%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU238+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 : n029.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 15.00s 2.80s % Output : Proof 17.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU238+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n029.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 : Wed Aug 23 12:55:37 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/sandbox/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 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 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 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 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 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 % 2.85/1.13 Prover 4: Preprocessing ... % 2.85/1.13 Prover 1: Preprocessing ... % 3.38/1.17 Prover 2: Preprocessing ... % 3.38/1.17 Prover 5: Preprocessing ... % 3.38/1.17 Prover 6: Preprocessing ... % 3.38/1.17 Prover 3: Preprocessing ... % 3.38/1.17 Prover 0: Preprocessing ... % 7.25/1.75 Prover 2: Proving ... % 7.25/1.76 Prover 5: Proving ... % 7.46/1.77 Prover 1: Warning: ignoring some quantifiers % 7.46/1.79 Prover 3: Warning: ignoring some quantifiers % 7.46/1.81 Prover 3: Constructing countermodel ... % 7.46/1.82 Prover 6: Proving ... % 7.46/1.82 Prover 1: Constructing countermodel ... % 8.19/1.92 Prover 4: Warning: ignoring some quantifiers % 8.66/1.95 Prover 4: Constructing countermodel ... % 9.65/2.11 Prover 0: Proving ... % 10.63/2.29 Prover 3: gave up % 10.63/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.21/2.33 Prover 7: Preprocessing ... % 11.72/2.42 Prover 1: gave up % 11.72/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.72/2.45 Prover 7: Warning: ignoring some quantifiers % 12.46/2.47 Prover 7: Constructing countermodel ... % 12.46/2.47 Prover 8: Preprocessing ... % 13.51/2.60 Prover 8: Warning: ignoring some quantifiers % 13.51/2.61 Prover 8: Constructing countermodel ... % 15.00/2.80 Prover 5: proved (2164ms) % 15.00/2.80 % 15.00/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.00/2.80 % 15.00/2.80 Prover 6: stopped % 15.00/2.81 Prover 0: stopped % 15.00/2.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.00/2.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.00/2.83 Prover 2: stopped % 15.00/2.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.00/2.84 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.00/2.86 Prover 10: Preprocessing ... % 15.00/2.88 Prover 11: Preprocessing ... % 15.00/2.90 Prover 13: Preprocessing ... % 15.00/2.91 Prover 10: Warning: ignoring some quantifiers % 15.00/2.92 Prover 10: Constructing countermodel ... % 15.00/2.92 Prover 16: Preprocessing ... % 16.13/2.99 Prover 8: gave up % 16.13/2.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 16.13/3.00 Prover 13: Warning: ignoring some quantifiers % 16.13/3.01 Prover 13: Constructing countermodel ... % 16.13/3.02 Prover 19: Preprocessing ... % 16.13/3.03 Prover 7: Found proof (size 46) % 16.13/3.03 Prover 7: proved (740ms) % 16.13/3.03 Prover 13: stopped % 16.13/3.03 Prover 4: stopped % 16.13/3.03 Prover 10: stopped % 16.65/3.04 Prover 16: Warning: ignoring some quantifiers % 16.65/3.04 Prover 16: Constructing countermodel ... % 16.65/3.05 Prover 16: stopped % 16.85/3.09 Prover 11: Warning: ignoring some quantifiers % 16.85/3.10 Prover 11: Constructing countermodel ... % 16.85/3.11 Prover 11: stopped % 17.18/3.14 Prover 19: Warning: ignoring some quantifiers % 17.18/3.15 Prover 19: Constructing countermodel ... % 17.33/3.16 Prover 19: stopped % 17.33/3.16 % 17.33/3.