%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0. % 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 15:25:57 EDT 2023 % Result : Theorem 11.48s 2.30s % Output : Proof 15.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SET676+3 : TPTP v8.1.2. Released v2.2.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n009.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 12:09:20 EDT 2023 % 0.14/0.35 % CPUTime : % 0.70/0.65 ________ _____ % 0.70/0.65 ___ __ \_________(_)________________________________ % 0.70/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.70/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.70/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.70/0.65 % 0.70/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.70/0.65 (2023-06-19) % 0.70/0.65 % 0.70/0.65 (c) Philipp Rümmer, 2009-2023 % 0.70/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.70/0.65 Amanda Stjerna. % 0.70/0.65 Free software under BSD-3-Clause. % 0.70/0.65 % 0.70/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.70/0.65 % 0.70/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.66 Running up to 7 provers in parallel. % 0.70/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.85/1.11 Prover 1: Preprocessing ... % 2.85/1.11 Prover 4: Preprocessing ... % 2.85/1.15 Prover 0: Preprocessing ... % 2.85/1.15 Prover 6: Preprocessing ... % 2.85/1.15 Prover 2: Preprocessing ... % 2.85/1.15 Prover 3: Preprocessing ... % 2.85/1.15 Prover 5: Preprocessing ... % 7.51/1.70 Prover 1: Constructing countermodel ... % 7.51/1.70 Prover 3: Constructing countermodel ... % 7.51/1.72 Prover 6: Proving ... % 7.51/1.72 Prover 5: Proving ... % 7.51/1.73 Prover 2: Proving ... % 10.66/2.17 Prover 4: Constructing countermodel ... % 10.66/2.22 Prover 0: Proving ... % 11.48/2.29 Prover 3: proved (1621ms) % 11.48/2.30 % 11.48/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.48/2.30 % 11.48/2.30 Prover 5: stopped % 12.11/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.11/2.31 Prover 6: stopped % 12.11/2.31 Prover 2: stopped % 12.11/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.11/2.32 Prover 0: stopped % 12.11/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.11/2.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.11/2.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.11/2.35 Prover 8: Preprocessing ... % 12.11/2.35 Prover 7: Preprocessing ... % 12.11/2.36 Prover 10: Preprocessing ... % 12.11/2.36 Prover 11: Preprocessing ... % 12.11/2.38 Prover 13: Preprocessing ... % 12.76/2.45 Prover 10: Warning: ignoring some quantifiers % 12.76/2.46 Prover 7: Warning: ignoring some quantifiers % 12.76/2.47 Prover 10: Constructing countermodel ... % 12.76/2.48 Prover 7: Constructing countermodel ... % 13.56/2.50 Prover 8: Warning: ignoring some quantifiers % 13.72/2.52 Prover 8: Constructing countermodel ... % 13.72/2.55 Prover 13: Warning: ignoring some quantifiers % 13.72/2.56 Prover 13: Constructing countermodel ... % 14.42/2.61 Prover 10: Found proof (size 25) % 14.42/2.61 Prover 10: proved (293ms) % 14.42/2.61 Prover 13: stopped % 14.42/2.61 Prover 1: stopped % 14.42/2.61 Prover 8: stopped % 14.42/2.61 Prover 4: stopped % 14.42/2.61 Prover 7: stopped % 14.83/2.75 Prover 11: Constructing countermodel ... % 14.83/2.76 Prover 11: stopped % 14.83/2.76 % 14.83/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.83/2.76 % 14.83/2.77 % SZS