%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU319+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 : n025.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 17:44:03 EDT 2023 % Result : Theorem 11.88s 2.43s % Output : Proof 13.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU319+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 : n025.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 : Thu Aug 24 00:33:51 EDT 2023 % 0.13/0.35 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.33/1.01 Prover 1: Preprocessing ... % 2.33/1.01 Prover 4: Preprocessing ... % 2.33/1.05 Prover 3: Preprocessing ... % 2.33/1.05 Prover 0: Preprocessing ... % 2.33/1.05 Prover 2: Preprocessing ... % 2.33/1.05 Prover 6: Preprocessing ... % 2.33/1.05 Prover 5: Preprocessing ... % 4.90/1.37 Prover 3: Warning: ignoring some quantifiers % 4.90/1.37 Prover 1: Warning: ignoring some quantifiers % 4.90/1.41 Prover 3: Constructing countermodel ... % 4.90/1.41 Prover 1: Constructing countermodel ... % 4.90/1.42 Prover 6: Proving ... % 4.90/1.43 Prover 5: Proving ... % 4.90/1.48 Prover 2: Proving ... % 5.22/1.50 Prover 4: Warning: ignoring some quantifiers % 5.22/1.52 Prover 4: Constructing countermodel ... % 6.58/1.64 Prover 0: Proving ... % 7.69/1.80 Prover 3: gave up % 7.69/1.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.22/1.86 Prover 7: Preprocessing ... % 9.07/1.98 Prover 7: Warning: ignoring some quantifiers % 9.07/1.99 Prover 1: gave up % 9.07/1.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.07/1.99 Prover 7: Constructing countermodel ... % 9.07/2.01 Prover 8: Preprocessing ... % 9.07/2.12 Prover 8: Warning: ignoring some quantifiers % 9.07/2.13 Prover 8: Constructing countermodel ... % 11.88/2.43 Prover 2: proved (1798ms) % 11.88/2.43 % 11.88/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.88/2.43 % 11.88/2.43 Prover 5: stopped % 11.88/2.44 Prover 6: stopped % 11.88/2.44 Prover 0: stopped % 12.53/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.53/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.53/2.44 Prover 8: gave up % 12.53/2.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.53/2.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.53/2.47 Prover 11: Preprocessing ... % 12.53/2.47 Prover 10: Preprocessing ... % 12.53/2.47 Prover 16: Preprocessing ... % 12.53/2.48 Prover 13: Preprocessing ... % 12.53/2.48 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.85/2.49 Prover 10: Warning: ignoring some quantifiers % 12.85/2.50 Prover 19: Preprocessing ... % 12.85/2.51 Prover 16: Warning: ignoring some quantifiers % 12.85/2.51 Prover 10: Constructing countermodel ... % 12.85/2.51 Prover 16: Constructing countermodel ... % 12.85/2.54 Prover 13: Warning: ignoring some quantifiers % 13.28/2.54 Prover 13: Constructing countermodel ... % 13.28/2.55 Prover 7: Found proof (size 58) % 13.28/2.55 Prover 7: proved (737ms) % 13.28/2.55 Prover 13: stopped % 13.28/2.55 Prover 4: stopped % 13.28/2.55 Prover 10: stopped % 13.39/2.55 Prover 16: stopped % 13.39/2.58 Prover 19: Warning: ignoring some quantifiers % 13.39/2.58 Prover 19: Constructing countermodel ... % 13.39/2.59 Prover 19: stopped % 13.39/2.60 Prover 11: Warning: ignoring some quantifiers % 13.39/2.61 Prover 11: Constructing countermodel ... % 13.70/2.61 Prover 11: stopped % 13.70/2.61 % 13.70/2.