%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET642+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 : n007.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 15:25:49 EDT 2023 % Result : Theorem 13.16s 2.50s % Output : Proof 16.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SET642+3 : TPTP v8.1.2. Released v2.2.0. % 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n007.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 11:25:26 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.93/1.12 Prover 1: Preprocessing ... % 2.93/1.12 Prover 4: Preprocessing ... % 2.93/1.16 Prover 5: Preprocessing ... % 2.93/1.16 Prover 6: Preprocessing ... % 2.93/1.16 Prover 0: Preprocessing ... % 2.93/1.16 Prover 3: Preprocessing ... % 2.93/1.16 Prover 2: Preprocessing ... % 6.75/1.66 Prover 5: Proving ... % 6.75/1.66 Prover 2: Proving ... % 6.75/1.68 Prover 1: Constructing countermodel ... % 6.75/1.69 Prover 6: Proving ... % 6.75/1.70 Prover 3: Constructing countermodel ... % 8.99/1.98 Prover 4: Constructing countermodel ... % 8.99/2.07 Prover 0: Proving ... % 13.16/2.49 Prover 2: proved (1863ms) % 13.16/2.49 % 13.16/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.16/2.50 % 13.16/2.50 Prover 3: stopped % 13.16/2.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.16/2.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.16/2.50 Prover 6: stopped % 13.16/2.50 Prover 0: stopped % 13.16/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.16/2.50 Prover 5: stopped % 13.16/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.16/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.79/2.56 Prover 10: Preprocessing ... % 13.79/2.57 Prover 7: Preprocessing ... % 14.00/2.59 Prover 11: Preprocessing ... % 14.00/2.59 Prover 8: Preprocessing ... % 14.00/2.59 Prover 13: Preprocessing ... % 14.30/2.63 Prover 10: Warning: ignoring some quantifiers % 14.30/2.65 Prover 10: Constructing countermodel ... % 14.30/2.68 Prover 7: Warning: ignoring some quantifiers % 14.30/2.69 Prover 7: Constructing countermodel ... % 14.30/2.70 Prover 13: Warning: ignoring some quantifiers % 14.30/2.70 Prover 13: Constructing countermodel ... % 14.30/2.72 Prover 8: Warning: ignoring some quantifiers % 14.77/2.73 Prover 8: Constructing countermodel ... % 16.12/2.87 Prover 7: Found proof (size 35) % 16.12/2.87 Prover 7: proved (369ms) % 16.12/2.87 Prover 13: stopped % 16.12/2.87 Prover 10: stopped % 16.12/2.87 Prover 4: stopped % 16.12/2.87 Prover 8: stopped % 16.12/2.87 Prover 1: stopped % 16.12/2.93 Prover 11: Constructing countermodel ... % 16.12/2.93 Prover 11: stopped % 16.12/2.93 % 16.12/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.12/2.94 % 16.12/2.94 % SZS output start Proof for theBenchmark % 16.12/2.94 Assumptions after simplification: % 16.12/2.94 --------------------------------- % 16.12/2.94 % 16.12/2.94 (p1) % 16.57/2.97 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.57/2.97 (cross_product(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.57/2.97 ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, % 16.57/2.97 set_type) | ? [v4: $i] : (relation_type(v1, v2) = v4 & $i(v4) & ! [v5: % 16.57/2.97 $i] : ( ~ $i(v5) | ~ subset(v0, v5) | ~ ilf_type(v5, v4) | subset(v0, % 16.57/2.97 v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.57/2.97 (relation_type(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.57/2.97 ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, % 16.57/2.97 set_type) | ? [v4: $i] : (cross_product(v1, v2) = v4 & $i(v4) & ! [v5: % 16.57/2.97 $i] : ( ~ $i(v5) | ~ subset(v0, v5) | ~ ilf_type(v5, v3) | subset(v0, % 16.57/2.97 v4)))) % 16.57/2.97 % 16.57/2.97 (p2) % 16.57/2.97 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.57/2.97 (cross_product(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.57/2.97 subset(v0, v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ % 16.57/2.97 ilf_type(v0, set_type) | ? [v4: $i] : (relation_type(v1, v2) = v4 & $i(v4) % 16.57/2.97 & ilf_type(v0, v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.57/2.97 $i] : ( ~ (relation_type(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.57/2.97 ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, % 16.57/2.97 set_type) | ilf_type(v0, v3) | ? [v4: $i] : (cross_product(v1, v2) = v4 & % 16.57/2.97 $i(v4) & ~ subset(v0, v4))) % 16.57/2.97 % 16.57/2.97 (p3) % 16.57/2.98 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.57/2.98 (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 16.57/2.98 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : % 16.57/2.98 (subset_type(v2) = v3 & relation_type(v0, v1) = v4 & $i(v4) & $i(v3) & ! % 16.57/2.98 [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v3)) & ! [v5: % 16.57/2.98 $i] : ( ~ $i(v5) | ~ ilf_type(v5, v3) | ilf_type(v5, v4)))) & ! [v0: % 16.57/2.98 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = v2) | ~ % 16.57/2.98 $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | % 16.57/2.98 ? [v3: $i] : ? [v4: $i] : (subset_type(v3) = v4 & cross_product(v0, v1) = % 16.57/2.98 v3 & $i(v4) & $i(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | % 16.57/2.98 ilf_type(v5, v2)) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v2) | % 16.57/2.98 ilf_type(v5, v4)))) % 16.57/2.98 % 16.57/2.98 (prove_relset_1_4) % 16.57/2.98 $i(set_type) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 16.57/2.98 $i] : (relation_type(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 16.57/2.98 $i(v0) & subset(v0, v4) & ilf_type(v4, v3) & ilf_type(v2, set_type) & % 16.57/2.98 ilf_type(v1, set_type) & ilf_type(v0, set_type) & ~ ilf_type(v0, v3)) % 16.57/2.98 % 16.57/2.98 (function-axioms) % 16.57/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.57/2.98 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 16.57/2.98 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cross_product(v3, % 16.57/2.98 v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 16.57/2.98 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~ % 16.57/2.98 (relation_type(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.57/2.98 (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0: $i] : % 16.57/2.98 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member_type(v2) = v1) | ~ % 16.57/2.98 (member_type(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 16.57/2.98 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) % 16.57/2.98 % 16.57/2.98 Further assumptions not needed in the proof: % 16.57/2.98 -------------------------------------------- % 16.57/2.98 p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p4, p5, p6, p7, p8, p9 % 16.57/2.98 % 16.57/2.98 Those formulas are unsatisfiable: % 16.57/2.98 --------------------------------- % 16.57/2.98 % 16.57/2.98 Begin of proof % 16.57/2.99 | % 16.57/2.99 | ALPHA: (p1) implies: % 16.57/2.