%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU075+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:42:28 EDT 2023 % Result : Theorem 10.98s 2.30s % Output : Proof 16.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU075+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 23 22:28:21 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.64 ________ _____ % 0.19/0.64 ___ __ \_________(_)________________________________ % 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.64 % 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.64 (2023-06-19) % 0.19/0.64 % 0.19/0.64 (c) Philipp Rümmer, 2009-2023 % 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.64 Amanda Stjerna. % 0.19/0.64 Free software under BSD-3-Clause. % 0.19/0.64 % 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.64 % 0.19/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.66 Running up to 7 provers in parallel. % 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.12/1.17 Prover 4: Preprocessing ... % 3.12/1.17 Prover 1: Preprocessing ... % 3.36/1.21 Prover 2: Preprocessing ... % 3.36/1.21 Prover 0: Preprocessing ... % 3.36/1.21 Prover 3: Preprocessing ... % 3.36/1.21 Prover 6: Preprocessing ... % 3.36/1.21 Prover 5: Preprocessing ... % 6.95/1.70 Prover 1: Warning: ignoring some quantifiers % 6.95/1.76 Prover 3: Warning: ignoring some quantifiers % 6.95/1.76 Prover 1: Constructing countermodel ... % 6.95/1.78 Prover 3: Constructing countermodel ... % 7.63/1.79 Prover 5: Proving ... % 7.69/1.79 Prover 6: Proving ... % 7.84/1.81 Prover 2: Proving ... % 9.20/2.00 Prover 4: Warning: ignoring some quantifiers % 9.20/2.05 Prover 4: Constructing countermodel ... % 9.87/2.10 Prover 0: Proving ... % 10.98/2.30 Prover 3: proved (1626ms) % 10.98/2.30 % 10.98/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.98/2.30 % 10.98/2.30 Prover 6: stopped % 10.98/2.30 Prover 0: stopped % 10.98/2.30 Prover 5: stopped % 11.46/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.46/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.46/2.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.46/2.31 Prover 2: stopped % 11.46/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.46/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.88/2.37 Prover 7: Preprocessing ... % 11.88/2.38 Prover 11: Preprocessing ... % 11.88/2.39 Prover 10: Preprocessing ... % 11.88/2.39 Prover 8: Preprocessing ... % 11.88/2.40 Prover 13: Preprocessing ... % 12.89/2.49 Prover 10: Warning: ignoring some quantifiers % 12.89/2.49 Prover 7: Warning: ignoring some quantifiers % 12.89/2.50 Prover 10: Constructing countermodel ... % 12.89/2.50 Prover 7: Constructing countermodel ... % 12.89/2.51 Prover 8: Warning: ignoring some quantifiers % 12.89/2.52 Prover 8: Constructing countermodel ... % 13.33/2.59 Prover 13: Warning: ignoring some quantifiers % 13.81/2.61 Prover 13: Constructing countermodel ... % 13.81/2.63 Prover 11: Warning: ignoring some quantifiers % 13.81/2.66 Prover 11: Constructing countermodel ... % 15.98/2.94 Prover 10: Found proof (size 67) % 15.98/2.94 Prover 10: proved (640ms) % 15.98/2.94 Prover 11: stopped % 15.98/2.94 Prover 13: stopped % 16.34/2.94 Prover 1: stopped % 16.34/2.94 Prover 7: stopped % 16.34/2.94 Prover 8: stopped % 16.34/2.95 