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.70/2.62 % 13.70/2.62 % SZS output start Proof for theBenchmark % 13.70/2.62 Assumptions after simplification: % 13.70/2.62 --------------------------------- % 13.70/2.62 % 13.70/2.62 (d6_pre_topc) % 13.70/2.65 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 13.70/2.65 | ~ top_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 & % 13.70/2.65 powerset(v2) = v3 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ % 13.70/2.65 (subset_difference(v2, v1, v4) = v5) | ~ $i(v4) | ~ open_subset(v5, % 13.70/2.65 v0) | ~ element(v4, v3) | closed_subset(v4, v0)) & ! [v4: $i] : ! % 13.70/2.65 [v5: $i] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ $i(v4) | ~ % 13.70/2.65 closed_subset(v4, v0) | ~ element(v4, v3) | open_subset(v5, v0)))) & ! % 13.70/2.65 [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 13.70/2.65 top_str(v0) | ? [v2: $i] : ? [v3: $i] : (cast_as_carrier_subset(v0) = v3 & % 13.70/2.65 powerset(v1) = v2 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ % 13.70/2.65 (subset_difference(v1, v3, v4) = v5) | ~ $i(v4) | ~ open_subset(v5, % 13.70/2.65 v0) | ~ element(v4, v2) | closed_subset(v4, v0)) & ! [v4: $i] : ! % 13.70/2.65 [v5: $i] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ $i(v4) | ~ % 13.70/2.65 closed_subset(v4, v0) | ~ element(v4, v2) | open_subset(v5, v0)))) % 13.70/2.65 % 13.70/2.65 (dt_k2_pre_topc) % 13.70/2.66 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 13.70/2.66 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 13.70/2.66 & powerset(v2) = v3 & $i(v3) & $i(v2) & element(v1, v3))) & ! [v0: $i] : % 13.70/2.66 ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ one_sorted_str(v0) | % 13.70/2.66 ? [v2: $i] : ? [v3: $i] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = % 13.70/2.66 v3 & $i(v3) & $i(v2) & element(v2, v3))) % 13.70/2.66 % 13.70/2.66 (dt_k3_subset_1) % 13.70/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 13.70/2.66 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~ % 13.70/2.66 element(v1, v3) | element(v2, v3)))) % 13.70/2.66 % 13.70/2.66 (dt_l1_pre_topc) % 13.70/2.66 ! [v0: $i] : ( ~ $i(v0) | ~ top_str(v0) | one_sorted_str(v0)) % 13.70/2.66 % 13.70/2.66 (t17_pre_topc) % 13.70/2.66 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 13.70/2.66 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 13.70/2.66 & powerset(v2) = v3 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ % 13.70/2.66 (subset_complement(v2, v4) = v5) | ~ $i(v4) | ~ element(v4, v3) | % 13.70/2.66 (subset_difference(v2, v1, v4) = v5 & $i(v5))) & ! [v4: $i] : ! [v5: % 13.70/2.66 $i] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ $i(v4) | ~ % 13.70/2.66 element(v4, v3) | (subset_complement(v2, v4) = v5 & $i(v5))))) & ! [v0: % 13.70/2.66 $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 13.70/2.66 one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (cast_as_carrier_subset(v0) % 13.70/2.66 = v3 & powerset(v1) = v2 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ( % 13.70/2.66 ~ (subset_complement(v1, v4) = v5) | ~ $i(v4) | ~ element(v4, v2) | % 13.70/2.66 (subset_difference(v1, v3, v4) = v5 & $i(v5))) & ! [v4: $i] : ! [v5: % 13.70/2.66 $i] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ $i(v4) | ~ % 13.70/2.66 element(v4, v2) | (subset_complement(v1, v4) = v5 & $i(v5))))) % 13.70/2.66 % 13.70/2.66 (t29_tops_1) % 13.70/2.