%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU238+3 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:34 EDT 2023 % Result : Theorem 13.84s 2.67s % Output : Proof 16.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU238+3 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n019.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 15:50:44 EDT 2023 % 0.13/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.85/1.20 Prover 4: Preprocessing ... % 2.85/1.21 Prover 1: Preprocessing ... % 3.42/1.24 Prover 0: Preprocessing ... % 3.42/1.24 Prover 3: Preprocessing ... % 3.42/1.24 Prover 5: Preprocessing ... % 3.42/1.24 Prover 2: Preprocessing ... % 3.42/1.24 Prover 6: Preprocessing ... % 7.10/1.75 Prover 5: Proving ... % 7.10/1.76 Prover 2: Proving ... % 7.10/1.76 Prover 1: Warning: ignoring some quantifiers % 7.48/1.80 Prover 1: Constructing countermodel ... % 7.48/1.82 Prover 3: Warning: ignoring some quantifiers % 8.02/1.85 Prover 3: Constructing countermodel ... % 8.02/1.85 Prover 6: Proving ... % 8.17/1.91 Prover 4: Warning: ignoring some quantifiers % 8.51/1.94 Prover 4: Constructing countermodel ... % 8.74/1.95 Prover 0: Proving ... % 10.52/2.25 Prover 3: gave up % 10.52/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.03/2.31 Prover 7: Preprocessing ... % 11.03/2.36 Prover 1: gave up % 11.03/2.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.72/2.37 Prover 7: Warning: ignoring some quantifiers % 11.72/2.38 Prover 7: Constructing countermodel ... % 11.86/2.41 Prover 8: Preprocessing ... % 12.70/2.57 Prover 8: Warning: ignoring some quantifiers % 13.18/2.59 Prover 8: Constructing countermodel ... % 13.84/2.67 Prover 5: proved (2009ms) % 13.84/2.67 % 13.84/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.84/2.67 % 13.84/2.68 Prover 2: stopped % 13.84/2.68 Prover 6: stopped % 13.84/2.68 Prover 0: stopped % 13.84/2.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.84/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.84/2.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.99/2.69 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.99/2.77 Prover 11: Preprocessing ... % 13.99/2.79 Prover 10: Preprocessing ... % 13.99/2.79 Prover 16: Preprocessing ... % 13.99/2.80 Prover 13: Preprocessing ... % 13.99/2.87 Prover 13: Warning: ignoring some quantifiers % 13.99/2.88 Prover 13: Constructing countermodel ... % 13.99/2.88 Prover 10: Warning: ignoring some quantifiers % 13.99/2.89 Prover 16: Warning: ignoring some quantifiers % 13.99/2.90 Prover 16: Constructing countermodel ... % 13.99/2.90 Prover 10: Constructing countermodel ... % 15.72/2.97 Prover 7: Found proof (size 46) % 15.72/2.97 Prover 7: proved (711ms) % 15.72/2.97 Prover 16: stopped % 15.72/2.97 Prover 10: stopped % 15.72/2.97 Prover 13: stopped % 15.72/2.97 Prover 8: stopped % 15.72/2.97 Prover 4: stopped % 15.72/2.98 Prover 11: Warning: ignoring some quantifiers % 15.72/2.99 Prover 11: Constructing countermodel ... % 15.72/3.00 Prover 11: stopped % 15.72/3.00 % 15.72/3.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.72/3.00 % 15.72/3.01 % SZS output start Proof for theBenchmark % 16.19/3.01 Assumptions after simplification: % 16.19/3.01 --------------------------------- % 16.19/3.01 % 16.19/3.01 (antisymmetry_r2_hidden) % 16.19/3.01 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v1, v0) | ~ in(v0, % 16.19/3.01 v1)) % 16.19/3.01 % 16.19/3.01 (commutativity_k2_xboole_0) % 16.19/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 16.19/3.03 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 