%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU356+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 : n005.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 17:44:16 EDT 2023 % Result : Theorem 8.36s 2.00s % Output : Proof 10.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU356+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Aug 23 13:27:38 EDT 2023 % 0.13/0.35 % 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 ... % 0.21/0.63 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 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 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 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 % 2.29/1.02 Prover 1: Preprocessing ... % 2.29/1.02 Prover 4: Preprocessing ... % 2.29/1.07 Prover 3: Preprocessing ... % 2.29/1.07 Prover 6: Preprocessing ... % 2.29/1.07 Prover 0: Preprocessing ... % 2.29/1.07 Prover 2: Preprocessing ... % 2.29/1.07 Prover 5: Preprocessing ... % 3.64/1.39 Prover 2: Proving ... % 3.64/1.40 Prover 5: Proving ... % 4.72/1.45 Prover 3: Warning: ignoring some quantifiers % 4.72/1.45 Prover 6: Proving ... % 4.72/1.47 Prover 3: Constructing countermodel ... % 4.72/1.48 Prover 1: Warning: ignoring some quantifiers % 4.72/1.49 Prover 1: Constructing countermodel ... % 6.60/1.73 Prover 4: Warning: ignoring some quantifiers % 6.60/1.74 Prover 0: Proving ... % 6.60/1.75 Prover 4: Constructing countermodel ... % 8.36/2.00 Prover 2: proved (1358ms) % 8.36/2.00 % 8.36/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.36/2.00 % 8.36/2.00 Prover 3: stopped % 8.36/2.01 Prover 5: stopped % 8.36/2.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.36/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.36/2.01 Prover 0: stopped % 8.36/2.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.36/2.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.36/2.02 Prover 6: stopped % 8.36/2.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.36/2.04 Prover 10: Preprocessing ... % 8.36/2.04 Prover 8: Preprocessing ... % 8.36/2.06 Prover 13: Preprocessing ... % 8.36/2.06 Prover 11: Preprocessing ... % 8.36/2.07 Prover 7: Preprocessing ... % 9.19/2.12 Prover 10: Warning: ignoring some quantifiers % 9.20/2.13 Prover 10: Constructing countermodel ... % 9.20/2.14 Prover 7: Warning: ignoring some quantifiers % 9.20/2.14 Prover 7: Constructing countermodel ... % 9.20/2.16 Prover 13: Warning: ignoring some quantifiers % 9.20/2.17 Prover 13: Constructing countermodel ... % 9.20/2.19 Prover 8: Warning: ignoring some quantifiers % 9.68/2.22 Prover 8: Constructing countermodel ... % 10.18/2.30 Prover 10: Found proof (size 28) % 10.18/2.31 Prover 10: proved (292ms) % 10.18/2.31 Prover 8: stopped % 10.18/2.31 Prover 13: stopped % 10.18/2.31 Prover 4: stopped % 10.18/2.31 Prover 1: stopped % 10.18/2.31 Prover 7: stopped % 10.18/2.31 Prover 11: Warning: ignoring some quantifiers % 10.18/2.32 Prover 11: Constructing countermodel ... % 10.18/2.33 Prover 11: stopped % 10.18/2.33 % 10.18/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.18/2.33 % 10.18/2.33 % SZS output start Proof