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.33/3.16 % 17.33/3.17 % SZS output start Proof for theBenchmark % 17.33/3.17 Assumptions after simplification: % 17.33/3.17 --------------------------------- % 17.33/3.17 % 17.33/3.17 (antisymmetry_r2_hidden) % 17.33/3.17 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v1, v0) | ~ in(v0, % 17.33/3.17 v1)) % 17.33/3.18 % 17.33/3.18 (commutativity_k2_xboole_0) % 17.33/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 17.33/3.19 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 17.33/3.19 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 17.33/3.19 | (set_union2(v1, v0) = v2 & $i(v2))) % 17.33/3.19 % 17.33/3.19 (d1_ordinal1) % 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 17.33/3.20 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0: % 17.33/3.20 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 17.33/3.20 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2))) % 17.33/3.20 % 17.33/3.20 (d8_xboole_0) % 17.33/3.20 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, % 17.33/3.20 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 17.33/3.20 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~ % 17.33/3.20 $i(v0) | ~ proper_subset(v0, v0)) % 17.33/3.20 % 17.33/3.20 (fc3_ordinal1) % 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) | % 17.33/3.20 ~ empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) % 17.33/3.20 | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 17.33/3.20 (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! % 17.33/3.20 [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ ordinal(v0) | % 17.33/3.20 ordinal(v1)) % 17.33/3.20 % 17.33/3.20 (redefinition_r1_ordinal1) % 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~ % 17.33/3.20 ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0: $i] : ! % 17.33/3.20 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal_subset(v0, v1) | ~ ordinal(v1) % 17.33/3.20 | ~ ordinal(v0) | subset(v0, v1)) % 17.33/3.20 % 17.33/3.20 (t10_ordinal1) % 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | in(v0, v1)) % 17.33/3.20 % 17.33/3.20 (t21_ordinal1) % 17.33/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0) % 17.33/3.20 | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) % 17.33/3.20 % 17.33/3.20 (t33_ordinal1) % 17.33/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) | ~ $i(v2) | ~ % 17.33/3.21 $i(v0) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | % 17.33/3.21 in(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) % 17.33/3.21 | ~ $i(v2) | ~ $i(v0) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | % 17.33/3.21 ordinal_subset(v1, v2)) % 17.33/3.21 % 17.33/3.21 (t41_ordinal1) % 17.33/3.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ $i(v1) | ~ % 17.33/3.21 $i(v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ % 17.33/3.21 in(v1, v0) | in(v2, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | % 17.33/3.21 being_limit_ordinal(v0) | ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 & % 17.33/3.21 $i(v2) & $i(v1) & ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) % 17.33/3.21 % 17.33/3.21 (t42_ordinal1) % 17.33/3.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & $i(v0) & ordinal(v0) & % 17.33/3.21 ((v2 = v0 & succ(v1) = v0 & being_limit_ordinal(v0) & ordinal(v1)) | ( ~ % 17.33/3.21 being_limit_ordinal(v0) & ! [v3: $i] : ( ~ (succ(v3) = v0) | ~ $i(v3) % 17.33/3.21 | ~ ordinal(v3))))) % 17.33/3.21 % 17.33/3.21 Further assumptions not needed in the proof: % 17.33/3.21 -------------------------------------------- % 17.33/3.21 antisymmetry_r2_xboole_0, cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1, % 17.33/3.21 cc2_ordinal1, cc3_ordinal1, connectedness_r1_ordinal1, dt_k1_ordinal1, % 17.33/3.21 