%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET665+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 : 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 15:25:54 EDT 2023 % Result : Theorem 77.82s 11.43s % Output : Proof 78.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET665+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Aug 26 10:32:10 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.63 ________ _____ % 0.18/0.63 ___ __ \_________(_)________________________________ % 0.18/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.63 % 0.18/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.63 (2023-06-19) % 0.18/0.63 % 0.18/0.63 (c) Philipp Rümmer, 2009-2023 % 0.18/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.63 Amanda Stjerna. % 0.18/0.63 Free software under BSD-3-Clause. % 0.18/0.63 % 0.18/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.63 % 0.18/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.65 Running up to 7 provers in parallel. % 0.18/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.29/1.27 Prover 1: Preprocessing ... % 3.29/1.27 Prover 4: Preprocessing ... % 3.82/1.32 Prover 6: Preprocessing ... % 3.82/1.32 Prover 0: Preprocessing ... % 3.82/1.32 Prover 3: Preprocessing ... % 3.82/1.32 Prover 5: Preprocessing ... % 3.82/1.33 Prover 2: Preprocessing ... % 11.39/2.43 Prover 3: Constructing countermodel ... % 11.54/2.45 Prover 1: Constructing countermodel ... % 11.54/2.50 Prover 5: Proving ... % 11.54/2.50 Prover 2: Proving ... % 11.95/2.53 Prover 6: Proving ... % 16.45/3.22 Prover 4: Constructing countermodel ... % 17.72/3.42 Prover 0: Proving ... % 71.15/10.47 Prover 2: stopped % 71.31/10.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 71.31/10.59 Prover 7: Preprocessing ... % 72.59/10.72 Prover 7: Warning: ignoring some quantifiers % 72.59/10.72 Prover 7: Constructing countermodel ... % 77.16/11.32 Prover 7: Found proof (size 62) % 77.16/11.32 Prover 7: proved (806ms) % 77.16/11.33 Prover 5: stopped % 77.16/11.33 Prover 3: stopped % 77.16/11.33 Prover 1: stopped % 77.16/11.33 Prover 4: stopped % 77.16/11.35 Prover 6: stopped % 77.82/11.42 Prover 0: stopped % 77.82/11.42 % 77.82/11.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 77.82/11.43 % 78.00/11.43 % SZS output start Proof for theBenchmark % 78.00/11.44 Assumptions after simplification: % 78.00/11.44 --------------------------------- % 78.00/11.44 % 78.00/11.44 (p1) % 78.06/11.46 $i(set_type) & $i(binary_relation_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 78.06/11.46 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ % 78.06/11.46 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v4, v0) | ~ % 78.06/11.46 subset(v0, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ % 78.06/11.46 ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) | % 78.06/11.46 member(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 78.06/11.46 ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) | % 78.06/11.46 subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, % 78.06/11.46 v3) = v4 & $i(v4) & $i(v3) & $i(v2) & member(v4, v0) & ilf_type(v3, % 78.06/11.46 set_type) & ilf_type(v2, set_type) & ~ member(v4, v1))) % 78.06/11.46 % 78.06/11.46 (p11) % 78.06/11.46 $i(set_type) & $i(binary_relation_type) & ! [v0: $i] : ( ~ $i(v0) | ~ % 78.06/11.46 relation_like(v0) | ~ ilf_type(v0, set_type) | ilf_type(v0, % 78.06/11.46 binary_relation_type)) & ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0, % 78.06/11.46 set_type) | ~ ilf_type(v0, binary_relation_type) | relation_like(v0)) % 78.06/11.46 % 78.06/11.46 (p13) % 78.06/11.47 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.06/11.47 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 78.06/11.47 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : % 78.06/11.47 (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) & ! % 78.06/11.47 [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5: % 78.06/11.47 $i] : ( ~ $i(v5) | ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) & ! [v0: % 78.06/11.47 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) = v2) | ~ % 78.06/11.47 $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | % 78.06/11.47 ? [v3: $i] : ? [v4: $i] : (subset_type(v2) = v3 & relation_type(v0, v1) = % 78.06/11.47 v4 & $i(v4) & $i(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | % 78.06/11.47 ilf_type(v5, v3)) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v3) | % 78.06/11.47 ilf_type(v5, v4)))) % 78.06/11.47 % 78.06/11.47 (p2) % 78.06/11.47 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 78.06/11.47 $i] : (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, % 78.06/11.47 v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~ % 78.06/11.47 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, % 78.06/11.47 set_type)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 78.06/11.47 [v4: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = % 78.06/11.47 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~ % 78.06/11.47 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, % 78.06/11.47 set_type) | member(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.06/11.47 [v3: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v2) = % 78.06/11.47 v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v2, v0) | ~ ilf_type(v2, % 78.06/11.47 set_type) | ~ ilf_type(v0, set_type) | member(v3, v1)) % 78.06/11.47 % 78.06/11.47 (p20) % 78.06/11.47 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.06/11.47 (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 78.06/11.47 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : (subset_type(v2) = % 78.06/11.47 v3 & $i(v3) & ! [v4: $i] : ( ~ $i(v4) | ~ ilf_type(v4, v3) | % 78.06/11.47 relation_like(v4)))) % 78.06/11.47 % 78.06/11.47 (p3) % 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 78.06/11.48 $i] : ! [v5: $i] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, % 78.06/11.48 v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 78.06/11.48 member(v2, v5) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ % 78.06/11.48 ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v1, v4)) & ! % 78.06/11.48 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 78.06/11.48 : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ % 78.06/11.48 $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ member(v2, v5) | ~ % 78.06/11.48 ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, % 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | member(v0, v3)) & ! [v0: $i] : ! % 78.06/11.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 78.06/11.48 (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ $i(v4) | % 78.06/11.48 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ member(v1, v4) | ~ member(v0, v3) | % 78.06/11.48 ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, % 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | member(v2, v5)) % 78.06/11.48 % 78.06/11.48 (p4) % 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.06/11.48 (relation_type(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0, % 78.06/11.48 v1) = v3 & $i(v3) & ilf_type(v3, v2))) & ! [v0: $i] : ! [v1: $i] : ! % 78.06/11.48 [v2: $i] : ( ~ (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 78.06/11.48 ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3: $i] : % 78.06/11.48 (relation_type(v0, v1) = v3 & $i(v3) & ilf_type(v2, v3))) % 78.06/11.48 % 78.06/11.48 (p6) % 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 78.06/11.48 (cross_product(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 78.06/11.48 % 78.06/11.48 (p7) % 78.06/11.48 $i(set_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 78.06/11.48 $i] : (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, % 78.06/11.48 v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~ % 78.06/11.48 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, % 78.06/11.48 set_type)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 78.06/11.48 [v4: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = % 78.06/11.48 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~ % 78.06/11.48 ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, % 78.06/11.48 set_type) | member(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.06/11.48 [v3: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v2) = % 78.06/11.48 v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v2, v0) | ~ ilf_type(v2, % 78.06/11.48 set_type) | ~ ilf_type(v0, set_type) | member(v3, v1)) % 78.06/11.48 % 78.06/11.48 (p8) % 78.06/11.48 $i(set_type) & $i(binary_relation_type) & ! [v0: $i] : ! [v1: $i] : ( ~ % 78.06/11.48 (identity_relation_of(v0) = v1) | ~ $i(v0) | ~ ilf_type(v0, set_type) | % 78.06/11.48 ilf_type(v1, binary_relation_type)) % 78.06/11.48 % 78.06/11.48 (prove_relset_1_28) % 78.06/11.48 $i(set_type) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cross_product(v0, % 78.06/11.48 v0) = v2 & identity_relation_of(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & % 78.06/11.48 ilf_type(v0, set_type) & ~ subset(v1, v2)) % 78.06/11.48 % 78.06/11.48 (function-axioms) % 78.06/11.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.06/11.48 (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0)) & ! [v0: % 78.06/11.48 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.06/11.48 (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0: % 78.06/11.48 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.06/11.48 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 78.06/11.48 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 78.06/11.48 (power_set(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 78.06/11.48 ~ (member_type(v2) = v1) | ~ (member_type(v2) = v0)) & ! [v0: $i] : ! % 78.06/11.48 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (subset_type(v2) = v1) | ~ % 78.06/11.48 (subset_type(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 78.06/11.48 | ~ (identity_relation_of(v2) = v1) | ~ (identity_relation_of(v2) = v0)) % 78.06/11.48 % 78.06/11.48 Further assumptions not needed in the proof: % 78.06/11.48 -------------------------------------------- % 78.06/11.48 p10, p12, p14, p15, p16, p17, p18, p19, p21, p22, p23, p24, p25, p26, p27, p5, % 78.06/11.48 p9 % 78.06/11.48 % 78.06/11.48 Those formulas are unsatisfiable: % 78.06/11.48 --------------------------------- % 78.06/11.48 % 78.06/11.48 Begin of proof % 78.06/11.48 | % 78.06/11.49 | ALPHA: (p1) implies: % 78.06/11.49 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, % 78.06/11.49 | binary_relation_type) | ~ ilf_type(v0, binary_relation_type) | % 78.06/11.49 | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 78.06/11.49 | (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & member(v4, % 78.06/11.49 | v0) & ilf_type(v3, set_type) & ilf_type(v2, set_type) & ~ % 78.06/11.49 | member(v4, v1))) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p3) implies: % 78.06/11.49 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.06/11.49 | ! [v5: $i] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, % 78.06/11.49 | v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 78.06/11.49 | member(v1, v4) | ~ member(v0, v3) | ~ ilf_type(v4, set_type) | ~ % 78.06/11.49 | ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, % 78.06/11.49 | set_type) | member(v2, v5)) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p4) implies: % 78.06/11.49 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) = % 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : (relation_type(v0, v1) = v3 & % 78.06/11.49 | $i(v3) & ilf_type(v2, v3))) % 78.06/11.49 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = % 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : (cross_product(v0, v1) = v3 & % 78.06/11.49 | $i(v3) & ilf_type(v3, v2))) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p6) implies: % 78.06/11.49 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) = % 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 78.06/11.49 | ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p7) implies: % 78.06/11.49 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 78.06/11.49 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | % 78.06/11.49 | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) | ~ % 78.06/11.49 | ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, % 78.06/11.49 | set_type) | member(v2, v0)) % 78.06/11.49 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.06/11.49 | (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, % 78.06/11.49 | v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ member(v4, v1) % 78.06/11.49 | | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ % 78.06/11.49 | ilf_type(v0, set_type)) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p8) implies: % 78.06/11.49 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation_of(v0) = v1) | ~ % 78.06/11.49 | $i(v0) | ~ ilf_type(v0, set_type) | ilf_type(v1, % 78.06/11.49 | binary_relation_type)) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p11) implies: % 78.06/11.49 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ relation_like(v0) | ~ ilf_type(v0, % 78.06/11.49 | set_type) | ilf_type(v0, binary_relation_type)) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p13) implies: % 78.06/11.49 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) = % 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : % 78.06/11.49 | (subset_type(v2) = v3 & relation_type(v0, v1) = v4 & $i(v4) & $i(v3) % 78.06/11.49 | & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, % 78.06/11.49 | v3)) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v3) | % 78.06/11.49 | ilf_type(v5, v4)))) % 78.06/11.49 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_type(v0, v1) = % 78.06/11.49 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 78.06/11.49 | ilf_type(v0, set_type) | ? [v3: $i] : ? [v4: $i] : % 78.06/11.49 | (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & $i(v4) & $i(v3) % 78.06/11.49 | & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v4) | ilf_type(v5, % 78.06/11.49 | v2)) & ! [v5: $i] : ( ~ $i(v5) | ~ ilf_type(v5, v2) | % 78.06/11.49 | ilf_type(v5, v4)))) % 78.06/11.49 | % 78.06/11.49 | ALPHA: (p20) implies: % 78.06/11.50 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cross_product(v0, v1) = % 78.06/11.50 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ilf_type(v1, set_type) | ~ % 78.06/11.50 | ilf_type(v0, set_type) | ? [v3: $i] : (subset_type(v2) = v3 & % 78.06/11.50 | $i(v3) & ! [v4: $i] : ( ~ $i(v4) | ~ ilf_type(v4, v3) | % 78.06/11.50 | relation_like(v4)))) % 78.06/11.50 | % 78.06/11.50 | ALPHA: (prove_relset_1_28) implies: % 78.06/11.50 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cross_product(v0, v0) = v2 % 78.06/11.50 | & identity_relation_of(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & % 78.06/11.50 | ilf_type(v0, set_type) & ~ subset(v1, v2)) % 78.06/11.50 | % 78.06/11.50 | ALPHA: (function-axioms) implies: % 78.06/11.50 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 78.06/11.50 | (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) % 78.06/11.50 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.06/11.50 | (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 78.06/11.50 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.06/11.50 | (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0)) % 78.06/11.50 | % 78.06/11.50 | DELTA: instantiating (13) with fresh symbols all_32_0, all_32_1, all_32_2 % 78.06/11.50 | gives: % 78.06/11.50 | (17) cross_product(all_32_2, all_32_2) = all_32_0 & % 78.06/11.50 | identity_relation_of(all_32_2) = all_32_1 & $i(all_32_0) & % 78.06/11.50 | $i(all_32_1) & $i(all_32_2) & ilf_type(all_32_2, set_type) & ~ % 78.06/11.50 | subset(all_32_1, all_32_0) % 78.06/11.50 | % 78.06/11.50 | ALPHA: (17) implies: % 78.06/11.50 | (18) ~ subset(all_32_1, all_32_0) % 78.06/11.50 | (19) ilf_type(all_32_2, set_type) % 78.06/11.50 | (20) $i(all_32_2) % 78.06/11.50 | (21) $i(all_32_1) % 78.06/11.50 | (22) $i(all_32_0) % 78.06/11.50 | (23) identity_relation_of(all_32_2) = all_32_1 % 78.06/11.50 | (24) cross_product(all_32_2, all_32_2) = all_32_0 % 78.06/11.50 | % 78.06/11.50 | GROUND_INST: instantiating (8) with all_32_2, all_32_1, simplifying with (19), % 78.06/11.50 | (20), (23) gives: % 78.06/11.50 | (25) ilf_type(all_32_1, binary_relation_type) % 78.06/11.50 | % 78.06/11.50 | GROUND_INST: instantiating (5) with all_32_2, all_32_2, all_32_0, simplifying % 78.06/11.50 | with (19), (20), (24) gives: % 78.06/11.50 | (26) ilf_type(all_32_0, set_type) % 78.06/11.50 | % 78.06/11.50 | GROUND_INST: instantiating (10) with all_32_2, all_32_2, all_32_0, simplifying % 78.06/11.50 | with (19), (20), (24) gives: % 78.06/11.50 | (27) ? [v0: $i] : ? [v1: $i] : (subset_type(all_32_0) = v0 & % 78.06/11.50 | relation_type(all_32_2, all_32_2) = v1 & $i(v1) & $i(v0) & ! [v2: % 78.06/11.50 | $i] : ( ~ $i(v2) | ~ ilf_type(v2, v1) | ilf_type(v2, v0)) & ! % 78.06/11.50 | [v2: $i] : ( ~ $i(v2) | ~ ilf_type(v2, v0) | ilf_type(v2, v1))) % 78.06/11.50 | % 78.06/11.50 | GROUND_INST: instantiating (12) with all_32_2, all_32_2, all_32_0, simplifying % 78.06/11.50 | with (19), (20), (24) gives: % 78.06/11.50 | (28) ? [v0: $i] : (subset_type(all_32_0) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 78.06/11.50 | $i(v1) | ~ ilf_type(v1, v0) | relation_like(v1))) % 78.06/11.50 | % 78.06/11.50 | GROUND_INST: instantiating (3) with all_32_2, all_32_2, all_32_0, simplifying % 78.06/11.50 | with (19), (20), (24) gives: % 78.06/11.50 | (29) ? [v0: $i] : (relation_type(all_32_2, all_32_2) = v0 & $i(v0) & % 78.06/11.50 | ilf_type(all_32_0, v0)) % 78.06/11.50 | % 78.06/11.50 | DELTA: instantiating (29) with fresh symbol all_40_0 gives: % 78.06/11.50 | (30) relation_type(all_32_2, all_32_2) = all_40_0 & $i(all_40_0) & % 78.06/11.50 | ilf_type(all_32_0, all_40_0) % 78.06/11.50 | % 78.06/11.50 | ALPHA: (30) implies: % 78.06/11.50 | (31) ilf_type(all_32_0, all_40_0) % 78.06/11.50 | (32) relation_type(all_32_2, all_32_2) = all_40_0 % 78.06/11.50 | % 78.06/11.50 | DELTA: instantiating (28) with fresh symbol all_42_0 gives: % 78.06/11.50 | (33) subset_type(all_32_0) = all_42_0 & $i(all_42_0) & ! [v0: $i] : ( ~ % 78.06/11.50 | $i(v0) | ~ ilf_type(v0, all_42_0) | relation_like(v0)) % 78.06/11.50 | % 78.06/11.50 | ALPHA: (33) implies: % 78.06/11.51 | (34) subset_type(all_32_0) = all_42_0 % 78.06/11.51 | (35) ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_42_0) | % 78.06/11.51 | relation_like(v0)) % 78.06/11.51 | % 78.06/11.51 | DELTA: instantiating (27) with fresh symbols all_45_0, all_45_1 gives: % 78.06/11.51 | (36) subset_type(all_32_0) = all_45_1 & relation_type(all_32_2, all_32_2) = % 78.06/11.51 | all_45_0 & $i(all_45_0) & $i(all_45_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 78.06/11.51 | ilf_type(v0, all_45_0) | ilf_type(v0, all_45_1)) & ! [v0: $i] : ( ~ % 78.06/11.51 | $i(v0) | ~ ilf_type(v0, all_45_1) | ilf_type(v0, all_45_0)) % 78.06/11.51 | % 78.06/11.51 | ALPHA: (36) implies: % 78.06/11.51 | (37) relation_type(all_32_2, all_32_2) = all_45_0 % 78.06/11.51 | (38) subset_type(all_32_0) = all_45_1 % 78.06/11.51 | (39) ! [v0: $i] : ( ~ $i(v0) | ~ ilf_type(v0, all_45_0) | ilf_type(v0, % 78.06/11.51 | all_45_1)) % 78.06/11.51 | % 78.06/11.51 | GROUND_INST: instantiating (16) with all_40_0, all_45_0, all_32_2, all_32_2, % 78.06/11.51 | simplifying with (32), (37) gives: % 78.06/11.51 | (40) all_45_0 = all_40_0 % 78.06/11.51 | % 78.06/11.51 | GROUND_INST: instantiating (14) with