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.57/2.99 | (relation_type(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.57/2.99 | ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, % 16.57/2.99 | set_type) | ? [v4: $i] : (cross_product(v1, v2) = v4 & $i(v4) & ! % 16.57/2.99 | [v5: $i] : ( ~ $i(v5) | ~ subset(v0, v5) | ~ ilf_type(v5, v3) | % 16.57/2.99 | subset(v0, v4)))) % 16.57/2.99 | % 16.57/2.99 | ALPHA: (p2) implies: % 16.57/2.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 16.57/2.99 | (relation_type(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 16.57/2.99 | ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, % 16.57/2.99 | set_type) | ilf_type(v0, v3) | ? [v4: $i] : (cross_product(v1, v2) % 16.57/2.99 | = v4 & $i(v4) & ~ subset(v0, v4))) % 16.57/2.99 | % 16.57/2.99 | ALPHA: (p3) implies: % 16.74/2.99 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = % 16.74/2.99 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 16.74/2.99 | ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : (subset_type(v3) % 16.74/2.99 | = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) & ! [v5: $i] : % 16.74/2.99 | ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5: $i] % 16.74/2.99 | : ( ~ $i(v5) | ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) % 16.74/2.99 | % 16.74/2.99 | ALPHA: (prove_relset_1_4) implies: % 16.74/2.99 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.74/2.99 | (relation_type(v1, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 16.74/2.99 | $i(v0) & subset(v0, v4) & ilf_type(v4, v3) & ilf_type(v2, set_type) & % 16.74/2.99 | ilf_type(v1, set_type) & ilf_type(v0, set_type) & ~ ilf_type(v0, % 16.74/2.99 | v3)) % 16.74/2.99 | % 16.74/2.99 | ALPHA: (function-axioms) implies: % 16.74/2.99 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.74/2.99 | (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 16.74/2.99 | % 16.74/2.99 | DELTA: instantiating (4) with fresh symbols all_23_0, all_23_1, all_23_2, % 16.74/2.99 | all_23_3, all_23_4 gives: % 16.74/2.99 | (6) relation_type(all_23_3, all_23_2) = all_23_1 & $i(all_23_0) & % 16.74/2.99 | $i(all_23_1) & $i(all_23_2) & $i(all_23_3) & $i(all_23_4) & % 16.74/2.99 | subset(all_23_4, all_23_0) & ilf_type(all_23_0, all_23_1) & % 16.74/2.99 | ilf_type(all_23_2, set_type) & ilf_type(all_23_3, set_type) & % 16.74/2.99 | ilf_type(all_23_4, set_type) & ~ ilf_type(all_23_4, all_23_1) % 16.74/2.99 | % 16.74/2.99 | ALPHA: (6) implies: % 16.74/2.99 | (7) ~ ilf_type(all_23_4, all_23_1) % 16.74/2.99 | (8) ilf_type(all_23_4, set_type) % 16.74/3.00 | (9) ilf_type(all_23_3, set_type) % 16.74/3.00 | (10) ilf_type(all_23_2, set_type) % 16.74/3.00 | (11) ilf_type(all_23_0, all_23_1) % 16.74/3.00 | (12) subset(all_23_4, all_23_0) % 16.74/3.00 | (13) $i(all_23_4) % 