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_xboole_0, dt_m1_subset_1, % 17.33/3.21 existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0, fc2_ordinal1, % 17.33/3.21 fc2_relat_1, fc2_xboole_0, fc3_xboole_0, fc4_relat_1, idempotence_k2_xboole_0, % 17.33/3.21 irreflexivity_r2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_relat_1, rc1_xboole_0, % 17.33/3.21 rc2_funct_1, rc2_ordinal1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, % 17.33/3.21 rc3_relat_1, rc4_funct_1, reflexivity_r1_ordinal1, reflexivity_r1_tarski, % 17.33/3.21 t1_boole, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, % 17.33/3.21 t7_boole, t8_boole % 17.33/3.21 % 17.33/3.21 Those formulas are unsatisfiable: % 17.33/3.21 --------------------------------- % 17.33/3.21 % 17.33/3.21 Begin of proof % 17.33/3.21 | % 17.33/3.21 | ALPHA: (commutativity_k2_xboole_0) implies: % 17.33/3.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 17.33/3.21 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 17.33/3.21 | % 17.33/3.21 | ALPHA: (d1_ordinal1) implies: % 17.33/3.21 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: % 17.33/3.21 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & % 17.33/3.21 | $i(v1))) % 17.33/3.21 | % 17.33/3.21 | ALPHA: (d8_xboole_0) implies: % 17.33/3.21 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 17.33/3.21 | subset(v0, v1) | proper_subset(v0, v1)) % 17.33/3.21 | % 17.33/3.21 | ALPHA: (fc3_ordinal1) implies: % 17.33/3.21 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ % 17.33/3.21 | ordinal(v0) | ordinal(v1)) % 17.33/3.22 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ~ % 17.33/3.22 | ordinal(v0) | epsilon_transitive(v1)) % 17.33/3.22 | % 17.33/3.22 | ALPHA: (redefinition_r1_ordinal1) implies: % 17.33/3.22 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 17.33/3.22 | ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, % 17.33/3.22 | v1)) % 17.33/3.22 | % 17.33/3.22 | ALPHA: (t33_ordinal1) implies: % 17.33/3.22 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v1) | ~ % 17.33/3.22 | $i(v2) | ~ $i(v0) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) % 17.33/3.22 | | ordinal_subset(v1, v2)) % 17.33/3.22 | % 17.33/3.22 | ALPHA: (t41_ordinal1) implies: % 17.33/3.22 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | being_limit_ordinal(v0) | % 17.33/3.22 | ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 & $i(v2) & $i(v1) & % 17.33/3.22 | ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) % 17.33/3.22 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 17.33/3.22 | $i(v1) | ~ $i(v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ % 17.33/3.22 | ordinal(v0) | ~ in(v1, v0) | in(v2, v0)) % 17.33/3.22 | % 17.33/3.22 | DELTA: instantiating (t42_ordinal1) with fresh symbols all_64_0, all_64_1, % 17.33/3.22 | all_64_2 gives: % 17.33/3.22 | (10) $i(all_64_1) & $i(all_64_2) & ordinal(all_64_2) & ((all_64_0 = % 17.33/3.22 | all_64_2 & succ(all_64_1) = all_64_2 & % 17.33/3.22 | being_limit_ordinal(all_64_2) & ordinal(all_64_1)) | ( ~ % 17.33/3.22 | being_limit_ordinal(all_64_2) & ! [v0: $i] : ( ~ (succ(v0) = % 17.33/3.22 | all_64_2) | ~ $i(v0) | ~ ordinal(v0)))) % 17.33/3.22 | % 17.33/3.22 | ALPHA: (10) implies: % 17.33/3.22 | (11) ordinal(all_64_2) % 17.33/3.22 | (12) $i(all_64_2) % 17.33/3.22 | (13) $i(all_64_1) % 17.33/3.22 | (14) (all_64_0 = all_64_2 & succ(all_64_1) = all_64_2 & % 17.33/3.22 | being_limit_ordinal(all_64_2) & ordinal(all_64_1)) | ( ~ % 17.33/3.22 | being_limit_ordinal(all_64_2) & ! [v0: $i] : ( ~ (succ(v0) = % 17.33/3.22 | all_64_2) | ~ $i(v0) | ~ ordinal(v0))) % 17.33/3.22 | % 17.33/3.22 | GROUND_INST: instantiating (8) with all_64_2, simplifying with (11), (12) % 