Prover 4: stopped % 16.34/2.95 % 16.34/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.34/2.95 % 16.34/2.95 % SZS output start Proof for theBenchmark % 16.34/2.96 Assumptions after simplification: % 16.34/2.96 --------------------------------- % 16.34/2.96 % 16.34/2.96 (d5_funct_1) % 16.34/2.98 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 16.34/2.98 relation(v0) | ~ function(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & % 16.34/2.98 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v4) = v3) | ~ $i(v4) % 16.34/2.98 | ~ $i(v3) | ~ $i(v1) | ~ in(v4, v2) | in(v3, v1)) & ! [v3: $i] : ( % 16.34/2.98 ~ $i(v3) | ~ $i(v1) | ~ in(v3, v1) | ? [v4: $i] : (apply(v0, v4) = v3 % 16.34/2.98 & $i(v4) & in(v4, v2))) & ? [v3: $i] : (v3 = v1 | ~ $i(v3) | ? [v4: % 16.34/2.98 $i] : ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v3) | % 16.34/2.98 ! [v7: $i] : ( ~ (apply(v0, v7) = v4) | ~ $i(v7) | ~ in(v7, v2))) % 16.34/2.98 & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) % 16.34/2.98 % 16.34/2.98 (t156_funct_1) % 16.34/2.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 % 16.34/2.99 = v2) & relation_composition(v1, v4) = v3 & relation_composition(v1, v2) = % 16.34/2.99 v3 & relation_rng(v1) = v0 & relation_dom(v4) = v0 & relation_dom(v2) = v0 & % 16.34/2.99 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v4) & relation(v2) & % 16.34/2.99 relation(v1) & function(v4) & function(v2) & function(v1)) % 16.34/2.99 % 16.34/2.99 (t23_funct_1) % 16.34/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (apply(v1, v0) = v2) | ~ $i(v1) % 16.34/2.99 | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v3: $i] : % 16.34/2.99 (relation_dom(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (apply(v4, % 16.34/2.99 v2) = v5) | ~ $i(v4) | ~ relation(v4) | ~ function(v4) | ~ % 16.34/2.99 in(v0, v3) | ? [v6: $i] : (relation_composition(v1, v4) = v6 & % 16.34/2.99 apply(v6, v0) = v5 & $i(v6) & $i(v5))))) % 16.34/2.99 % 16.34/2.99 (t9_funct_1) % 16.34/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (relation_dom(v2) = % 16.34/2.99 v1) | ~ (relation_dom(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ relation(v2) % 16.34/2.99 | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3: $i] : ? % 16.34/2.99 [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3) % 16.34/2.99 = v4 & $i(v5) & $i(v4) & $i(v3) & in(v3, v1))) % 16.34/2.99 % 16.34/2.99 (function-axioms) % 16.34/3.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.34/3.00 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 16.34/3.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 16.34/3.00 ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 16.34/3.00 $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = % 16.34/3.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.34/3.00 (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! % 16.34/3.00 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 16.34/3.00 (relation_dom(v2) = v0)) % 16.34/3.00 % 16.34/3.00 Further assumptions not needed in the proof: % 16.34/3.00 -------------------------------------------- % 16.34/3.00 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k5_relat_1, % 16.34/3.00 existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_funct_1, fc1_subset_1, % 