for theBenchmark % 10.18/2.33 Assumptions after simplification: % 10.18/2.33 --------------------------------- % 10.18/2.33 % 10.18/2.33 (d7_yellow_0) % 10.18/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) = % 10.18/2.36 v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relstr_set_smaller(v0, v2, % 10.18/2.36 v3) | ~ element(v3, v1) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, v2) | % 10.18/2.36 ? [v4: $i] : ($i(v4) & (( ~ (v4 = v3) & relstr_set_smaller(v0, v2, v4) & % 10.18/2.36 element(v4, v1) & ! [v5: $i] : ( ~ $i(v5) | ~ relstr_set_smaller(v0, % 10.18/2.36 v2, v5) | ~ element(v5, v1) | related(v0, v4, v5))) | % 10.18/2.36 (relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0, v3, % 10.18/2.36 v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.18/2.36 (the_carrier(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ ex_sup_of_relstr_set(v0, % 10.18/2.36 v2) | ~ rel_str(v0) | ? [v3: $i] : ($i(v3) & relstr_set_smaller(v0, v2, % 10.18/2.36 v3) & element(v3, v1) & ! [v4: $i] : (v4 = v3 | ~ $i(v4) | ~ % 10.18/2.36 relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | ? [v5: $i] : % 10.18/2.36 ($i(v5) & relstr_set_smaller(v0, v2, v5) & element(v5, v1) & ~ % 10.18/2.36 related(v0, v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~ % 10.18/2.36 relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | related(v0, v3, % 10.18/2.36 v4)))) % 10.18/2.36 % 10.18/2.36 (t15_yellow_0) % 10.18/2.37 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v1 % 10.18/2.37 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & antisymmetric_relstr(v0) & rel_str(v0) % 10.18/2.37 & ((relstr_set_smaller(v0, v2, v3) & element(v3, v1) & ~ % 10.18/2.37 ex_sup_of_relstr_set(v0, v2) & ! [v4: $i] : ( ~ $i(v4) | ~ % 10.18/2.37 relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | related(v0, v3, % 10.18/2.37 v4))) | (ex_sup_of_relstr_set(v0, v2) & ! [v4: $i] : ( ~ $i(v4) | % 10.18/2.37 ~ relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | ? [v5: $i] : % 10.18/2.37 ($i(v5) & relstr_set_smaller(v0, v2, v5) & element(v5, v1) & ~ % 10.18/2.37 related(v0, v4, v5)))))) % 10.18/2.37 % 10.18/2.37 (t25_orders_2) % 10.72/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 10.72/2.37 (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ % 10.72/2.37 antisymmetric_relstr(v0) | ~ related(v0, v3, v2) | ~ related(v0, v2, v3) | % 10.72/2.37 ~ element(v3, v1) | ~ element(v2, v1) | ~ rel_str(v0)) % 10.72/2.37 % 10.72/2.37 Further assumptions not needed in the proof: % 10.72/2.37 -------------------------------------------- % 10.72/2.37 dt_l1_orders_2, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, % 10.72/2.37 existence_l1_orders_2, existence_l1_struct_0, existence_m1_subset_1 % 10.72/2.37 % 10.72/2.37 Those formulas are unsatisfiable: % 10.72/2.37 --------------------------------- % 10.72/2.37 % 10.72/2.37 Begin of proof % 10.72/2.37 | % 10.72/2.37 | ALPHA: (d7_yellow_0) implies: % 10.72/2.