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 13.70/2.67 (subset_complement(v1, v3) = v4 & the_carrier(v0) = v1 & powerset(v1) = v2 & % 13.70/2.67 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & element(v3, v2) & top_str(v0) & % 13.70/2.67 ((open_subset(v4, v0) & ~ closed_subset(v3, v0)) | (closed_subset(v3, v0) & % 13.70/2.67 ~ open_subset(v4, v0)))) % 13.70/2.67 % 13.70/2.67 (function-axioms) % 13.70/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 13.70/2.67 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 13.70/2.67 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 13.70/2.67 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 13.70/2.67 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.70/2.67 (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! % 13.70/2.67 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.70/2.67 (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) & % 13.70/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) % 13.70/2.67 | ~ (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 13.70/2.67 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 13.70/2.67 % 13.70/2.67 Further assumptions not needed in the proof: % 13.70/2.67 -------------------------------------------- % 13.70/2.67 dt_k1_zfmisc_1, dt_k4_xboole_0, dt_k6_subset_1, dt_l1_struct_0, dt_m1_subset_1, % 13.70/2.67 dt_u1_struct_0, existence_l1_pre_topc, existence_l1_struct_0, % 13.70/2.67 existence_m1_subset_1, involutiveness_k3_subset_1, redefinition_k6_subset_1, % 13.70/2.67 reflexivity_r1_tarski, t3_subset % 13.70/2.67 % 13.70/2.67 Those formulas are unsatisfiable: % 13.70/2.67 --------------------------------- % 13.70/2.67 % 13.70/2.67 Begin of proof % 13.70/2.67 | % 13.70/2.67 | ALPHA: (d6_pre_topc) implies: % 13.70/2.67 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 13.70/2.67 | top_str(v0) | ? [v2: $i] : ? [v3: $i] : (cast_as_carrier_subset(v0) % 13.70/2.67 | = v3 & powerset(v1) = v2 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: % 13.70/2.67 | $i] : ( ~ (subset_difference(v1, v3, v4) = v5) | ~ $i(v4) | ~ % 13.70/2.67 | open_subset(v5, v0) | ~ element(v4, v2) | closed_subset(v4, v0)) % 13.70/2.67 | & ! [v4: $i] : ! [v5: $i] : ( ~ (subset_difference(v1, v3, v4) = % 13.70/2.67 | v5) | ~ $i(v4) | ~ closed_subset(v4, v0) | ~ element(v4, v2) % 13.70/2.67 | | open_subset(v5, v0)))) % 13.70/2.67 | % 13.70/2.67 | ALPHA: (dt_k2_pre_topc) implies: % 13.70/2.67 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 13.70/2.67 | one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : % 13.70/2.67 | (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & $i(v3) & % 13.70/2.67 | $i(v2) & element(v2, v3))) % 13.70/2.67 | % 13.70/2.67 | ALPHA: (t17_pre_topc) implies: % 13.70/2.67 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 13.70/2.67 | one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : % 13.70/2.67 | (cast_as_carrier_subset(v0) = v3 & powerset(v1) = v2 & $i(v3) & % 13.70/2.67 | $i(v2) & ! [v4: $i] : ! [v5: $i] : ( ~ (subset_complement(v1, v4) % 13.70/2.67 | = v5) | ~ $i(v4) | ~ element(v4, v2) | (subset_difference(v1, % 13.70/2.67 | v3, v4) = v5 & $i(v5))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 13.70/2.67 | (subset_difference(v1, v3, v4) = v5) | ~ $i(v4) | ~ element(v4, % 13.70/2.67 | v2) | (subset_complement(v1, v4) = v5 & $i(v5))))) % 13.70/2.68 | % 13.70/2.68 | ALPHA: (function-axioms) implies: % 13.70/2.