16.34/3.00 fc1_xboole_0, fc4_relat_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, % 16.34/3.00 fc9_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1, % 16.34/3.00 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, % 16.34/3.00 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 16.34/3.00 t6_boole, t7_boole, t8_boole % 16.34/3.00 % 16.34/3.00 Those formulas are unsatisfiable: % 16.34/3.00 --------------------------------- % 16.34/3.00 % 16.34/3.00 Begin of proof % 16.34/3.00 | % 16.34/3.00 | ALPHA: (function-axioms) implies: % 16.34/3.00 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.34/3.00 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 16.34/3.00 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.34/3.00 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 16.34/3.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.34/3.00 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 16.34/3.00 | v2) = v0)) % 16.34/3.00 | % 16.34/3.00 | DELTA: instantiating (t156_funct_1) with fresh symbols all_48_0, all_48_1, % 16.34/3.00 | all_48_2, all_48_3, all_48_4 gives: % 16.34/3.00 | (4) ~ (all_48_0 = all_48_2) & relation_composition(all_48_3, all_48_0) = % 16.34/3.00 | all_48_1 & relation_composition(all_48_3, all_48_2) = all_48_1 & % 16.34/3.00 | relation_rng(all_48_3) = all_48_4 & relation_dom(all_48_0) = all_48_4 & % 16.34/3.00 | relation_dom(all_48_2) = all_48_4 & $i(all_48_0) & $i(all_48_1) & % 16.34/3.00 | $i(all_48_2) & $i(all_48_3) & $i(all_48_4) & relation(all_48_0) & % 16.34/3.00 | relation(all_48_2) & relation(all_48_3) & function(all_48_0) & % 16.34/3.00 | function(all_48_2) & function(all_48_3) % 16.34/3.00 | % 16.34/3.00 | ALPHA: (4) implies: % 16.34/3.00 | (5) ~ (all_48_0 = all_48_2) % 16.34/3.00 | (6) function(all_48_3) % 16.34/3.00 | (7) function(all_48_2) % 16.34/3.00 | (8) function(all_48_0) % 16.34/3.00 | (9) relation(all_48_3) % 16.34/3.00 | (10) relation(all_48_2) % 16.34/3.00 | (11) relation(all_48_0) % 16.34/3.00 | (12) $i(all_48_4) % 16.34/3.01 | (13) $i(all_48_3) % 16.34/3.01 | (14) $i(all_48_2) % 16.34/3.01 | (15) $i(all_48_0) % 16.34/3.01 | (16) relation_dom(all_48_2) = all_48_4 % 16.34/3.01 | (17) relation_dom(all_48_0) = all_48_4 % 16.34/3.01 | (18) relation_rng(all_48_3) = all_48_4 % 16.34/3.01 | (19) relation_composition(all_48_3, all_48_2) = all_48_1 % 16.34/3.01 | (20) relation_composition(all_48_3, all_48_0) = all_48_1 % 16.34/3.01 | % 16.34/3.01 | GROUND_INST: instantiating (t9_funct_1) with all_48_2, all_48_4, all_48_0, % 16.34/3.01 | simplifying with (7), (8), (10), (11), (14), (15), (16), (17) % 16.34/3.01 | gives: % 16.34/3.01 | (21) all_48_0 = all_48_2 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ % 16.34/3.01 | (v2 = v1) & apply(all_48_0, v0) = v2 & apply(all_48_2, v0) = v1 & % 16.34/3.01 | $i(v2) & $i(v1) & $i(v0) & in(v0, all_48_4)) % 16.34/3.01 | % 16.34/3.01 | GROUND_INST: instantiating (t9_funct_1) with all_48_0, all_48_4, all_48_2, % 16.34/3.01 | simplifying with (7), (8), (10), (11), (14), (15), (16), (17) % 16.34/3.01 | gives: % 16.34/3.01 | (22) all_48_0 = all_48_2 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ % 16.34/3.01 | (v2 = v1) & apply(all_48_0, v0) = v1 & apply(all_48_2, v0) = v2 & % 16.34/3.01 | $i(v2) & $i(v1) & $i(v0) & in(v0, all_48_4)) % 16.34/3.01 | % 16.34/3.01 | GROUND_INST: instantiating (d5_funct_1) with all_48_3, all_48_4, simplifying % 16.34/3.01 | with (6), (9), (13), (18) gives: % 16.34/3.01 | (23) ? [v0: $i] : (relation_dom(all_48_3) = v0 & $i(v0) & ! [v1: $i] : ! % 16.34/3.01 | [v2: $i] : ( ~ (apply(all_48_3, v2) = v1) | ~ $i(v2) | ~ $i(v1) | % 16.34/3.01 | ~ $i(all_48_4) | ~ in(v2, v0) | in(v1, all_48_4)) & ! [v1: $i] : % 16.34/3.01 | ( ~ $i(v1) | ~ $i(all_48_4) | ~ in(v1, all_48_4) | ? [v2: $i] : % 16.34/3.01 | (apply(all_48_3, v2) = v1 & $i(v2) & in(v2, v0))) & ? [v1: any] : % 16.34/3.01 | (v1 = all_48_4 | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 16.34/3.01 | : ($i(v3) & $i(v2) & ( ~ in(v2, v1) | ! [v5: $i] : ( ~ % 16.34/3.01 | (apply(all_48_3, v5) = v2) | ~ $i(v5) | ~ in(v5, v0))) & % 16.34/3.01 | (in(v2, v1) | (v4 = v2 & apply(all_48_3, v3) = v2 & in(v3, % 16.34/3.01 | v0)))))) % 16.34/3.01 | % 16.34/3.01 | DELTA: instantiating (23) with fresh symbol all_56_0 gives: % 16.34/3.01 | (24) relation_dom(all_48_3) = all_56_0 & $i(all_56_0) & ! [v0: $i] : ! % 16.34/3.01 | [v1: $i] : ( ~ (apply(all_48_3, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 16.34/3.01 | $i(all_48_4) | ~ in(v1, all_56_0) | in(v0, all_48_4)) & ! [v0: $i] % 16.34/3.01 | : ( ~ $i(v0) | ~ $i(all_48_4) | ~ in(v0, all_48_4) | ? [v1: $i] : % 16.34/3.01 | (apply(all_48_3, v1) = v0 & $i(v1) & in(v1, all_56_0))) & ? [v0: % 16.34/3.01 | any] : (v0 = all_48_4 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? % 16.34/3.01 | [v3: $i] : ($i(v2) & $i(v1) & ( ~ in(v1, v0) | ! [v4: $i] : ( ~ % 16.34/3.01 | (apply(all_48_3, v4) = v1) | ~ $i(v4) | ~ in(v4, all_56_0))) % 16.34/3.01 | & (in(v1, v0) | (v3 = v1 & apply(all_48_3, v2) = v1 & in(v2, % 16.34/3.01 | all_56_0))))) % 16.34/3.02 | % 16.34/3.02 | ALPHA: (24) implies: % 16.34/3.02 | (25) relation_dom(all_48_3) = all_56_0 % 16.34/3.02 | (26) ! [v0: $i] : ( ~ $i(v0) | ~ $i(all_48_4) | ~ in(v0, all_48_4) | ? % 16.34/3.02 | [v1: $i] : (apply(all_48_3, v1) = v0 & $i(v1) & in(v1, all_56_0))) % 16.34/3.02 | % 16.34/3.02 | BETA: splitting (22) gives: % 16.34/3.02 | % 16.34/3.02 | Case 1: % 16.34/3.02 | | % 16.34/3.02 | | (27) all_48_0 = all_48_2 % 16.34/3.02 | | % 16.34/3.02 | | REDUCE: (5), (27) imply: % 16.34/3.02 | | (28) $false % 16.34/3.02 | | % 16.34/3.02 | | CLOSE: (28) is inconsistent. % 16.34/3.02 | | % 16.34/3.02 | Case 2: % 16.34/3.02 | | % 16.34/3.02 | | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 16.34/3.02 | | apply(all_48_0, v0) = v1 & apply(all_48_2, v0) = v2 & $i(v2) & % 16.34/3.02 | | $i(v1) & $i(v0) & in(v0, all_48_4)) % 16.34/3.02 | | % 16.34/3.02 | | DELTA: instantiating (29) with fresh symbols all_64_0, all_64_1, all_64_2 % 16.34/3.02 | | gives: % 16.34/3.02 | | (30) ~ (all_64_0 = all_64_1) & apply(all_48_0, all_64_2) = all_64_1 & % 16.34/3.02 | | apply(all_48_2, all_64_2) = all_64_0 & $i(all_64_0) & $i(all_64_1) & % 16.34/3.02 | | $i(all_64_2) & in(all_64_2, all_48_4) % 16.34/3.02 | | % 16.34/3.02 | | ALPHA: (30) implies: % 16.34/3.02 | | (31) ~ (all_64_0 = all_64_1) % 16.34/3.02 | | (32) in(all_64_2, all_48_4) % 16.34/3.02 | | (33) $i(all_64_2) % 16.34/3.02 | | (34) apply(all_48_2, all_64_2) = all_64_0 % 16.34/3.02 | | (35) apply(all_48_0, all_64_2) = all_64_1 % 16.34/3.02 | | % 16.34/3.02 | | BETA: splitting (21) gives: % 16.34/3.02 | | % 16.34/3.02 | | Case 1: % 16.34/3.02 | | | % 16.34/3.02 | | | (36) all_48_0 = all_48_2 % 16.34/3.02 | | | % 16.34/3.02 | | | REDUCE: (5), (36) imply: % 16.34/3.02 | | | (37) $false % 16.34/3.02 | | | % 16.34/3.02 | | | CLOSE: (37) is inconsistent. % 16.34/3.02 | | | % 16.34/3.02 | | Case 2: % 16.34/3.02 | | | % 16.34/3.02 | | | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 16.34/3.02 | | | apply(all_48_0, v0) = v2 & apply(all_48_2, v0) = v1 & $i(v2) & % 16.34/3.02 | | | $i(v1) & $i(v0) & in(v0, all_48_4)) % 16.34/3.02 | | | % 16.34/3.02 | | | DELTA: instantiating (38) with fresh symbols all_69_0, all_69_1, all_69_2 % 16.34/3.02 | | | gives: % 16.34/3.02 | | | (39) ~ (all_69_0 = all_69_1) & apply(all_48_0, all_69_2) = all_69_0 & % 16.34/3.02 | | | apply(all_48_2, all_69_2) = all_69_1 & $i(all_69_0) & $i(all_69_1) % 16.34/3.02 | | | & $i(all_69_2) & in(all_69_2, all_48_4) % 16.34/3.02 | | | % 16.34/3.02 | | | ALPHA: (39) implies: % 16.34/3.02 | | | (40) in(all_69_2, all_48_4) % 16.34/3.02 | | | (41) $i(all_69_2) % 16.34/3.02 | | | (42) apply(all_48_2, all_69_2) = all_69_1 % 16.34/3.02 | | | % 16.34/3.02 | | | GROUND_INST: instantiating (26) with all_64_2, simplifying with (12), % 16.34/3.02 | | | (32), (33) gives: % 16.34/3.02 | | | (43) ? [v0: $i] : (apply(all_48_3, v0) = all_64_2 & $i(v0) & in(v0, % 16.34/3.02 | | | all_56_0)) % 16.34/3.02 | | | % 16.34/3.02 | | | GROUND_INST: instantiating (26) with all_69_2, simplifying with (12), % 16.34/3.02 | | | (40), (41) gives: % 16.34/3.02 | | | (44) ? [v0: $i] : (apply(all_48_3, v0) = all_69_2 & $i(v0) & in(v0, % 16.34/3.02 | | | all_56_0)) % 16.34/3.02 | | | % 16.34/3.02 | | | DELTA: instantiating (43) with fresh symbol all_77_0 gives: % 16.34/3.02 | | | (45) apply(all_48_3, all_77_0) = all_64_2 & $i(all_77_0) & in(all_77_0, % 16.34/3.02 | | | all_56_0) % 16.34/3.02 | | | % 16.34/3.02 | | | ALPHA: (45) implies: % 16.34/3.02 | | | (46) in(all_77_0, all_56_0) % 16.34/3.02 | | | (47) $i(all_77_0) % 16.34/3.02 | | | (48) apply(all_48_3, all_77_0) = all_64_2 % 16.34/3.02 | | | % 16.34/3.02 | | | DELTA: instantiating (44) with fresh symbol all_79_0 gives: % 16.34/3.02 | | | (49) apply(all_48_3, all_79_0) = all_69_2 & $i(all_79_0) & in(all_79_0, % 16.34/3.02 | | | all_56_0) % 16.34/3.02 | | | % 16.34/3.02 | | | ALPHA: (49) implies: % 16.34/3.03 | | | (50) in(all_79_0, all_56_0) % 16.34/3.03 | | | (51) $i(all_79_0) % 16.34/3.03 | | | (52) apply(all_48_3, all_79_0) = all_69_2 % 16.34/3.03 | | | % 16.34/3.03 | | | GROUND_INST: instantiating (t23_funct_1) with all_77_0, all_48_3, % 16.34/3.03 | | | all_64_2, simplifying with (6), (9), (13), (47), (48) gives: % 16.34/3.03 | | | (53) ? [v0: $i] : (relation_dom(all_48_3) = v0 & $i(v0) & ! [v1: $i] % 16.34/3.03 | | | : ! [v2: $i] : ( ~ (apply(v1, all_64_2) = v2) | ~ $i(v1) | ~ % 16.34/3.03 | | | relation(v1) | ~ function(v1) | ~ in(all_77_0, v0) | ? [v3: % 16.34/3.03 | | | $i] : (relation_composition(all_48_3, v1) = v3 & apply(v3, % 16.34/3.03 | | | all_77_0) = v2 & $i(v3) & $i(v2)))) % 16.34/3.03 | | | % 16.34/3.03 | | | GROUND_INST: instantiating (t23_funct_1) with all_79_0, all_48_3, % 16.34/3.03 | | | all_69_2, simplifying with (6), (9), (13), (51), (52) gives: % 16.34/3.03 | | | (54) ? [v0: $i] : (relation_dom(all_48_3) = v0 & $i(v0) & ! [v1: $i] % 16.34/3.03 | | | : ! [v2: $i] : ( ~ (apply(v1, all_69_2) = v2) | ~ $i(v1) | ~ % 16.34/3.03 | | | relation(v1) | ~ function(v1) | ~ in(all_79_0, v0) | ? [v3: % 16.34/3.03 | | | $i] : (relation_composition(all_48_3, v1) = v3 & apply(v3, % 16.34/3.03 | | | all_79_0) = v2 & $i(v3) & $i(v2)))) % 16.34/3.03 | | | % 16.34/3.03 | | | DELTA: instantiating (54) with fresh symbol all_103_0 gives: % 16.34/3.03 | | | (55) relation_dom(all_48_3) = all_103_0 & $i(all_103_0) & ! [v0: $i] : % 16.34/3.03 | | | ! [v1: $i] : ( ~ (apply(v0, all_69_2) = v1) | ~ $i(v0) | ~ % 16.34/3.03 | | | relation(v0) | ~ function(v0) | ~ in(all_79_0, all_103_0) | ? % 16.34/3.03 | | | [v2: $i] : (relation_composition(all_48_3, v0) = v2 & apply(v2, % 16.34/3.03 | | | all_79_0) = v1 & $i(v2) & $i(v1))) % 16.34/3.03 | | | % 16.34/3.03 | | | ALPHA: (55) implies: % 16.34/3.03 | | | (56) relation_dom(all_48_3) = all_103_0 % 16.34/3.03 | | | (57) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(v0, all_69_2) = v1) | ~ % 16.34/3.03 | | | $i(v0) | ~ relation(v0) | ~ function(v0) | ~ in(all_79_0, % 16.34/3.03 | | | all_103_0) | ? [v2: $i] : (relation_composition(all_48_3, v0) % 16.34/3.03 | | | = v2 & apply(v2, all_79_0) = v1 & $i(v2) & $i(v1))) % 16.34/3.03 | | | % 16.34/3.03 | | | DELTA: instantiating (53) with fresh symbol all_106_0 gives: % 16.34/3.03 | | | (58) relation_dom(all_48_3) = all_106_0 & $i(all_106_0) & ! [v0: $i] : % 16.34/3.03 | | | ! [v1: $i] : ( ~ (apply(v0, all_64_2) = v1) | ~ $i(v0) | ~ % 16.34/3.03 | | | relation(v0) | ~ function(v0) | ~ in(all_77_0, all_106_0) | ? % 16.34/3.03 | | | [v2: $i] : (relation_composition(all_48_3, v0) = v2 & apply(v2, % 16.34/3.03 | | | all_77_0) = v1 & $i(v2) & $i(v1))) % 16.34/3.03 | | | % 16.34/3.03 | | | ALPHA: (58) implies: % 16.34/3.03 | | | (59) relation_dom(all_48_3) = all_106_0 % 16.34/3.03 | | | (60) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(v0, all_64_2) = v1) | ~ % 16.34/3.03 | | | $i(v0) | ~ relation(v0) | ~ function(v0) | ~ in(all_77_0, % 16.34/3.03 | | | all_106_0) | ? [v2: $i] : (relation_composition(all_48_3, v0) % 16.34/3.03 | | | = v2 & apply(v2, all_77_0) = v1 & $i(v2) & $i(v1))) % 16.34/3.03 | | | % 16.34/3.03 | | | GROUND_INST: instantiating (1) with all_56_0, all_106_0, all_48_3, % 16.34/3.03 | | | simplifying with (25), (59) gives: % 16.34/3.03 | | | (61) all_106_0 = all_56_0 % 16.34/3.03 | | | % 16.34/3.03 | | | GROUND_INST: instantiating (1) with all_103_0, all_106_0, all_48_3, % 16.34/3.03 | | | simplifying with (56), (59) gives: % 16.34/3.03 | | | (62) all_106_0 = all_103_0 % 16.34/3.03 | | | % 16.34/3.03 | | | COMBINE_EQS: (61), (62) imply: % 16.34/3.03 | | | (63) all_103_0 = all_56_0 % 16.34/3.03 | | | % 16.34/3.03 | | | GROUND_INST: instantiating (60) with all_48_2, all_64_0, simplifying with % 16.34/3.03 | | | (7), (10), (14), (34) gives: % 16.34/3.03 | | | (64) ~ in(all_77_0, all_106_0) | ? [v0: $i] : % 16.34/3.03 | | | (relation_composition(all_48_3, all_48_2) = v0 & apply(v0, % 16.34/3.03 | | | all_77_0) = all_64_0 & $i(v0) & $i(all_64_0)) % 16.34/3.03 | | | % 16.34/3.04 | | | GROUND_INST: instantiating (57) with all_48_2, all_69_1, simplifying