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v1) | % 10.72/2.38 | ~ $i(v2) | ~ $i(v0) | ~ ex_sup_of_relstr_set(v0, v2) | ~ % 10.72/2.38 | rel_str(v0) | ? [v3: $i] : ($i(v3) & relstr_set_smaller(v0, v2, v3) % 10.72/2.38 | & element(v3, v1) & ! [v4: $i] : (v4 = v3 | ~ $i(v4) | ~ % 10.72/2.38 | relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | ? [v5: $i] % 10.72/2.38 | : ($i(v5) & relstr_set_smaller(v0, v2, v5) & element(v5, v1) & ~ % 10.72/2.38 | related(v0, v4, v5))) & ! [v4: $i] : ( ~ $i(v4) | ~ % 10.72/2.38 | relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | related(v0, % 10.72/2.38 | v3, v4)))) % 10.72/2.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.72/2.38 | (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ % 10.72/2.38 | relstr_set_smaller(v0, v2, v3) | ~ element(v3, v1) | ~ rel_str(v0) % 10.72/2.38 | | ex_sup_of_relstr_set(v0, v2) | ? [v4: $i] : ($i(v4) & (( ~ (v4 = % 10.72/2.38 | v3) & relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ! % 10.72/2.38 | [v5: $i] : ( ~ $i(v5) | ~ relstr_set_smaller(v0, v2, v5) | ~ % 10.72/2.38 | element(v5, v1) | related(v0, v4, v5))) | % 10.72/2.38 | (relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ~ % 10.72/2.38 | related(v0, v3, v4))))) % 10.72/2.38 | % 10.72/2.38 | DELTA: instantiating (t15_yellow_0) with fresh symbols all_11_0, all_11_1, % 10.72/2.38 | all_11_2, all_11_3 gives: % 10.72/2.38 | (3) the_carrier(all_11_3) = all_11_2 & $i(all_11_0) & $i(all_11_1) & % 10.72/2.38 | $i(all_11_2) & $i(all_11_3) & antisymmetric_relstr(all_11_3) & % 10.72/2.38 | rel_str(all_11_3) & ((relstr_set_smaller(all_11_3, all_11_1, all_11_0) % 10.72/2.38 | & element(all_11_0, all_11_2) & ~ ex_sup_of_relstr_set(all_11_3, % 10.72/2.38 | all_11_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 10.72/2.38 | relstr_set_smaller(all_11_3, all_11_1, v0) | ~ element(v0, % 10.72/2.38 | all_11_2) | related(all_11_3, all_11_0, v0))) | % 10.72/2.38 | (ex_sup_of_relstr_set(all_11_3, all_11_1) & ! [v0: $i] : ( ~ $i(v0) % 10.72/2.38 | | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | ~ element(v0, % 10.72/2.38 | all_11_2) | ? [v1: $i] : ($i(v1) & % 10.72/2.38 | relstr_set_smaller(all_11_3, all_11_1, v1) & element(v1, % 10.72/2.38 | all_11_2) & ~ related(all_11_3, v0, v1))))) % 10.72/2.38 | % 10.72/2.38 | ALPHA: (3) implies: % 10.72/2.38 | (4) rel_str(all_11_3) % 10.72/2.38 | (5) antisymmetric_relstr(all_11_3) % 10.72/2.38 | (6) $i(all_11_3) % 10.72/2.38 | (7) $i(all_11_1) % 10.72/2.38 | (8) $i(all_11_0) % 10.72/2.38 | (9) the_carrier(all_11_3) = all_11_2 % 10.72/2.38 | (10) (relstr_set_smaller(all_11_3, all_11_1, all_11_0) & element(all_11_0, % 10.72/2.38 | all_11_2) & ~ ex_sup_of_relstr_set(all_11_3, all_11_1) & ! [v0: % 10.72/2.38 | $i] : ( ~ $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | % 10.72/2.38 | ~ element(v0, all_11_2) | related(all_11_3, all_11_0, v0))) | % 10.72/2.38 | (ex_sup_of_relstr_set(all_11_3, all_11_1) & ! [v0: $i] : ( ~ $i(v0) | % 10.72/2.38 | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | ~ element(v0, % 10.72/2.38 | all_11_2) | ? [v1: $i] : ($i(v1) & relstr_set_smaller(all_11_3, % 10.72/2.38 | all_11_1, v1) & element(v1, all_11_2) & ~ related(all_11_3, % 10.72/2.38 | v0, v1)))) % 10.72/2.38 | % 