17.33/3.22 | gives: % 17.33/3.22 | (15) being_limit_ordinal(all_64_2) | ? [v0: $i] : ? [v1: $i] : (succ(v0) % 17.33/3.22 | = v1 & $i(v1) & $i(v0) & ordinal(v0) & in(v0, all_64_2) & ~ in(v1, % 17.33/3.22 | all_64_2)) % 17.33/3.22 | % 17.33/3.22 | BETA: splitting (14) gives: % 17.33/3.22 | % 17.33/3.22 | Case 1: % 17.33/3.22 | | % 17.33/3.22 | | (16) all_64_0 = all_64_2 & succ(all_64_1) = all_64_2 & % 17.33/3.22 | | being_limit_ordinal(all_64_2) & ordinal(all_64_1) % 17.33/3.22 | | % 17.33/3.22 | | ALPHA: (16) implies: % 17.33/3.22 | | (17) ordinal(all_64_1) % 17.33/3.22 | | (18) being_limit_ordinal(all_64_2) % 17.33/3.22 | | (19) succ(all_64_1) = all_64_2 % 17.33/3.22 | | % 17.33/3.22 | | GROUND_INST: instantiating (t10_ordinal1) with all_64_1, all_64_2, % 17.33/3.23 | | simplifying with (13), (19) gives: % 17.33/3.23 | | (20) in(all_64_1, all_64_2) % 17.33/3.23 | | % 17.33/3.23 | | GROUND_INST: instantiating (2) with all_64_1, all_64_2, simplifying with % 17.33/3.23 | | (13), (19) gives: % 17.65/3.23 | | (21) ? [v0: $i] : (singleton(all_64_1) = v0 & set_union2(all_64_1, v0) = % 17.65/3.23 | | all_64_2 & $i(v0) & $i(all_64_2)) % 17.65/3.23 | | % 17.65/3.23 | | DELTA: instantiating (21) with fresh symbol all_117_0 gives: % 17.65/3.23 | | (22) singleton(all_64_1) = all_117_0 & set_union2(all_64_1, all_117_0) = % 17.65/3.23 | | all_64_2 & $i(all_117_0) & $i(all_64_2) % 17.65/3.23 | | % 17.65/3.23 | | ALPHA: (22) implies: % 17.65/3.23 | | (23) $i(all_117_0) % 17.65/3.23 | | (24) set_union2(all_64_1, all_117_0) = all_64_2 % 17.65/3.23 | | % 17.65/3.23 | | GROUND_INST: instantiating (9) with all_64_2, all_64_1, all_64_2, % 17.65/3.23 | | simplifying with (11), (12), (13), (17), (18), (19), (20) % 17.65/3.23 | | gives: % 17.65/3.23 | | (25) in(all_64_2, all_64_2) % 17.65/3.23 | | % 17.65/3.23 | | GROUND_INST: instantiating (1) with all_117_0, all_64_1, all_64_2, % 17.65/3.23 | | simplifying with (13), (23), (24) gives: % 17.65/3.23 | | (26) set_union2(all_117_0, all_64_1) = all_64_2 & $i(all_64_2) % 17.65/3.23 | | % 17.65/3.23 | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with all_64_2, all_64_2, % 17.65/3.23 | | simplifying with (12), (25) gives: % 17.65/3.23 | | (27) $false % 17.65/3.23 | | % 17.65/3.23 | | CLOSE: (27) is inconsistent. % 17.65/3.23 | | % 17.65/3.23 | Case 2: % 17.65/3.23 | | % 17.65/3.23 | | (28) ~ being_limit_ordinal(all_64_2) & ! [v0: $i] : ( ~ (succ(v0) = % 17.65/3.23 | | all_64_2) | ~ $i(v0) | ~ ordinal(v0)) % 17.65/3.23 | | % 17.65/3.23 | | ALPHA: (28) implies: % 17.65/3.23 | | (29) ~ being_limit_ordinal(all_64_2) % 17.65/3.23 | | (30) ! [v0: $i] : ( ~ (succ(v0) = all_64_2) | ~ $i(v0) | ~ % 17.65/3.23 | | ordinal(v0)) % 17.65/3.23 | | % 17.65/3.23 | | BETA: splitting (15) gives: % 17.65/3.23 | | % 17.65/3.23 | | Case 1: % 17.65/3.23 | | | % 17.65/3.23 | | | (31) being_limit_ordinal(all_64_2) % 17.65/3.23 | | | % 17.65/3.23 | | | PRED_UNIFY: (29), (31) imply: % 17.65/3.23 | | | (32) $false % 17.65/3.23 | | | % 17.65/3.23 | | | CLOSE: (32) is inconsistent. % 17.65/3.23 | | | % 17.65/3.23 | | Case 2: % 17.65/3.23 | | | % 17.65/3.23 | | | (33) ? [v0: $i] : ? [v1: $i] : (succ(v0) = v1 & $i(v1) & $i(v0) & % 17.65/3.23 | | | ordinal(v0) & in(v0, all_64_2) & ~ in(v1, all_64_2)) % 17.65/3.23 | | | % 17.65/3.23 | | | DELTA: instantiating (33) with fresh symbols all_116_0, all_116_1 gives: % 17.65/3.23 | | | (34) succ(all_116_1) = all_116_0 & $i(all_116_0) & $i(all_116_1) & % 17.65/3.23 | | | ordinal(all_116_1) & in(all_116_1, all_64_2) & ~ in(all_116_0, % 17.65/3.23 | | | all_64_2) % 17.65/3.23 | | | % 17.65/3.23 | | | ALPHA: (34) implies: % 17.65/3.23 | | | (35) ~ in(all_116_0, all_64_2) % 17.65/3.23 | | | (36) in(all_116_1, all_64_2) % 