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 13.70/2.68 | v1) | ~ (powerset(v2) = v0)) % 13.70/2.68 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.70/2.68 | (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = % 13.70/2.68 | v0)) % 13.70/2.68 | % 13.70/2.68 | DELTA: instantiating (t29_tops_1) with fresh symbols all_18_0, all_18_1, % 13.70/2.68 | all_18_2, all_18_3, all_18_4 gives: % 13.70/2.68 | (6) subset_complement(all_18_3, all_18_1) = all_18_0 & % 13.70/2.68 | the_carrier(all_18_4) = all_18_3 & powerset(all_18_3) = all_18_2 & % 13.70/2.68 | $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & $i(all_18_3) & % 13.70/2.68 | $i(all_18_4) & element(all_18_1, all_18_2) & top_str(all_18_4) & % 13.70/2.68 | ((open_subset(all_18_0, all_18_4) & ~ closed_subset(all_18_1, % 13.70/2.68 | all_18_4)) | (closed_subset(all_18_1, all_18_4) & ~ % 13.70/2.68 | open_subset(all_18_0, all_18_4))) % 13.70/2.68 | % 13.70/2.68 | ALPHA: (6) implies: % 13.70/2.68 | (7) top_str(all_18_4) % 13.70/2.68 | (8) element(all_18_1, all_18_2) % 13.70/2.68 | (9) $i(all_18_4) % 13.70/2.68 | (10) $i(all_18_3) % 13.70/2.68 | (11) $i(all_18_1) % 13.70/2.68 | (12) powerset(all_18_3) = all_18_2 % 13.70/2.68 | (13) the_carrier(all_18_4) = all_18_3 % 13.70/2.68 | (14) subset_complement(all_18_3, all_18_1) = all_18_0 % 13.70/2.68 | (15) (open_subset(all_18_0, all_18_4) & ~ closed_subset(all_18_1, % 13.70/2.68 | all_18_4)) | (closed_subset(all_18_1, all_18_4) & ~ % 13.70/2.68 | open_subset(all_18_0, all_18_4)) % 13.70/2.68 | % 13.70/2.68 | GROUND_INST: instantiating (dt_l1_pre_topc) with all_18_4, simplifying with % 13.70/2.68 | (7), (9) gives: % 13.70/2.68 | (16) one_sorted_str(all_18_4) % 13.70/2.68 | % 13.70/2.68 | GROUND_INST: instantiating (1) with all_18_4, all_18_3, simplifying with (7), % 13.70/2.68 | (9), (13) gives: % 13.70/2.68 | (17) ? [v0: $i] : ? [v1: $i] : (cast_as_carrier_subset(all_18_4) = v1 & % 13.70/2.68 | powerset(all_18_3) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 13.70/2.68 | $i] : ( ~ (subset_difference(all_18_3, v1, v2) = v3) | ~ $i(v2) | % 13.70/2.68 | ~ open_subset(v3, all_18_4) | ~ element(v2, v0) | % 13.70/2.68 | closed_subset(v2, all_18_4)) & ! [v2: $i] : ! [v3: $i] : ( ~ % 13.70/2.68 | (subset_difference(all_18_3, v1, v2) = v3) | ~ $i(v2) | ~ % 13.70/2.68 | closed_subset(v2, all_18_4) | ~ element(v2, v0) | open_subset(v3, % 13.70/2.68 | all_18_4))) % 13.70/2.68 | % 13.70/2.68 | GROUND_INST: instantiating (dt_k3_subset_1) with all_18_3, all_18_1, all_18_0, % 13.70/2.68 | simplifying with (10), (11), (14) gives: % 13.70/2.68 | (18) ? [v0: $i] : (powerset(all_18_3) = v0 & $i(v0) & ( ~ % 13.70/2.68 | element(all_18_1, v0) | element(all_18_0, v0))) % 13.70/2.68 | % 13.70/2.68 | DELTA: instantiating (18) with fresh symbol all_26_0 