16.19/3.03 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 16.19/3.03 | (set_union2(v1, v0) = v2 & $i(v2))) % 16.19/3.03 % 16.19/3.03 (d1_ordinal1) % 16.19/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 16.19/3.04 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0: % 16.19/3.04 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 16.19/3.04 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2))) % 16.19/3.04 % 16.19/3.04 (d8_xboole_0) % 16.19/3.04 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, % 16.19/3.04 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 16.19/3.04 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~ % 16.19/3.04 $i(v0) | ~ proper_subset(v0, v0)) % 16.19/3.04 % 16.19/3.04 (fc3_ordinal1) % 16.19/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) | % 16.19/3.04 ~ empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) % 16.19/3.04 | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.19/3.04 (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! % 16.19/3.04 [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) | % 16.19/3.04 ordinal(v1)) % 16.19/3.04 % 16.19/3.04 (redefinition_r1_ordinal1) % 16.19/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~ % 16.19/3.04 ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0: $i] : ! % 16.19/3.04 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal_subset(v0, v1) | ~ ordinal(v1) % 16.19/3.04 | ~ ordinal(v0) | subset(v0, v1)) % 16.19/3.04 % 16.19/3.04 (t10_ordinal1) % 16.19/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | in(v0, v1)) % 16.19/3.04 % 16.19/3.04 (t21_ordinal1) % 16.19/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0) % 16.19/3.04 | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) % 16.19/3.04 % 16.19/3.04 (t33_ordinal1) % 16.19/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) | ~ $i(v2) | ~ % 16.19/3.05 $i(v0) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | % 16.19/3.05 in(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) % 16.19/3.05 | ~ $i(v2) | ~ $i(v0) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | % 16.19/3.05 ordinal_subset(v1, v2)) % 16.19/3.05 % 16.19/3.05 (t41_ordinal1) % 16.19/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~ % 16.19/3.05 $i(v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ % 16.19/3.05 in(v1, v0) | in(v2, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | % 16.19/3.05 being_limit_ordinal(v0) | ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 & % 16.19/3.05 $i(v2) & $i(v1) & ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) % 16.19/3.05 % 16.19/3.05 (t42_ordinal1) % 16.19/3.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ordinal(v0) & % 16.19/3.05 ((v2 = v0 & succ(v1) = v0 & being_limit_ordinal(v0) & ordinal(v1)) | ( ~ % 16.19/3.05 being_limit_ordinal(v0) & ! [v3: $i] : ( ~ (succ(v3) = v0) | ~ $i(v3) % 16.19/3.05 | ~ ordinal(v3))))) % 16.19/3.05 % 16.19/3.05 Further assumptions not needed in the proof: % 16.19/3.05 -------------------------------------------- % 16.19/3.05 antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1, % 16.19/3.05 cc2_ordinal1, cc3_ordinal1, connectedness_r1_ordinal1, existence_m1_subset_1, % 16.19/3.05 fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_ordinal1, fc2_relat_1, % 16.19/3.05 fc2_xboole_0, fc3_xboole_0, fc4_relat_1, idempotence_k2_xboole_0, % 16.19/3.05 irreflexivity_r2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0, % 16.19/3.05 rc2_funct_1, rc2_ordinal1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, % 16.19/3.05 rc3_relat_1, rc4_funct_1, rc5_funct_1, reflexivity_r1_ordinal1, % 16.19/3.05 reflexivity_r1_tarski, t1_boole, t1_subset, t2_subset, t3_subset, t4_subset, % 16.19/3.05 t5_subset, t6_boole, t7_boole, t8_boole % 16.19/3.05 % 16.19/3.05 Those formulas are unsatisfiable: % 16.19/3.05 --------------------------------- % 16.19/3.05 % 16.19/3.05 Begin of proof % 16.19/3.05 | % 16.19/3.05 | ALPHA: (commutativity_k2_xboole_0) implies: % 16.19/3.