with % 16.34/3.04 | | | (7), (10), (14), (42) gives: % 16.34/3.04 | | | (65) ~ in(all_79_0, all_103_0) | ? [v0: $i] : % 16.34/3.04 | | | (relation_composition(all_48_3, all_48_2) = v0 & apply(v0, % 16.34/3.04 | | | all_79_0) = all_69_1 & $i(v0) & $i(all_69_1)) % 16.34/3.04 | | | % 16.34/3.04 | | | GROUND_INST: instantiating (60) with all_48_0, all_64_1, simplifying with % 16.34/3.04 | | | (8), (11), (15), (35) gives: % 16.34/3.04 | | | (66) ~ in(all_77_0, all_106_0) | ? [v0: $i] : % 16.34/3.04 | | | (relation_composition(all_48_3, all_48_0) = v0 & apply(v0, % 16.34/3.04 | | | all_77_0) = all_64_1 & $i(v0) & $i(all_64_1)) % 16.34/3.04 | | | % 16.34/3.04 | | | BETA: splitting (66) gives: % 16.34/3.04 | | | % 16.34/3.04 | | | Case 1: % 16.34/3.04 | | | | % 16.34/3.04 | | | | (67) ~ in(all_77_0, all_106_0) % 16.34/3.04 | | | | % 16.34/3.04 | | | | REDUCE: (61), (67) imply: % 16.34/3.04 | | | | (68) ~ in(all_77_0, all_56_0) % 16.34/3.04 | | | | % 16.34/3.04 | | | | PRED_UNIFY: (46), (68) imply: % 16.34/3.04 | | | | (69) $false % 16.34/3.04 | | | | % 16.34/3.04 | | | | CLOSE: (69) is inconsistent. % 16.34/3.04 | | | | % 16.34/3.04 | | | Case 2: % 16.34/3.04 | | | | % 16.34/3.04 | | | | (70) in(all_77_0, all_106_0) % 16.34/3.04 | | | | (71) ? [v0: $i] : (relation_composition(all_48_3, all_48_0) = v0 & % 16.34/3.04 | | | | apply(v0, all_77_0) = all_64_1 & $i(v0) & $i(all_64_1)) % 16.34/3.04 | | | | % 16.34/3.04 | | | | DELTA: instantiating (71) with fresh symbol all_169_0 gives: % 16.34/3.04 | | | | (72) relation_composition(all_48_3, all_48_0) = all_169_0 & % 16.34/3.04 | | | | apply(all_169_0, all_77_0) = all_64_1 & $i(all_169_0) & % 16.34/3.04 | | | | $i(all_64_1) % 16.34/3.04 | | | | % 16.34/3.04 | | | | ALPHA: (72) implies: % 16.34/3.04 | | | | (73) apply(all_169_0, all_77_0) = all_64_1 % 16.34/3.04 | | | | (74) relation_composition(all_48_3, all_48_0) = all_169_0 % 16.34/3.04 | | | | % 16.34/3.04 | | | | BETA: splitting (65) gives: % 16.34/3.04 | | | | % 16.34/3.04 | | | | Case 1: % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | (75) ~ in(all_79_0, all_103_0) % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | REDUCE: (63), (75) imply: % 16.34/3.04 | | | | | (76) ~ in(all_79_0, all_56_0) % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | PRED_UNIFY: (50), (76) imply: % 16.34/3.04 | | | | | (77) $false % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | CLOSE: (77) is inconsistent. % 16.34/3.04 | | | | | % 16.34/3.04 | | | | Case 2: % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | (78) ? [v0: $i] : (relation_composition(all_48_3, all_48_2) = v0 & % 16.34/3.04 | | | | | apply(v0, all_79_0) = all_69_1 & $i(v0) & $i(all_69_1)) % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | DELTA: instantiating (78) with fresh symbol all_175_0 gives: % 16.34/3.04 | | | | | (79) relation_composition(all_48_3, all_48_2) = all_175_0 & % 16.34/3.04 | | | | | apply(all_175_0, all_79_0) = all_69_1 & $i(all_175_0) & % 16.34/3.04 | | | | | $i(all_69_1) % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | ALPHA: (79) implies: % 16.34/3.04 | | | | | (80) relation_composition(all_48_3, all_48_2) = all_175_0 % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | BETA: splitting (64) gives: % 16.34/3.04 | | | | | % 16.34/3.04 | | | | | Case 1: % 16.34/3.04 | | | | | | % 16.34/3.04 | | | | | | (81) ~ in(all_77_0, all_106_0) % 16.34/3.04 | | | | | | % 16.34/3.04 | | | | | | REDUCE: (61), (81) imply: % 16.34/3.04 | | | | | | (82) ~ in(all_77_0, all_56_0) % 16.34/3.04 | | | | | | % 16.34/3.04 | | | | | | PRED_UNIFY: (46), (82) imply: % 16.34/3.04 | | | | | | (83) $false % 16.34/3.04 | | | | | | % 16.34/3.04 | | | | | | CLOSE: (83) is inconsistent. % 16.34/3.04 | | | | | | % 16.34/3.04 | | | | | Case 2: % 16.34/3.04 | | | | | | % 16.34/3.04 | | | | | | (84) ? [v0: $i] : (relation_composition(all_48_3, all_48_2) = v0 % 16.34/3.04 | | | | | | & apply(v0, all_77_0) = all_64_0 & $i(v0) & $i(all_64_0)) % 16.34/3.04 | | | | | | % 16.34/3.04 | | | | | | DELTA: instantiating (84) with fresh symbol all_181_0 gives: % 16.82/3.04 | | | | | | (85) relation_composition(all_48_3, all_48_2) = all_181_0 & % 16.82/3.04 | | | | | | apply(all_181_0, all_77_0) = all_64_0 & $i(all_181_0) & % 16.82/3.04 | | | | | | $i(all_64_0) % 16.82/3.04 | | | | | | % 16.82/3.04 | | | | | | ALPHA: (85) implies: % 16.82/3.04 | | | | | | (86) apply(all_181_0, all_77_0) = all_64_0 % 16.82/3.04 | | | | | | (87) relation_composition(all_48_3, all_48_2) = all_181_0 % 16.82/3.04 | | | | | | % 16.82/3.04 | | | | | | GROUND_INST: instantiating (3) with all_48_1, all_181_0, all_48_2, % 16.82/3.04 | | | | | | all_48_3, simplifying with (19), (87) gives: % 16.82/3.04 | | | | | | (88) all_181_0 = all_48_1 % 16.82/3.04 | | | | | | % 16.82/3.04 | | | | | | GROUND_INST: instantiating (3) with all_175_0, all_181_0, all_48_2, % 16.82/3.04 | | | | | | all_48_3, simplifying with (80), (87) gives: % 16.82/3.04 | | | | | | (89) all_181_0 = all_175_0 % 16.82/3.04 | | | | | | % 16.82/3.04 | | | | | | GROUND_INST: instantiating (3) with all_48_1, all_169_0, all_48_0, % 16.82/3.04 | | | | | | all_48_3, simplifying with (20), (74) gives: % 16.82/3.04 | | | | | | (90) all_169_0 = all_48_1 % 16.82/3.04 | | | | | | % 16.82/3.04 | | | | | | COMBINE_EQS: (88), (89) imply: % 16.82/3.04 | | | | | | (91) all_175_0 = all_48_1 % 16.82/3.04 | | | | | | % 16.82/3.05 | | | | | | REDUCE: (86), (88) imply: % 16.82/3.05 | | | | | | (92) apply(all_48_1, all_77_0) = all_64_0 % 16.82/3.05 | | | | | | % 16.82/3.05 | | | | | | REDUCE: (73), (90) imply: % 16.82/3.05 | | | | | | (93) apply(all_48_1, all_77_0) = all_64_1 % 16.82/3.05 | | | | | | % 16.82/3.05 | | | | | | GROUND_INST: instantiating (2) with all_64_1, all_64_0, all_77_0, % 16.82/3.05 | | | | | | all_48_1, simplifying with (92), (93) gives: % 16.82/3.05 | | | | | | (94) all_64_0 = all_64_1 % 16.82/3.05 | | | | | | % 16.82/3.05 | | | | | | REDUCE: (31), (94) imply: % 16.82/3.05 | | | | | | (95) $false % 16.82/3.05 | | | | | | % 16.82/3.05 | | | | | | CLOSE: (95) is inconsistent. % 16.82/3.05 | | | | | | % 16.82/3.05 | | | | | End of split % 16.82/3.05 | | | | | % 16.82/3.05 | | | | End of split % 16.82/3.05 | | | | % 16.82/3.05 | | | End of split % 16.82/3.05 | | | % 16.82/3.05 | | End of split % 16.82/3.05 | | % 16.82/3.05 | End of split % 16.82/3.05 | % 16.82/3.05 End of proof % 16.82/3.05 % SZS output end Proof for theBenchmark % 16.82/3.05 % 16.82/3.05 2408ms %------------------------------------------------------------------------------