17.65/3.23 | | | (37) ordinal(all_116_1) % 17.65/3.23 | | | (38) $i(all_116_1) % 17.65/3.23 | | | (39) succ(all_116_1) = all_116_0 % 17.65/3.23 | | | % 17.65/3.23 | | | GROUND_INST: instantiating (7) with all_116_1, all_116_0, all_64_2, % 17.65/3.23 | | | simplifying with (11), (12), (36), (37), (38), (39) gives: % 17.65/3.23 | | | (40) ordinal_subset(all_116_0, all_64_2) % 17.65/3.23 | | | % 17.65/3.23 | | | GROUND_INST: instantiating (5) with all_116_1, all_116_0, simplifying with % 17.65/3.24 | | | (37), (38), (39) gives: % 17.65/3.24 | | | (41) epsilon_transitive(all_116_0) % 17.65/3.24 | | | % 17.65/3.24 | | | GROUND_INST: instantiating (4) with all_116_1, all_116_0, simplifying with % 17.65/3.24 | | | (37), (38), (39) gives: % 17.65/3.24 | | | (42) ordinal(all_116_0) % 17.65/3.24 | | | % 17.65/3.24 | | | GROUND_INST: instantiating (30) with all_116_1, simplifying with (37), % 17.65/3.24 | | | (38) gives: % 17.65/3.24 | | | (43) ~ (succ(all_116_1) = all_64_2) % 17.65/3.24 | | | % 17.65/3.24 | | | GROUND_INST: instantiating (2) with all_116_1, all_116_0, simplifying with % 17.65/3.24 | | | (38), (39) gives: % 17.65/3.24 | | | (44) ? [v0: $i] : (singleton(all_116_1) = v0 & set_union2(all_116_1, % 17.65/3.24 | | | v0) = all_116_0 & $i(v0) & $i(all_116_0)) % 17.65/3.24 | | | % 17.65/3.24 | | | DELTA: instantiating (44) with fresh symbol all_128_0 gives: % 17.65/3.24 | | | (45) singleton(all_116_1) = all_128_0 & set_union2(all_116_1, % 17.65/3.24 | | | all_128_0) = all_116_0 & $i(all_128_0) & $i(all_116_0) % 17.65/3.24 | | | % 17.65/3.24 | | | ALPHA: (45) implies: % 17.65/3.24 | | | (46) $i(all_116_0) % 17.65/3.24 | | | (47) $i(all_128_0) % 17.65/3.24 | | | (48) set_union2(all_116_1, all_128_0) = all_116_0 % 17.65/3.24 | | | % 17.65/3.24 | | | PRED_UNIFY: (39), (43) imply: % 17.65/3.24 | | | (49) ~ (all_116_0 = all_64_2) % 17.65/3.24 | | | % 17.65/3.24 | | | GROUND_INST: instantiating (6) with all_116_0, all_64_2, simplifying with % 17.65/3.24 | | | (11), (12), (40), (42), (46) gives: % 17.65/3.24 | | | (50) subset(all_116_0, all_64_2) % 17.65/3.24 | | | % 17.65/3.24 | | | GROUND_INST: instantiating (1) with all_128_0, all_116_1, all_116_0, % 17.65/3.24 | | | simplifying with (38), (47), (48) gives: % 17.65/3.24 | | | (51) set_union2(all_128_0, all_116_1) = all_116_0 & $i(all_116_0) % 17.65/3.24 | | | % 17.65/3.24 | | | GROUND_INST: instantiating (3) with all_116_0, all_64_2, simplifying with % 17.65/3.24 | | | (12), (46), (50) gives: % 17.65/3.24 | | | (52) all_116_0 = all_64_2 | proper_subset(all_116_0, all_64_2) % 17.65/3.24 | | | % 17.65/3.24 | | | BETA: splitting (52) gives: % 17.65/3.24 | | | % 17.65/3.24 | | | Case 1: % 17.65/3.24 | | | | % 17.65/3.24 | | | | (53) proper_subset(all_116_0, all_64_2) % 17.65/3.24 | | | | % 17.65/3.24 | | | | GROUND_INST: instantiating (t21_ordinal1) with all_116_0, all_64_2, % 17.65/3.24 | | | | simplifying with (11), (12), (35), (41), (46), (53) gives: % 17.65/3.24 | | | | (54) $false % 17.65/3.24 | | | | % 17.65/3.24 | | | | CLOSE: (54) is inconsistent. % 17.65/3.24 | | | | % 17.65/3.24 | | | Case 2: % 17.65/3.24 | | | | % 17.65/3.24 | | | | (55) all_116_0 = all_64_2 % 17.65/3.24 | | | | % 17.65/3.24 | | | | REDUCE: (49), (55) imply: % 17.65/3.24 | | | | (56) $false % 17.65/3.24 | | | | % 17.65/3.24 | | | | CLOSE: (56) is inconsistent. % 17.65/3.24 | | | | % 17.65/3.24 | | | End of split % 17.65/3.24 | | | % 17.65/3.24 | | End of split % 17.65/3.24 | | % 17.65/3.24 | End of split % 17.65/3.24 | % 17.65/3.24 End of proof % 17.65/3.24 % SZS output end Proof for theBenchmark % 17.65/3.24 % 17.65/3.24 2630ms %------------------------------------------------------------------------------