gives: % 13.70/2.68 | (19) powerset(all_18_3) = all_26_0 & $i(all_26_0) & ( ~ element(all_18_1, % 13.70/2.68 | all_26_0) | element(all_18_0, all_26_0)) % 13.70/2.68 | % 13.70/2.68 | ALPHA: (19) implies: % 13.70/2.68 | (20) powerset(all_18_3) = all_26_0 % 13.70/2.68 | (21) ~ element(all_18_1, all_26_0) | element(all_18_0, all_26_0) % 13.70/2.68 | % 13.70/2.68 | DELTA: instantiating (17) with fresh symbols all_29_0, all_29_1 gives: % 13.70/2.68 | (22) cast_as_carrier_subset(all_18_4) = all_29_0 & powerset(all_18_3) = % 13.70/2.69 | all_29_1 & $i(all_29_0) & $i(all_29_1) & ! [v0: $i] : ! [v1: $i] : ( % 13.70/2.69 | ~ (subset_difference(all_18_3, all_29_0, v0) = v1) | ~ $i(v0) | ~ % 13.70/2.69 | open_subset(v1, all_18_4) | ~ element(v0, all_29_1) | % 13.70/2.69 | closed_subset(v0, all_18_4)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.70/2.69 | (subset_difference(all_18_3, all_29_0, v0) = v1) | ~ $i(v0) | ~ % 13.70/2.69 | closed_subset(v0, all_18_4) | ~ element(v0, all_29_1) | % 13.70/2.69 | open_subset(v1, all_18_4)) % 13.70/2.69 | % 13.70/2.69 | ALPHA: (22) implies: % 13.70/2.69 | (23) powerset(all_18_3) = all_29_1 % 13.70/2.69 | (24) cast_as_carrier_subset(all_18_4) = all_29_0 % 13.70/2.69 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (subset_difference(all_18_3, all_29_0, % 13.70/2.69 | v0) = v1) | ~ $i(v0) | ~ closed_subset(v0, all_18_4) | ~ % 13.70/2.69 | element(v0, all_29_1) | open_subset(v1, all_18_4)) % 13.70/2.69 | (26) ! [v0: $i] : ! [v1: $i] : ( ~ (subset_difference(all_18_3, all_29_0, % 13.70/2.69 | v0) = v1) | ~ $i(v0) | ~ open_subset(v1, all_18_4) | ~ % 13.70/2.69 | element(v0, all_29_1) | closed_subset(v0, all_18_4)) % 13.70/2.69 | % 13.70/2.69 | GROUND_INST: instantiating (4) with all_18_2, all_29_1, all_18_3, simplifying % 13.70/2.69 | with (12), (23) gives: % 13.70/2.69 | (27) all_29_1 = all_18_2 % 13.70/2.69 | % 13.70/2.69 | GROUND_INST: instantiating (4) with all_26_0, all_29_1, all_18_3, simplifying % 13.70/2.69 | with (20), (23) gives: % 13.70/2.69 | (28) all_29_1 = all_26_0 % 13.70/2.69 | % 13.70/2.69 | COMBINE_EQS: (27), (28) imply: % 13.70/2.69 | (29) all_26_0 = all_18_2 % 13.70/2.69 | % 13.70/2.69 | BETA: splitting (21) gives: % 13.70/2.69 | % 13.70/2.69 | Case 1: % 13.70/2.69 | | % 13.70/2.69 | | (30) ~ element(all_18_1, all_26_0) % 13.70/2.69 | | % 13.70/2.69 | | REDUCE: (29), (30) imply: % 13.70/2.69 | | (31) ~ element(all_18_1, all_18_2) % 13.70/2.69 | | % 13.70/2.69 | | PRED_UNIFY: (8), (31) imply: % 13.70/2.69 | | (32) $false % 13.70/2.69 | | % 13.70/2.69 | | CLOSE: (32) is inconsistent. % 13.70/2.69 | | % 13.70/2.69 | Case 2: % 13.70/2.69 | | % 13.70/2.69 | | (33) element(all_18_1, all_26_0) % 13.70/2.69 | | % 13.70/2.69 | | GROUND_INST: instantiating (3) with all_18_4, all_18_3, simplifying with % 13.70/2.69 | | (9), (13), (16) gives: % 13.70/2.69 | | (34) ? [v0: $i] : ? [v1: $i] : (cast_as_carrier_subset(all_18_4) = v1 & % 13.70/2.69 | | powerset(all_18_3) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 13.70/2.69 | | $i] : ( ~ (subset_complement(all_18_3, v2) = v3) | ~ $i(v2) | % 13.70/2.69 | | ~ element(v2, v0) | (subset_difference(all_18_3, v1, v2) = v3 & % 13.70/2.69 | | $i(v3))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 