10.72/2.39 | BETA: splitting (10) gives: % 10.72/2.39 | % 10.72/2.39 | Case 1: % 10.72/2.39 | | % 10.72/2.39 | | (11) relstr_set_smaller(all_11_3, all_11_1, all_11_0) & element(all_11_0, % 10.72/2.39 | | all_11_2) & ~ ex_sup_of_relstr_set(all_11_3, all_11_1) & ! [v0: % 10.72/2.39 | | $i] : ( ~ $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | % 10.72/2.39 | | ~ element(v0, all_11_2) | related(all_11_3, all_11_0, v0)) % 10.72/2.39 | | % 10.72/2.39 | | ALPHA: (11) implies: % 10.72/2.39 | | (12) ~ ex_sup_of_relstr_set(all_11_3, all_11_1) % 10.72/2.39 | | (13) element(all_11_0, all_11_2) % 10.72/2.39 | | (14) relstr_set_smaller(all_11_3, all_11_1, all_11_0) % 10.72/2.39 | | (15) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, % 10.72/2.39 | | v0) | ~ element(v0, all_11_2) | related(all_11_3, all_11_0, % 10.72/2.39 | | v0)) % 10.72/2.39 | | % 10.72/2.39 | | GROUND_INST: instantiating (2) with all_11_3, all_11_2, all_11_1, all_11_0, % 10.72/2.39 | | simplifying with (4), (6), (7), (8), (9), (12), (13), (14) % 10.72/2.39 | | gives: % 10.72/2.39 | | (16) ? [v0: $i] : ($i(v0) & (( ~ (v0 = all_11_0) & % 10.72/2.39 | | relstr_set_smaller(all_11_3, all_11_1, v0) & element(v0, % 10.72/2.39 | | all_11_2) & ! [v1: $i] : ( ~ $i(v1) | ~ % 10.72/2.39 | | relstr_set_smaller(all_11_3, all_11_1, v1) | ~ element(v1, % 10.72/2.39 | | all_11_2) | related(all_11_3, v0, v1))) | % 10.72/2.39 | | (relstr_set_smaller(all_11_3, all_11_1, v0) & element(v0, % 10.72/2.39 | | all_11_2) & ~ related(all_11_3, all_11_0, v0)))) % 10.72/2.39 | | % 10.72/2.39 | | DELTA: instantiating (16) with fresh symbol all_40_0 gives: % 10.72/2.39 | | (17) $i(all_40_0) & (( ~ (all_40_0 = all_11_0) & % 10.72/2.39 | | relstr_set_smaller(all_11_3, all_11_1, all_40_0) & % 10.72/2.39 | | element(all_40_0, all_11_2) & ! [v0: $i] : ( ~ $i(v0) | ~ % 10.72/2.39 | | relstr_set_smaller(all_11_3, all_11_1, v0) | ~ element(v0, % 10.72/2.39 | | all_11_2) | related(all_11_3, all_40_0, v0))) | % 10.72/2.39 | | (relstr_set_smaller(all_11_3, all_11_1, all_40_0) & % 10.72/2.39 | | element(all_40_0, all_11_2) & ~ related(all_11_3, all_11_0, % 10.72/2.39 | | all_40_0))) % 10.72/2.39 | | % 10.72/2.39 | | ALPHA: (17) implies: % 10.72/2.39 | | (18) $i(all_40_0) % 10.72/2.39 | | (19) ( ~ (all_40_0 = all_11_0) & relstr_set_smaller(all_11_3, all_11_1, % 10.72/2.39 | | all_40_0) & element(all_40_0, all_11_2) & ! [v0: $i] : ( ~ % 10.72/2.39 | | $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | ~ % 10.72/2.39 | | element(v0, all_11_2) | related(all_11_3, all_40_0, v0))) | % 10.72/2.39 | | (relstr_set_smaller(all_11_3, all_11_1, all_40_0) & % 10.72/2.39 | | element(all_40_0, all_11_2) & ~ related(all_11_3, all_11_0, % 10.72/2.39 | | all_40_0)) % 10.72/2.39 | | % 10.85/2.39 | | BETA: splitting (19) gives: % 10.85/2.39 | | % 10.85/2.39 | | Case 1: % 10.85/2.39 | | | % 10.85/2.39 | | | (20) ~ (all_40_0 = all_11_0) & relstr_set_smaller(all_11_3, all_11_1, % 10.85/2.39 | | | all_40_0) & element(all_40_0, all_11_2) & ! [v0: $i] : ( ~ % 10.85/2.40 | | | $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | ~ % 10.85/2.40 | | | element(v0, all_11_2) | related(all_11_3, all_40_0, v0)) % 10.85/2.40 | | | % 10.85/2.40 | | | ALPHA: (20) implies: % 10.85/2.40 | | | (21) ~ (all_40_0 = all_11_0) % 10.85/2.40 | | | (22) element(all_40_0, all_11_2) % 10.85/2.40 | | | (23) relstr_set_smaller(all_11_3, all_11_1, all_40_0) % 10.85/2.40 | | | (24) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_set_smaller(all_11_3, % 10.85/2.40 | | | all_11_1, v0) | ~ element(v0, all_11_2) | related(all_11_3, % 10.85/2.40 | | | all_40_0, v0)) % 10.85/2.40 | | | % 10.85/2.40 | | | GROUND_INST: instantiating (24) with all_11_0, simplifying with (8), (13), % 10.85/2.40 | | | (14) gives: % 10.85/2.40 | | | (25) related(all_11_3, all_40_0, all_11_0) % 10.85/2.40 | | | % 10.85/2.40 | | | GROUND_INST: instantiating (15) with all_40_0, simplifying with (18), % 10.85/2.40 | | | (22), (23) gives: % 10.85/2.40 | | | (26) related(all_11_3, all_11_0, all_40_0) % 10.85/2.40 | | | % 10.85/2.40 | | | GROUND_INST: instantiating (t25_orders_2) with all_11_3, all_11_2, % 10.85/2.40 | | | all_11_0, all_40_0, simplifying with (4), (5), (6), (8), (9), % 10.85/2.40 | | | (13), (18), (22), (25), (26) gives: % 10.85/2.40 | | | (27) all_40_0 = all_11_0 % 10.85/2.40 | | | % 10.85/2.40 | | | REDUCE: (21), (27) imply: % 10.85/2.40 | | | (28) $false % 10.85/2.40 | | | % 10.85/2.40 | | | CLOSE: (28) is inconsistent. % 10.85/2.40 | | | % 10.85/2.40 | | Case 2: % 10.85/2.40 | | | % 10.85/2.40 | | | (29) relstr_set_smaller(all_11_3, all_11_1, all_40_0) & % 10.85/2.40 | | | element(all_40_0, all_11_2) & ~ related(all_11_3, all_11_0, % 10.85/2.40 | | | all_40_0) % 10.85/2.40 | | | % 10.85/2.40 | | | ALPHA: (29) implies: % 10.85/2.40 | | | (30) ~ related(all_11_3, all_11_0, all_40_0) % 10.85/2.40 | | | (31) element(all_40_0, all_11_2) % 10.85/2.40 | | | (32) relstr_set_smaller(all_11_3, all_11_1, all_40_0) % 10.85/2.40 | | | % 10.85/2.40 | | | GROUND_INST: instantiating (15) with all_40_0, simplifying with (18), % 10.85/2.40 | | | (30), (31), (32) gives: % 10.85/2.40 | | | (33) $false % 10.85/2.40 | | | % 10.85/2.40 | | | CLOSE: (33) is inconsistent. % 10.85/2.40 | | | % 10.85/2.40 | | End of split % 10.85/2.40 | | % 10.85/2.40 | Case 2: % 10.85/2.40 | | % 10.85/2.40 | | (34) ex_sup_of_relstr_set(all_11_3, all_11_1) & ! [v0: $i] : ( ~ $i(v0) % 10.85/2.40 | | | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | ~ element(v0, % 10.85/2.40 | | all_11_2) | ? [v1: $i] : ($i(v1) & relstr_set_smaller(all_11_3, % 10.85/2.40 | | all_11_1, v1) & element(v1, all_11_2) & ~ related(all_11_3, % 10.85/2.40 | | v0, v1))) % 10.85/2.40 | | % 10.85/2.40 | | ALPHA: (34) implies: % 10.85/2.40 | | (35) ex_sup_of_relstr_set(all_11_3, all_11_1) % 10.85/2.40 | | (36) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, % 10.85/2.40 | | v0) | ~ element(v0, all_11_2) | ? [v1: $i] : ($i(v1) & % 10.85/2.40 | | relstr_set_smaller(all_11_3, all_11_1, v1) & element(v1, % 10.85/2.40 | | all_11_2) & ~ related(all_11_3, v0, v1))) % 10.85/2.40 | | % 10.85/2.41 | | GROUND_INST: instantiating (1) with all_11_3, all_11_2, all_11_1, % 10.85/2.41 | | simplifying