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 16.19/3.05 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 16.19/3.05 | % 16.19/3.05 | ALPHA: (d1_ordinal1) implies: % 16.19/3.05 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: % 16.19/3.05 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & % 16.19/3.05 | $i(v1))) % 16.19/3.05 | % 16.19/3.05 | ALPHA: (d8_xboole_0) implies: % 16.19/3.05 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 16.19/3.05 | subset(v0, v1) | proper_subset(v0, v1)) % 16.19/3.05 | % 16.19/3.05 | ALPHA: (fc3_ordinal1) implies: % 16.19/3.05 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ % 16.19/3.05 | ordinal(v0) | ordinal(v1)) % 16.19/3.05 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ % 16.19/3.05 | ordinal(v0) | epsilon_transitive(v1)) % 16.19/3.05 | % 16.19/3.05 | ALPHA: (redefinition_r1_ordinal1) implies: % 16.19/3.05 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 16.19/3.05 | ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, % 16.19/3.05 | v1)) % 16.19/3.05 | % 16.19/3.05 | ALPHA: (t33_ordinal1) implies: % 16.19/3.05 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) | ~ % 16.19/3.06 | $i(v2) | ~ $i(v0) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) % 16.19/3.06 | | ordinal_subset(v1, v2)) % 16.19/3.06 | % 16.19/3.06 | ALPHA: (t41_ordinal1) implies: % 16.19/3.06 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | being_limit_ordinal(v0) | % 16.19/3.06 | ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 & $i(v2) & $i(v1) & % 16.19/3.06 | ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) % 16.19/3.06 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 16.19/3.06 | $i(v1) | ~ $i(v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ % 16.19/3.06 | ordinal(v0) | ~ in(v1, v0) | in(v2, v0)) % 16.19/3.06 | % 16.19/3.06 | DELTA: instantiating (t42_ordinal1) with fresh symbols all_66_0, all_66_1, % 16.19/3.06 | all_66_2 gives: % 16.19/3.06 | (10) $i(all_66_1) & $i(all_66_2) & ordinal(all_66_2) & ((all_66_0 = % 16.19/3.06 | all_66_2 & succ(all_66_1) = all_66_2 & % 16.19/3.06 | being_limit_ordinal(all_66_2) & ordinal(all_66_1)) | ( ~ % 16.19/3.06 | being_limit_ordinal(all_66_2) & ! [v0: $i] : ( ~ (succ(v0) = % 16.19/3.06 | all_66_2) | ~ $i(v0) | ~ ordinal(v0)))) % 16.19/3.06 | % 16.19/3.06 | ALPHA: (10) implies: % 16.19/3.06 | (11) ordinal(all_66_2) % 16.19/3.06 | (12) $i(all_66_2) % 16.19/3.06 | (13) $i(all_66_1) % 16.19/3.06 | (14) (all_66_0 = all_66_2 & succ(all_66_1) = all_66_2 & % 16.19/3.06 | being_limit_ordinal(all_66_2) & ordinal(all_66_1)) | ( ~ % 16.19/3.06 | being_limit_ordinal(all_66_2) & ! [v0: $i] : ( ~ (succ(v0) = % 16.19/3.06 | all_66_2) | ~ $i(v0) | ~ ordinal(v0))) % 16.19/3.06 | % 16.19/3.06 | GROUND_INST: instantiating (8) with all_66_2, simplifying with (11), (12) % 16.19/3.06 | gives: % 16.19/3.06 | (15) being_limit_ordinal(all_66_2) | ? [v0: $i] : ? [v1: $i] : (succ(v0) % 16.19/3.06 | = v1 & $i(v1) & $i(v0) & ordinal(v0) & in(v0, all_66_2) & ~ in(v1, % 16.19/3.06 | all_66_2)) % 16.19/3.06 | % 16.19/3.06 | BETA: splitting (14) gives: % 16.19/3.06 | % 