output start Proof for theBenchmark % 14.83/2.77 Assumptions after simplification: % 14.83/2.77 --------------------------------- % 14.83/2.77 % 14.83/2.77 (p1) % 15.31/2.79 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.31/2.79 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 15.31/2.79 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0, % 15.31/2.79 v1) = v3 & $i(v3) & ilf_type(v3, v2))) % 15.31/2.79 % 15.31/2.79 (p3) % 15.31/2.79 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.31/2.79 (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 15.31/2.80 set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 15.31/2.80 % 15.31/2.80 (p4) % 15.31/2.80 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of_type(v0) % 15.31/2.80 = v1) | ~ $i(v0) | ~ ilf_type(v0, set_type) | ? [v2: $i] : % 15.31/2.80 (relation_type(v0, v0) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ % 15.31/2.80 ilf_type(v3, v2) | ~ ilf_type(v3, set_type) | ilf_type(v3, v1)) & ! % 15.31/2.80 [v3: $i] : ( ~ $i(v3) | ~ ilf_type(v3, v1) | ~ ilf_type(v3, set_type) | % 15.31/2.80 ilf_type(v3, v2)))) % 15.31/2.80 % 15.31/2.80 (p7) % 15.31/2.80 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.31/2.80 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 15.31/2.80 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : % 15.31/2.80 (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) & ! % 15.31/2.80 [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5: % 15.31/2.80 $i] : ( ~ $i(v5) | ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) % 15.31/2.80 % 15.31/2.80 (prove_relset_1_41) % 15.31/2.80 $i(set_type) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 15.31/2.80 (identity_relation_of_type(v0) = v2 & cross_product(v0, v0) = v1 & $i(v2) & % 15.31/2.80 $i(v1) & $i(v0) & ilf_type(v0, set_type) & ~ ilf_type(v1, v2)) % 15.31/2.80 % 15.31/2.80 (function-axioms) % 15.31/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.31/2.80 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 15.31/2.80 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_type(v3, % 15.31/2.80 v2) = v1) | ~ (relation_type(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 15.31/2.80 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ % 15.31/2.80 (cross_product(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.31/2.80 (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0: $i] : % 15.31/2.80 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member_type(v2) = v1) | ~ % 15.31/2.80 (member_type(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 15.31/2.80 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) & ! [v0: $i] : ! % 15.31/2.80 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation_of_type(v2) = v1) | % 15.31/2.80 ~ (identity_relation_of_type(v2) = v0)) % 15.31/2.80 % 15.31/2.80 Further assumptions not needed in the proof: % 15.31/2.80 -------------------------------------------- % 15.31/2.80 p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p2, p5, p6, p8, p9 % 15.31/2.80 % 15.31/2.80 Those formulas are unsatisfiable: % 15.31/2.80 --------------------------------- % 15.31/2.80 % 15.31/2.80 Begin of proof % 15.31/2.81 | % 15.31/2.81 | ALPHA: (p1) implies: % 15.31/2.