | | | | | (51) ~ (all_176_1 = 0) | (all_176_0 = 0 & all_137_0 = 0) % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | BETA: splitting (51) gives: % 13.81/2.71 | | | | | % 13.81/2.71 | | | | | Case 1: % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | (52) ~ (all_176_1 = 0) % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | GROUND_INST: instantiating (6) with 0, all_176_1, all_40_2, % 13.81/2.71 | | | | | | all_63_1, simplifying with (27), (50) gives: % 13.81/2.71 | | | | | | (53) all_176_1 = 0 % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | REDUCE: (52), (53) imply: % 13.81/2.71 | | | | | | (54) $false % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | CLOSE: (54) is inconsistent. % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | Case 2: % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | (55) all_176_0 = 0 & all_137_0 = 0 % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | ALPHA: (55) implies: % 13.81/2.71 | | | | | | (56) all_137_0 = 0 % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | REDUCE: (46), (56) imply: % 13.81/2.71 | | | | | | (57) $false % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | | CLOSE: (57) is inconsistent. % 13.81/2.71 | | | | | | % 13.81/2.71 | | | | | End of split % 13.81/2.71 | | | | | % 13.81/2.71 | | | | End of split % 13.81/2.71 | | | | % 13.81/2.71 | | | Case 2: % 13.81/2.71 | | | | % 13.81/2.71 | | | | (58) all_97_0 = 0 % 13.81/2.71 | | | | % 13.81/2.71 | | | | COMBINE_EQS: (39), (58) imply: % 13.81/2.71 | | | | (59) all_48_0 = 0 % 13.81/2.71 | | | | % 13.81/2.71 | | | | REDUCE: (19), (59) imply: % 13.81/2.71 | | | | (60) $false % 13.81/2.71 | | | | % 13.81/2.71 | | | | CLOSE: (60) is inconsistent. % 13.81/2.71 | | | | % 13.81/2.71 | | | End of split % 13.81/2.71 | | | % 13.81/2.71 | | End of split % 13.81/2.71 | | % 13.81/2.71 | End of split % 13.81/2.71 | % 13.81/2.71 End of proof % 13.81/2.71 % SZS output end Proof for theBenchmark % 13.81/2.71 % 13.81/2.71 2087ms %------------------------------------------------------------------------------