16.19/3.06 | Case 1: % 16.19/3.06 | | % 16.19/3.06 | | (16) all_66_0 = all_66_2 & succ(all_66_1) = all_66_2 & % 16.19/3.06 | | being_limit_ordinal(all_66_2) & ordinal(all_66_1) % 16.19/3.06 | | % 16.19/3.06 | | ALPHA: (16) implies: % 16.19/3.06 | | (17) ordinal(all_66_1) % 16.19/3.06 | | (18) being_limit_ordinal(all_66_2) % 16.19/3.06 | | (19) succ(all_66_1) = all_66_2 % 16.19/3.06 | | % 16.19/3.06 | | GROUND_INST: instantiating (t10_ordinal1) with all_66_1, all_66_2, % 16.19/3.06 | | simplifying with (13), (19) gives: % 16.19/3.06 | | (20) in(all_66_1, all_66_2) % 16.19/3.06 | | % 16.19/3.06 | | GROUND_INST: instantiating (2) with all_66_1, all_66_2, simplifying with % 16.19/3.06 | | (13), (19) gives: % 16.19/3.06 | | (21) ? [v0: $i] : (singleton(all_66_1) = v0 & set_union2(all_66_1, v0) = % 16.19/3.06 | | all_66_2 & $i(v0) & $i(all_66_2)) % 16.19/3.06 | | % 16.19/3.06 | | DELTA: instantiating (21) with fresh symbol all_119_0 gives: % 16.19/3.06 | | (22) singleton(all_66_1) = all_119_0 & set_union2(all_66_1, all_119_0) = % 16.19/3.06 | | all_66_2 & $i(all_119_0) & $i(all_66_2) % 16.19/3.06 | | % 16.19/3.06 | | ALPHA: (22) implies: % 16.19/3.06 | | (23) $i(all_119_0) % 16.19/3.06 | | (24) set_union2(all_66_1, all_119_0) = all_66_2 % 16.19/3.06 | | % 16.19/3.06 | | GROUND_INST: instantiating (9) with all_66_2, all_66_1, all_66_2, % 16.19/3.06 | | simplifying with (11), (12), (13), (17), (18), (19), (20) % 16.19/3.06 | | gives: % 16.19/3.06 | | (25) in(all_66_2, all_66_2) % 16.19/3.06 | | % 16.19/3.06 | | GROUND_INST: instantiating (1) with all_119_0, all_66_1, all_66_2, % 16.19/3.06 | | simplifying with (13), (23), (24) gives: % 16.19/3.07 | | (26) set_union2(all_119_0, all_66_1) = all_66_2 & $i(all_66_2) % 16.19/3.07 | | % 16.19/3.07 | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with all_66_2, all_66_2, % 16.19/3.07 | | simplifying with (12), (25) gives: % 16.19/3.07 | | (27) $false % 16.19/3.07 | | % 16.19/3.07 | | CLOSE: (27) is inconsistent. % 16.19/3.07 | | % 16.19/3.07 | Case 2: % 16.19/3.07 | | % 16.19/3.07 | | (28) ~ being_limit_ordinal(all_66_2) & ! [v0: $i] : ( ~ (succ(v0) = % 16.19/3.07 | | all_66_2) | ~ $i(v0) | ~ ordinal(v0)) % 16.19/3.07 | | % 16.19/3.07 | | ALPHA: (28) implies: % 16.19/3.07 | | (29) ~ being_limit_ordinal(all_66_2) % 16.19/3.07 | | (30) ! [v0: $i] : ( ~ (succ(v0) = all_66_2) | ~ $i(v0) | ~ % 16.19/3.07 | | ordinal(v0)) % 16.19/3.07 | | % 16.19/3.07 | | BETA: splitting (15) gives: % 16.19/3.07 | | % 16.19/3.07 | | Case 1: % 16.19/3.07 | | | % 16.19/3.07 | | | (31) being_limit_ordinal(all_66_2) % 16.19/3.07 | | | % 16.19/3.07 | | | PRED_UNIFY: (29), (31) imply: % 16.19/3.07 | | | (32) $false % 16.19/3.07 | | | % 16.19/3.07 | | | CLOSE: (32) is inconsistent. % 16.19/3.07 | | | % 16.19/3.07 | | Case 2: % 16.19/3.07 | | | % 16.19/3.07 | | | (33) ? [v0: $i] : ? [v1: $i] : (succ(v0) = v1 & $i(v1) & $i(v0) & % 16.19/3.07 | | | ordinal(v0) & in(v0, all_66_2) & ~ in(v1, all_66_2)) % 16.19/3.07 | | | % 16.19/3.07 | | | DELTA: instantiating (33) with fresh symbols all_118_0, all_118_1 gives: % 16.19/3.07 | | | (34) succ(all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1) & % 16.19/3.07 | | | ordinal(all_118_1) & in(all_118_1, all_66_2) & ~ in(all_118_0, % 16.19/3.07 | | | all_66_2) % 16.19/3.07 | | | % 16.19/3.07 | | | ALPHA: (34) implies: % 16.19/3.07 | | | (35) ~ in(all_118_0, all_66_2) % 16.19/3.07 | | | (36) in(all_118_1, all_66_2) % 16.19/3.07 | | | (37) ordinal(all_118_1) % 16.19/3.07 | | | (38) $i(all_118_1) % 16.19/3.07 | | | (39) succ(all_118_1) = all_118_0 % 16.19/3.07 | | | % 16.19/3.07 | | | GROUND_INST: instantiating (7) with all_118_1, all_118_0, all_66_2, % 16.19/3.07 | | | simplifying with (11), (12), (36), (37), (38), (39) gives: % 16.19/3.07 | | | (40) ordinal_subset(all_118_0, all_66_2) % 16.19/3.07 | | | % 16.19/3.07 | | | GROUND_INST: instantiating (5) with all_118_1, all_118_0, simplifying with % 16.19/3.07 | | | (37), (38), (39) gives: % 16.19/3.07 | | | (41) epsilon_transitive(all_118_0) % 16.19/3.07 | | | % 16.19/3.07 | | | GROUND_INST: instantiating (4) with all_118_1, all_118_0, simplifying with % 16.19/3.07 | | | (37), (38), (39) gives: % 16.19/3.07 | | | (42) ordinal(all_118_0) % 16.19/3.07 | | | % 16.19/3.07 | | | GROUND_INST: instantiating (30) with all_118_1, simplifying with (37), % 16.19/3.07 | | | (38) gives: % 16.19/3.07 | | | (43) ~ (succ(all_118_1) = all_66_2) % 16.19/3.07 | | | % 16.19/3.07 | | | GROUND_INST: instantiating (2) with all_118_1, all_118_0, simplifying with % 16.19/3.07 | | | (38), (39) gives: % 16.19/3.07 | | | (44) ? [v0: $i] : (singleton(all_118_1) = v0 & set_union2(all_118_1, % 16.19/3.07 | | | v0) = all_118_0 & $i(v0) & $i(all_118_0)) % 16.19/3.07 | | | % 16.19/3.07 | | | DELTA: instantiating (44) with fresh symbol all_130_0 gives: % 16.19/3.07 | | | (45) singleton(all_118_1) = all_130_0 & set_union2(all_118_1, % 16.19/3.07 | | | all_130_0) = all_118_0 & $i(all_130_0) & $i(all_118_0) % 16.19/3.07 | | | % 16.19/3.07 | | | ALPHA: (45) implies: % 16.19/3.07 | | | (46) $i(all_118_0) % 16.52/3.07 | | | (47) $i(all_130_0) % 16.52/3.07 | | | (48) set_union2(all_118_1, all_130_0) = all_118_0 % 16.52/3.07 | | | % 16.52/3.07 | | | PRED_UNIFY: (39), (43) imply: % 16.52/3.07 | | | (49) ~ (all_118_0 = all_66_2) % 16.52/3.07 | | | % 16.52/3.07 | | | GROUND_INST: instantiating (6) with all_118_0, all_66_2, simplifying with % 16.52/3.07 | | | (11), (12), (40), (42), (46) gives: % 16.52/3.07 | | | (50) subset(all_118_0, all_66_2) % 16.52/3.07 | | | % 16.52/3.08 | | | GROUND_INST: instantiating (1) with all_130_0, all_118_1, all_118_0, % 16.52/3.08 | | | simplifying with (38), (47), (48) gives: % 16.52/3.08 | | | (51) set_union2(all_130_0, all_118_1) = all_118_0 & $i(all_118_0) % 16.52/3.08 | | | % 16.52/3.08 | | | GROUND_INST: instantiating (3) with all_118_0, all_66_2, simplifying with % 16.52/3.08 | | | (12), (46), (50) gives: % 16.52/3.08 | | | (52) all_118_0 = all_66_2 | proper_subset(all_118_0, all_66_2) % 16.52/3.08 | | | % 16.52/3.08 | | | BETA: splitting (52) gives: % 16.52/3.08 | | | % 16.52/3.08 | | | Case 1: % 16.52/3.08 | | | | % 16.52/3.08 | | | | (53) proper_subset(all_118_0, all_66_2) % 16.52/3.08 | | | | % 16.52/3.08 | | | | GROUND_INST: instantiating (t21_ordinal1) with all_118_0, all_66_2, % 16.52/3.08 | | | | simplifying with (11), (12), (35), (41), (46), (53) gives: % 16.52/3.08 | | | | (54) $false % 16.52/3.08 | | | | % 16.52/3.08 | | | | CLOSE: (54) is inconsistent. % 16.52/3.08 | | | | % 16.52/3.08 | | | Case 2: % 16.52/3.08 | | | | % 16.52/3.08 | | | | (55) all_118_0 = all_66_2 % 16.52/3.08 | | | | % 16.52/3.08 | | | | REDUCE: (49), (55) imply: % 16.52/3.08 | | | | (56) $false % 16.52/3.08 | | | | % 16.52/3.08 | | | | CLOSE: (56) is inconsistent. % 16.52/3.08 | | | | % 16.52/3.08 | | | End of split % 16.52/3.08 | | | % 16.52/3.08 | | End of split % 16.52/3.08 | | % 16.52/3.08 | End of split % 16.52/3.08 | % 16.52/3.08 End of proof % 16.52/3.08 % SZS output end Proof for theBenchmark % 16.52/3.08 % 16.52/3.08 2448ms %------------------------------------------------------------------------------