16.74/3.00 | (14) $i(all_23_3) % 16.74/3.00 | (15) $i(all_23_2) % 16.74/3.00 | (16) $i(all_23_0) % 16.74/3.00 | (17) relation_type(all_23_3, all_23_2) = all_23_1 % 16.74/3.00 | % 16.74/3.00 | GROUND_INST: instantiating (1) with all_23_2, all_23_3, all_23_2, all_23_1, % 16.74/3.00 | simplifying with (9), (10), (14), (15), (17) gives: % 16.74/3.00 | (18) ? [v0: $i] : (cross_product(all_23_3, all_23_2) = v0 & $i(v0) & ! % 16.74/3.00 | [v1: $i] : ( ~ $i(v1) | ~ subset(all_23_2, v1) | ~ ilf_type(v1, % 16.74/3.00 | all_23_1) | subset(all_23_2, v0))) % 16.74/3.00 | % 16.74/3.00 | GROUND_INST: instantiating (1) with all_23_3, all_23_3, all_23_2, all_23_1, % 16.74/3.00 | simplifying with (9), (10), (14), (15), (17) gives: % 16.74/3.00 | (19) ? [v0: $i] : (cross_product(all_23_3, all_23_2) = v0 & $i(v0) & ! % 16.74/3.00 | [v1: $i] : ( ~ $i(v1) | ~ subset(all_23_3, v1) | ~ ilf_type(v1, % 16.74/3.00 | all_23_1) | subset(all_23_3, v0))) % 16.74/3.00 | % 16.74/3.00 | GROUND_INST: instantiating (2) with all_23_4, all_23_3, all_23_2, all_23_1, % 16.74/3.00 | simplifying with (7), (8), (9), (10), (13), (14), (15), (17) % 16.74/3.00 | gives: % 16.74/3.00 | (20) ? [v0: $i] : (cross_product(all_23_3, all_23_2) = v0 & $i(v0) & ~ % 16.74/3.00 | subset(all_23_4, v0)) % 16.74/3.00 | % 16.74/3.00 | GROUND_INST: instantiating (1) with all_23_4, all_23_3, all_23_2, all_23_1, % 16.74/3.00 | simplifying with (8), (9), (10), (13), (14), (15), (17) gives: % 16.74/3.00 | (21) ? [v0: $i] : (cross_product(all_23_3, all_23_2) = v0 & $i(v0) & ! % 16.74/3.00 | [v1: $i] : ( ~ $i(v1) | ~ subset(all_23_4, v1) | ~ ilf_type(v1, % 16.74/3.00 | all_23_1) | subset(all_23_4, v0))) % 16.74/3.00 | % 16.74/3.00 | GROUND_INST: instantiating (3) with all_23_3, all_23_2, all_23_1, simplifying % 16.74/3.00 | with (9), (10), (14), (15), (17) gives: % 16.74/3.00 | (22) ? [v0: $i] : ? [v1: $i] : (subset_type(v0) = v1 & % 16.74/3.00 | cross_product(all_23_3, all_23_2) = v0 & $i(v1) & $i(v0) & ! [v2: % 16.74/3.00 | $i] : ( ~ $i(v2) | ~ ilf_type(v2, v1) | ilf_type(v2, all_23_1)) & % 16.74/3.00 | ! [v2: $i] : ( ~ $i(v2) | ~ ilf_type(v2, all_23_1) | ilf_type(v2, % 16.74/3.00 | v1))) % 16.74/3.00 | % 16.74/3.00 | DELTA: instantiating (20) with fresh symbol all_37_0 gives: % 16.74/3.00 | (23) cross_product(all_23_3, all_23_2) = all_37_0 & $i(all_37_0) & ~ % 16.74/3.00 | subset(all_23_4, all_37_0) % 16.74/3.00 | % 16.74/3.00 | ALPHA: (23) implies: % 16.74/3.00 | (24) ~ subset(all_23_4, all_37_0) % 16.74/3.00 | (25) cross_product(all_23_3, all_23_2) = all_37_0 % 16.74/3.00 | % 16.74/3.00 | DELTA: instantiating (21) with fresh symbol all_39_0 gives: % 16.74/3.00 | (26) cross_product(all_23_3, all_23_2) = all_39_0 & $i(all_39_0) & ! [v0: % 16.74/3.00 | $i] : ( ~ $i(v0) | ~ subset(all_23_4, v0) | ~ ilf_type(v0, % 16.74/3.00 | all_23_1) | subset(all_23_4, all_39_0)) % 16.74/3.00 | % 16.74/3.00 | ALPHA: (26) implies: % 16.74/3.00 | (27) cross_product(all_23_3, all_23_2) = all_39_0 % 16.74/3.00 | (28) ! [v0: $i] : ( ~ $i(v0) | ~ subset(all_23_4, v0) | ~ ilf_type(v0, % 16.74/3.00 | all_23_1) | subset(all_23_4, all_39_0)) % 16.74/3.00 | % 16.74/3.00 | GROUND_INST: instantiating (28) with all_23_0, simplifying with (11), (12), % 16.74/3.00 | (16) gives: % 16.74/3.00 | (29) subset(all_23_4, all_39_0) % 16.74/3.00 | % 16.74/3.00 | DELTA: instantiating (19) with fresh symbol all_43_0 gives: % 16.74/3.00 | (30) cross_product(all_23_3, all_23_2) = all_43_0 & $i(all_43_0) & ! [v0: % 16.74/3.00 | $i] : ( ~ $i(v0) | ~ subset(all_23_3, v0) | ~ ilf_type(v0, % 16.74/3.00 | all_23_1) | subset(all_23_3, all_43_0)) % 16.74/3.00 | % 16.74/3.00 | ALPHA: (30) implies: % 16.74/3.00 | (31) cross_product(all_23_3, all_23_2) = all_43_0 % 16.74/3.00 | % 16.74/3.01 | DELTA: instantiating (18) with fresh symbol all_46_0 gives: % 16.74/3.01 | (32) cross_product(all_23_3, all_23_2) = all_46_0 & $i(all_46_0) & ! [v0: % 16.74/3.01 | $i] : ( ~ $i(v0) | ~ subset(all_23_2, v0) | ~ ilf_type(v0, % 16.74/3.01 | all_23_1) | subset(all_23_2, all_46_0)) % 16.74/3.01 | % 16.74/3.01 | ALPHA: (32) implies: % 16.74/3.01 | (33) cross_product(all_23_3, all_23_2) = all_46_0 % 16.74/3.01 | % 16.74/3.01 | DELTA: instantiating (22) with fresh symbols all_49_0, all_49_1 gives: % 16.74/3.01 | (34) subset_type(all_49_1) = all_49_0 & cross_product(all_23_3, all_23_2) = % 16.74/3.01 | all_49_1 & $i(all_49_0) & $i(all_49_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 16.74/3.01 | ilf_type(v0, all_49_0) | ilf_type(v0, all_23_1)) & ! [v0: $i] : ( ~ % 16.74/3.01 | $i(v0) | ~ ilf_type(v0, all_23_1) | ilf_type(v0, all_49_0)) % 16.74/3.01 | % 16.74/3.01 | ALPHA: (34) implies: % 16.74/3.01 | (35) cross_product(all_23_3, all_23_2) = all_49_1 % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (5) with all_43_0, all_46_0, all_23_2, all_23_3, % 16.74/3.01 | simplifying with (31), (33) gives: % 16.74/3.01 | (36) all_46_0 = all_43_0 % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (5) with all_37_0, all_46_0, all_23_2, all_23_3, % 16.74/3.01 | simplifying with (25), (33) gives: % 16.74/3.01 | (37) all_46_0 = all_37_0 % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (5) with all_43_0, all_49_1, all_23_2, all_23_3, % 16.74/3.01 | simplifying with (31), (35) gives: % 16.74/3.01 | (38) all_49_1 = all_43_0 % 16.74/3.01 | % 16.74/3.01 | GROUND_INST: instantiating (5) with all_39_0, all_49_1, all_23_2, all_23_3, % 16.74/3.01 | simplifying with (27), (35) gives: % 16.74/3.01 | (39) all_49_1 = all_39_0 % 16.74/3.01 | % 16.74/3.01 | PRED_UNIFY: (24), (29) imply: % 16.74/3.01 | (40) ~ (all_39_0 = all_37_0) % 16.74/3.01 | % 16.74/3.01 | COMBINE_EQS: (38), (39) imply: % 16.74/3.01 | (41) all_43_0 = all_39_0 % 16.74/3.01 | % 16.74/3.01 | SIMP: (41) implies: % 16.74/3.01 | (42) all_43_0 = all_39_0 % 16.74/3.01 | % 16.74/3.01 | COMBINE_EQS: (36), (37) imply: % 16.74/3.01 | (43) all_43_0 = all_37_0 % 16.74/3.01 | % 16.74/3.01 | SIMP: (43) implies: % 16.74/3.01 | (44) all_43_0 = all_37_0 % 16.74/3.01 | % 16.74/3.01 | COMBINE_EQS: (42), (44) imply: % 16.74/3.01 | (45) all_39_0 = all_37_0 % 16.74/3.01 | % 16.74/3.01 | REDUCE: (40), (45) imply: % 16.74/3.01 | (46) $false % 16.74/3.01 | % 16.74/3.01 | CLOSE: (46) is inconsistent. % 16.74/3.01 | % 16.74/3.01 End of proof % 16.74/3.01 % SZS output end Proof for theBenchmark % 16.74/3.01 % 16.74/3.01 2400ms %------------------------------------------------------------------------------