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = % 15.31/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 15.31/2.81 | ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0, v1) = v3 & % 15.31/2.81 | $i(v3) & ilf_type(v3, v2))) % 15.31/2.81 | % 15.31/2.81 | ALPHA: (p3) implies: % 15.31/2.81 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) = % 15.31/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 15.31/2.81 | ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 15.31/2.81 | % 15.31/2.81 | ALPHA: (p4) implies: % 15.31/2.81 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of_type(v0) = v1) | % 15.31/2.81 | ~ $i(v0) | ~ ilf_type(v0, set_type) | ? [v2: $i] : % 15.31/2.81 | (relation_type(v0, v0) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ % 15.31/2.81 | ilf_type(v3, v2) | ~ ilf_type(v3, set_type) | ilf_type(v3, v1)) % 15.31/2.81 | & ! [v3: $i] : ( ~ $i(v3) | ~ ilf_type(v3, v1) | ~ ilf_type(v3, % 15.31/2.81 | set_type) | ilf_type(v3, v2)))) % 15.31/2.81 | % 15.31/2.81 | ALPHA: (p7) implies: % 15.31/2.81 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = % 15.31/2.81 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 15.31/2.81 | ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : (subset_type(v3) % 15.31/2.81 | = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) & ! [v5: $i] : % 15.31/2.81 | ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5: $i] % 15.31/2.81 | : ( ~ $i(v5) | ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) % 15.31/2.81 | % 15.31/2.81 | ALPHA: (prove_relset_1_41) implies: % 15.31/2.81 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 15.31/2.81 | (identity_relation_of_type(v0) = v2 & cross_product(v0, v0) = v1 & % 15.31/2.81 | $i(v2) & $i(v1) & $i(v0) & ilf_type(v0, set_type) & ~ ilf_type(v1, % 15.31/2.81 | v2)) % 15.31/2.81 | % 15.31/2.81 | ALPHA: (function-axioms) implies: % 15.31/2.81 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.31/2.81 | (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 15.31/2.81 | % 15.31/2.81 | DELTA: instantiating (5) with fresh symbols all_23_0, all_23_1, all_23_2 % 15.31/2.81 | gives: % 15.31/2.81 | (7) identity_relation_of_type(all_23_2) = all_23_0 & % 15.31/2.81 | cross_product(all_23_2, all_23_2) = all_23_1 & $i(all_23_0) & % 15.31/2.81 | $i(all_23_1) & $i(all_23_2) & ilf_type(all_23_2, set_type) & ~ % 15.31/2.81 | ilf_type(all_23_1, all_23_0) % 15.31/2.82 | % 15.31/2.82 | ALPHA: (7) implies: % 15.43/2.82 | (8) ~ ilf_type(all_23_1, all_23_0) % 15.43/2.82 | (9) ilf_type(all_23_2, set_type) % 15.43/2.82 | (10) $i(all_23_2) % 15.43/2.82 | (11) cross_product(all_23_2, all_23_2) = all_23_1 % 15.43/2.82 | (12) identity_relation_of_type(all_23_2) = all_23_0 % 15.43/2.82 | % 15.43/2.82 | GROUND_INST: instantiating (2) with all_23_2, all_23_2, all_23_1, simplifying % 15.43/2.82 | with (9), (10), (11) gives: % 15.43/2.82 | (13) ilf_type(all_23_1, set_type) % 15.43/2.82 | % 15.43/2.82 | GROUND_INST: instantiating (3) with all_23_2, all_23_0, simplifying with (9), % 15.43/2.82 | (10), (12) gives: % 15.43/2.82 | (14) ? [v0: $i] : (relation_type(all_23_2, all_23_2) = v0 & $i(v0) & ! % 15.43/2.82 | [v1: $i] : ( ~ $i(v1) | ~ ilf_type(v1, v0) | ~ ilf_type(v1, % 15.43/2.82 | set_type) | ilf_type(v1, all_23_0)) & ! [v1: $i] : ( ~ $i(v1) | % 15.43/2.82 | ~ ilf_type(v1, all_23_0) | ~ ilf_type(v1, set_type) | % 15.43/2.82 | ilf_type(v1, v0))) % 15.43/2.82 | % 15.43/2.82 | DELTA: instantiating (14) with fresh symbol all_36_0 gives: % 15.43/2.82 | (15) relation_type(all_23_2, all_23_2) = all_36_0 & $i(all_36_0) & ! [v0: % 15.43/2.82 | $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_36_0) | ~ ilf_type(v0, % 15.43/2.82 | set_type) | ilf_type(v0, all_23_0)) & ! [v0: $i] : ( ~ $i(v0) | % 15.43/2.82 | ~ ilf_type(v0, all_23_0) | ~ ilf_type(v0, set_type) | ilf_type(v0, % 15.43/2.82 | all_36_0)) % 15.43/2.82 | % 15.43/2.82 | ALPHA: (15) implies: % 15.43/2.82 | (16) relation_type(all_23_2, all_23_2) = all_36_0 % 15.43/2.82 | (17) ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_36_0) | ~ ilf_type(v0, % 15.43/2.82 | set_type) | ilf_type(v0, all_23_0)) % 15.43/2.82 | % 15.43/2.82 | GROUND_INST: instantiating (4) with all_23_2, all_23_2, all_36_0, simplifying % 15.43/2.82 | with (9), (10), (16) gives: % 15.43/2.82 | (18) ? [v0: $i] : ? [v1: $i] : (subset_type(v0) = v1 & % 15.43/2.82 | cross_product(all_23_2, all_23_2) = v0 & $i(v1) & $i(v0) & ! [v2: % 15.43/2.82 | $i] : ( ~ $i(v2) | ~ ilf_type(v2, v1) | ilf_type(v2, all_36_0)) & % 15.43/2.82 | ! [v2: $i] : ( ~ $i(v2) | ~ ilf_type(v2, all_36_0) | ilf_type(v2, % 15.43/2.82 | v1))) % 15.43/2.82 | % 15.43/2.82 | GROUND_INST: instantiating (1) with all_23_2, all_23_2, all_36_0, simplifying % 15.43/2.82 | with (9), (10), (16) gives: % 15.47/2.82 | (19) ? [v0: $i] : (cross_product(all_23_2, all_23_2) = v0 & $i(v0) & % 15.47/2.82 | ilf_type(v0, all_36_0)) % 15.47/2.82 | % 15.47/2.82 | DELTA: instantiating (19) with fresh symbol all_48_0 gives: % 15.47/2.82 | (20) cross_product(all_23_2, all_23_2) = all_48_0 & $i(all_48_0) & % 15.47/2.82 | ilf_type(all_48_0, all_36_0) % 15.47/2.82 | % 15.47/2.82 | ALPHA: (20) implies: % 15.47/2.82 | (21) ilf_type(all_48_0, all_36_0) % 15.47/2.82 | (22) $i(all_48_0) % 15.47/2.82 | (23) cross_product(all_23_2, all_23_2) = all_48_0 % 15.47/2.82 | % 15.47/2.82 | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1 gives: % 15.47/2.83 | (24) subset_type(all_50_1) = all_50_0 & cross_product(all_23_2, all_23_2) = % 15.47/2.83 | all_50_1 & $i(all_50_0) & $i(all_50_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 15.47/2.83 | ilf_type(v0, all_50_0) | ilf_type(v0, all_36_0)) & ! [v0: $i] : ( ~ % 15.47/2.83 | $i(v0) | ~ ilf_type(v0, all_36_0) | ilf_type(v0, all_50_0)) % 15.47/2.83 | % 15.47/2.83 | ALPHA: (24) implies: % 15.47/2.83 | (25) cross_product(all_23_2, all_23_2) = all_50_1 % 15.47/2.83 | % 15.47/2.83 | GROUND_INST: instantiating (6) with all_23_1, all_50_1, all_23_2, all_23_2, % 15.47/2.83 | simplifying with (11), (25) gives: % 15.47/2.83 | (26) all_50_1 = all_23_1 % 15.47/2.83 | % 15.47/2.83 | GROUND_INST: instantiating (6) with all_48_0, all_50_1, all_23_2, all_23_2, % 15.47/2.83 | simplifying with (23), (25) gives: % 15.47/2.83 | (27) all_50_1 = all_48_0 % 15.47/2.83 | % 15.47/2.83 | COMBINE_EQS: (26), (27) imply: % 15.47/2.83 | (28) all_48_0 = all_23_1 % 15.47/2.83 | % 15.47/2.83 | REDUCE: (22), (28) imply: % 15.47/2.83 | (29) $i(all_23_1) % 15.47/2.83 | % 15.47/2.83 | REDUCE: (21), (28) imply: % 15.47/2.83 | (30) ilf_type(all_23_1, all_36_0) % 15.47/2.83 | % 15.47/2.83 | GROUND_INST: instantiating (17) with all_23_1, simplifying with (8), (13), % 15.47/2.83 | (29), (30) gives: % 15.47/2.83 | (31) $false % 15.47/2.83 | % 15.47/2.83 | CLOSE: (31) is inconsistent. % 15.47/2.83 | % 15.47/2.83 End of proof % 15.47/2.83 % SZS output end Proof for theBenchmark % 15.47/2.83 % 15.47/2.83 2178ms %------------------------------------------------------------------------------