with (4), (6), (7), (9), (35) gives: % 10.85/2.41 | | (37) ? [v0: $i] : ($i(v0) & relstr_set_smaller(all_11_3, all_11_1, v0) & % 10.85/2.41 | | element(v0, all_11_2) & ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ % 10.85/2.41 | | relstr_set_smaller(all_11_3, all_11_1, v1) | ~ element(v1, % 10.85/2.41 | | all_11_2) | ? [v2: $i] : ($i(v2) & % 10.85/2.41 | | relstr_set_smaller(all_11_3, all_11_1, v2) & element(v2, % 10.85/2.41 | | all_11_2) & ~ related(all_11_3, v1, v2))) & ! [v1: $i] : ( % 10.85/2.41 | | ~ $i(v1) | ~ relstr_set_smaller(all_11_3, all_11_1, v1) | ~ % 10.85/2.41 | | element(v1, all_11_2) | related(all_11_3, v0, v1))) % 10.85/2.41 | | % 10.85/2.41 | | DELTA: instantiating (37) with fresh symbol all_39_0 gives: % 10.85/2.41 | | (38) $i(all_39_0) & relstr_set_smaller(all_11_3, all_11_1, all_39_0) & % 10.85/2.41 | | element(all_39_0, all_11_2) & ! [v0: any] : (v0 = all_39_0 | ~ % 10.85/2.41 | | $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | ~ % 10.85/2.41 | | element(v0, all_11_2) | ? [v1: $i] : ($i(v1) & % 10.85/2.41 | | relstr_set_smaller(all_11_3, all_11_1, v1) & element(v1, % 10.85/2.41 | | all_11_2) & ~ related(all_11_3, v0, v1))) & ! [v0: $i] : ( ~ % 10.85/2.41 | | $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, v0) | ~ % 10.85/2.41 | | element(v0, all_11_2) | related(all_11_3, all_39_0, v0)) % 10.85/2.41 | | % 10.85/2.41 | | ALPHA: (38) implies: % 10.85/2.41 | | (39) element(all_39_0, all_11_2) % 10.85/2.41 | | (40) relstr_set_smaller(all_11_3, all_11_1, all_39_0) % 10.85/2.41 | | (41) $i(all_39_0) % 10.85/2.41 | | (42) ! [v0: $i] : ( ~ $i(v0) | ~ relstr_set_smaller(all_11_3, all_11_1, % 10.85/2.41 | | v0) | ~ element(v0, all_11_2) | related(all_11_3, all_39_0, % 10.85/2.41 | | v0)) % 10.85/2.41 | | % 10.85/2.41 | | GROUND_INST: instantiating (36) with all_39_0, simplifying with (39), (40), % 10.85/2.41 | | (41) gives: % 10.85/2.41 | | (43) ? [v0: $i] : ($i(v0) & relstr_set_smaller(all_11_3, all_11_1, v0) & % 10.85/2.41 | | element(v0, all_11_2) & ~ related(all_11_3, all_39_0, v0)) % 10.85/2.41 | | % 10.85/2.41 | | DELTA: instantiating (43) with fresh symbol all_48_0 gives: % 10.85/2.41 | | (44) $i(all_48_0) & relstr_set_smaller(all_11_3, all_11_1, all_48_0) & % 10.85/2.41 | | element(all_48_0, all_11_2) & ~ related(all_11_3, all_39_0, % 10.85/2.41 | | all_48_0) % 10.85/2.41 | | % 10.85/2.41 | | ALPHA: (44) implies: % 10.85/2.41 | | (45) ~ related(all_11_3, all_39_0, all_48_0) % 10.85/2.41 | | (46) element(all_48_0, all_11_2) % 10.85/2.41 | | (47) relstr_set_smaller(all_11_3, all_11_1, all_48_0) % 10.85/2.41 | | (48) $i(all_48_0) % 10.85/2.41 | | % 10.85/2.41 | | GROUND_INST: instantiating (42) with all_48_0, simplifying with (45), (46), % 10.85/2.41 | | (47), (48) gives: % 10.85/2.41 | | (49) $false % 10.85/2.41 | | % 10.85/2.41 | | CLOSE: (49) is inconsistent. % 10.85/2.41 | | % 10.85/2.41 | End of split % 10.85/2.41 | % 10.85/2.41 End of proof % 10.85/2.41 % SZS output end Proof for theBenchmark % 10.85/2.41 % 10.85/2.41 1791ms %------------------------------------------------------------------------------