13.70/2.69 | | (subset_difference(all_18_3, v1, v2) = v3) | ~ $i(v2) | ~ % 13.70/2.69 | | element(v2, v0) | (subset_complement(all_18_3, v2) = v3 & % 13.70/2.69 | | $i(v3)))) % 13.70/2.69 | | % 13.70/2.69 | | GROUND_INST: instantiating (2) with all_18_4, all_18_3, simplifying with % 13.70/2.69 | | (9), (13), (16) gives: % 13.70/2.69 | | (35) ? [v0: $i] : ? [v1: $i] : (cast_as_carrier_subset(all_18_4) = v0 & % 13.70/2.69 | | powerset(all_18_3) = v1 & $i(v1) & $i(v0) & element(v0, v1)) % 13.70/2.69 | | % 13.70/2.69 | | DELTA: instantiating (35) with fresh symbols all_52_0, all_52_1 gives: % 13.70/2.69 | | (36) cast_as_carrier_subset(all_18_4) = all_52_1 & powerset(all_18_3) = % 13.70/2.69 | | all_52_0 & $i(all_52_0) & $i(all_52_1) & element(all_52_1, all_52_0) % 13.70/2.69 | | % 13.70/2.69 | | ALPHA: (36) implies: % 13.70/2.69 | | (37) powerset(all_18_3) = all_52_0 % 13.70/2.69 | | (38) cast_as_carrier_subset(all_18_4) = all_52_1 % 13.70/2.69 | | % 13.70/2.69 | | DELTA: instantiating (34) with fresh symbols all_54_0, all_54_1 gives: % 13.70/2.69 | | (39) cast_as_carrier_subset(all_18_4) = all_54_0 & powerset(all_18_3) = % 13.70/2.69 | | all_54_1 & $i(all_54_0) & $i(all_54_1) & ! [v0: $i] : ! [v1: $i] : % 13.70/2.69 | | ( ~ (subset_complement(all_18_3, v0) = v1) | ~ $i(v0) | ~ % 13.70/2.69 | | element(v0, all_54_1) | (subset_difference(all_18_3, all_54_0, v0) % 13.70/2.69 | | = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.70/2.69 | | (subset_difference(all_18_3, all_54_0, v0) = v1) | ~ $i(v0) | ~ % 13.70/2.69 | | element(v0, all_54_1) | (subset_complement(all_18_3, v0) = v1 & % 13.70/2.69 | | $i(v1))) % 13.70/2.69 | | % 13.70/2.70 | | ALPHA: (39) implies: % 13.70/2.70 | | (40) powerset(all_18_3) = all_54_1 % 13.70/2.70 | | (41) cast_as_carrier_subset(all_18_4) = all_54_0 % 13.70/2.70 | | (42) ! [v0: $i] : ! [v1: $i] : ( ~ (subset_complement(all_18_3, v0) = % 13.70/2.70 | | v1) | ~ $i(v0) | ~ element(v0, all_54_1) | % 13.70/2.70 | | (subset_difference(all_18_3, all_54_0, v0) = v1 & $i(v1))) % 13.70/2.70 | | % 13.70/2.70 | | GROUND_INST: instantiating (42) with all_18_1, all_18_0, simplifying with % 13.70/2.70 | | (11), (14) gives: % 13.70/2.70 | | (43) ~ element(all_18_1, all_54_1) | (subset_difference(all_18_3, % 13.70/2.70 | | all_54_0, all_18_1) = all_18_0 & $i(all_18_0)) % 13.70/2.70 | | % 13.70/2.70 | | GROUND_INST: instantiating (4) with all_18_2, all_54_1, all_18_3, % 13.70/2.70 | | simplifying with (12), (40) gives: % 13.70/2.70 | | (44) all_54_1 = all_18_2 % 13.70/2.70 | | % 13.70/2.70 | | GROUND_INST: instantiating (4) with all_52_0, all_54_1, all_18_3, % 13.70/2.70 | | simplifying with (37), (40) gives: % 13.70/2.70 | | (45) all_54_1 = all_52_0 % 13.70/2.70 | | % 13.70/2.70 | | GROUND_INST: instantiating (5) with all_29_0, all_54_0, all_18_4, % 13.70/2.70 | | simplifying with (24), (41) gives: % 13.70/2.70 | | (46) all_54_0 = all_29_0 % 13.70/2.70 | | % 13.70/2.70 | | GROUND_INST: instantiating (5) with all_52_1, all_54_0, all_18_4, % 13.70/2.70 | | simplifying with (38), (41) gives: % 13.70/2.70 | | (47) all_54_0 = all_52_1 % 13.70/2.70 | | % 13.70/2.70 | | COMBINE_EQS: (46), (47) imply: % 13.70/2.70 | | (48) all_52_1 = all_29_0 % 13.70/2.70 | | % 13.70/2.70 | | COMBINE_EQS: (44), (45) imply: % 13.70/2.70 | | (49) all_52_0 = all_18_2 % 13.70/2.70 | | % 13.70/2.70 | | BETA: splitting (43) gives: % 13.70/2.70 | | % 13.70/2.70 | | Case 1: % 13.70/2.70 | | | % 13.70/2.70 | | | (50) ~ element(all_18_1, all_54_1) % 13.70/2.70 | | | % 13.70/2.70 | | | REDUCE: (44), (50) imply: % 13.70/2.70 | | | (51) ~ element(all_18_1, all_18_2) % 13.70/2.70 | | | % 13.70/2.70 | | | PRED_UNIFY: (8), (51) imply: % 13.70/2.70 | | | (52) $false % 13.70/2.70 | | | % 13.70/2.70 | | | CLOSE: (52) is inconsistent. % 13.70/2.70 | | | % 13.70/2.70 | | Case 2: % 13.70/2.70 | | | % 13.70/2.70 | | | (53) element(all_18_1, all_54_1) % 13.70/2.70 | | | (54) subset_difference(all_18_3, all_54_0, all_18_1) = all_18_0 & % 13.70/2.70 | | | $i(all_18_0) % 13.70/2.70 | | | % 13.70/2.70 | | | ALPHA: (54) implies: % 13.70/2.70 | | | (55) subset_difference(all_18_3, all_54_0, all_18_1) = all_18_0 % 13.70/2.70 | | | % 13.70/2.70 | | | REDUCE: (46), (55) imply: % 13.70/2.70 | | | (56) subset_difference(all_18_3, all_29_0, all_18_1) = all_18_0 % 13.70/2.70 | | | % 13.70/2.70 | | | BETA: splitting (15) gives: % 13.70/2.70 | | | % 13.70/2.70 | | | Case 1: % 13.70/2.70 | | | | % 13.70/2.70 | | | | (57) open_subset(all_18_0, all_18_4) & ~ closed_subset(all_18_1, % 13.70/2.70 | | | | all_18_4) % 13.70/2.70 | | | | % 13.70/2.70 | | | | ALPHA: (57) implies: % 13.70/2.70 | | | | (58) ~ closed_subset(all_18_1, all_18_4) % 13.70/2.70 | | | | (59) open_subset(all_18_0, all_18_4) % 13.70/2.70 | | | | % 13.70/2.70 | | | | GROUND_INST: instantiating (26) with all_18_1, all_18_0, simplifying % 13.70/2.70 | | | | with (11), (56), (58), (59) gives: % 13.70/2.70 | | | | (60) ~ element(all_18_1, all_29_1) % 13.70/2.70 | | | | % 13.70/2.70 | | | | REDUCE: (27), (60) imply: % 13.70/2.70 | | | | (61) ~ element(all_18_1, all_18_2) % 13.70/2.70 | | | | % 13.70/2.70 | | | | PRED_UNIFY: (8), (61) imply: % 13.70/2.70 | | | | (62) $false % 13.70/2.70 | | | | % 13.70/2.70 | | | | CLOSE: (62) is inconsistent. % 13.70/2.70 | | | | % 13.70/2.70 | | | Case 2: % 13.70/2.70 | | | | % 13.70/2.70 | | | | (63) closed_subset(all_18_1, all_18_4) & ~ open_subset(all_18_0, % 13.70/2.70 | | | | all_18_4) % 13.70/2.70 | | | | % 13.70/2.70 | | | | ALPHA: (63) implies: % 13.70/2.70 | | | | (64) ~ open_subset(all_18_0, all_18_4) % 13.70/2.70 | | | | (65) closed_subset(all_18_1, all_18_4) % 13.70/2.70 | | | | % 13.70/2.70 | | | | GROUND_INST: instantiating (25) with all_18_1, all_18_0, simplifying % 13.70/2.70 | | | | with (11), (56), (64), (65) gives: % 13.70/2.70 | | | | (66) ~ element(all_18_1, all_29_1) % 13.70/2.70 | | | | % 13.70/2.70 | | | | REDUCE: (27), (66) imply: % 13.70/2.70 | | | | (67) ~ element(all_18_1, all_18_2) % 13.70/2.70 | | | | % 13.70/2.70 | | | | PRED_UNIFY: (8), (67) imply: % 13.70/2.70 | | | | (68) $false % 13.70/2.70 | | | | % 13.70/2.70 | | | | CLOSE: (68) is inconsistent. % 13.70/2.70 | | | | % 13.70/2.70 | | | End of split % 13.70/2.70 | | | % 13.70/2.70 | | End of split % 13.70/2.70 | | % 13.70/2.70 | End of split % 13.70/2.70 | % 13.70/2.70 End of proof % 13.70/2.70 % SZS output end Proof for theBenchmark % 13.70/2.71 % 13.70/2.71 2094ms %------------------------------------------------------------------------------