all_42_0, all_45_1, all_32_0, simplifying % 78.06/11.51 | with (34), (38) gives: % 78.06/11.51 | (41) all_45_1 = all_42_0 % 78.06/11.51 | % 78.06/11.51 | GROUND_INST: instantiating (39) with all_32_0, simplifying with (22) gives: % 78.06/11.51 | (42) ~ ilf_type(all_32_0, all_45_0) | ilf_type(all_32_0, all_45_1) % 78.06/11.51 | % 78.06/11.51 | GROUND_INST: instantiating (35) with all_32_0, simplifying with (22) gives: % 78.06/11.51 | (43) ~ ilf_type(all_32_0, all_42_0) | relation_like(all_32_0) % 78.06/11.51 | % 78.06/11.51 | GROUND_INST: instantiating (11) with all_32_2, all_32_2, all_40_0, simplifying % 78.06/11.51 | with (19), (20), (32) gives: % 78.06/11.51 | (44) ? [v0: $i] : ? [v1: $i] : (subset_type(v0) = v1 & % 78.06/11.51 | cross_product(all_32_2, all_32_2) = v0 & $i(v1) & $i(v0) & ! [v2: % 78.06/11.51 | $i] : ( ~ $i(v2) | ~ ilf_type(v2, v1) | ilf_type(v2, all_40_0)) & % 78.06/11.51 | ! [v2: $i] : ( ~ $i(v2) | ~ ilf_type(v2, all_40_0) | ilf_type(v2, % 78.06/11.51 | v1))) % 78.06/11.51 | % 78.06/11.51 | GROUND_INST: instantiating (4) with all_32_2, all_32_2, all_40_0, simplifying % 78.06/11.51 | with (19), (20), (32) gives: % 78.06/11.51 | (45) ? [v0: $i] : (cross_product(all_32_2, all_32_2) = v0 & $i(v0) & % 78.06/11.51 | ilf_type(v0, all_40_0)) % 78.06/11.51 | % 78.06/11.51 | DELTA: instantiating (45) with fresh symbol all_62_0 gives: % 78.06/11.51 | (46) cross_product(all_32_2, all_32_2) = all_62_0 & $i(all_62_0) & % 78.06/11.51 | ilf_type(all_62_0, all_40_0) % 78.06/11.51 | % 78.06/11.51 | ALPHA: (46) implies: % 78.06/11.51 | (47) $i(all_62_0) % 78.06/11.51 | (48) cross_product(all_32_2, all_32_2) = all_62_0 % 78.06/11.51 | % 78.06/11.51 | DELTA: instantiating (44) with fresh symbols all_64_0, all_64_1 gives: % 78.06/11.51 | (49) subset_type(all_64_1) = all_64_0 & cross_product(all_32_2, all_32_2) = % 78.06/11.51 | all_64_1 & $i(all_64_0) & $i(all_64_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 78.06/11.51 | ilf_type(v0, all_64_0) | ilf_type(v0, all_40_0)) & ! [v0: $i] : ( ~ % 78.06/11.51 | $i(v0) | ~ ilf_type(v0, all_40_0) | ilf_type(v0, all_64_0)) % 78.06/11.51 | % 78.06/11.51 | ALPHA: (49) implies: % 78.06/11.51 | (50) cross_product(all_32_2, all_32_2) = all_64_1 % 78.06/11.51 | % 78.06/11.51 | BETA: splitting (42) gives: % 78.06/11.51 | % 78.06/11.51 | Case 1: % 78.06/11.51 | | % 78.41/11.51 | | (51) ~ ilf_type(all_32_0, all_45_0) % 78.41/11.51 | | % 78.41/11.51 | | REDUCE: (40), (51) imply: % 78.41/11.51 | | (52) ~ ilf_type(all_32_0, all_40_0) % 78.41/11.51 | | % 78.41/11.51 | | PRED_UNIFY: (31), (52) imply: % 78.41/11.51 | | (53) $false % 78.41/11.51 | | % 78.41/11.51 | | CLOSE: (53) is inconsistent. % 78.41/11.51 | | % 78.41/11.51 | Case 2: % 78.41/11.51 | | % 78.41/11.51 | | (54) ilf_type(all_32_0, all_45_1) % 78.41/11.51 | | % 78.41/11.51 | | REDUCE: (41), (54) imply: % 78.41/11.51 | | (55) ilf_type(all_32_0, all_42_0) % 78.41/11.51 | | % 78.41/11.51 | | BETA: splitting (43) gives: % 78.41/11.51 | | % 78.41/11.51 | | Case 1: % 78.41/11.51 | | | % 78.41/11.51 | | | (56) ~ ilf_type(all_32_0, all_42_0) % 78.41/11.51 | | | % 78.41/11.51 | | | PRED_UNIFY: (55), (56) imply: % 78.41/11.51 | | | (57) $false % 78.41/11.51 | | | % 78.41/11.51 | | | CLOSE: (57) is inconsistent. % 78.41/11.51 | | | % 78.41/11.51 | | Case 2: % 78.41/11.51 | | | % 78.41/11.51 | | | (58) relation_like(all_32_0) % 78.41/11.51 | | | % 78.41/11.51 | | | GROUND_INST: instantiating (15) with all_32_0, all_64_1, all_32_2, % 78.41/11.51 | | | all_32_2, simplifying with (24), (50) gives: % 78.41/11.52 | | | (59) all_64_1 = all_32_0 % 78.41/11.52 | | | % 78.41/11.52 | | | GROUND_INST: instantiating (15) with all_62_0, all_64_1, all_32_2, % 78.41/11.52 | | | all_32_2, simplifying with (48), (50) gives: % 78.41/11.52 | | | (60) all_64_1 = all_62_0 % 78.41/11.52 | | | % 78.41/11.52 | | | COMBINE_EQS: (59), (60) imply: % 78.41/11.52 | | | (61) all_62_0 = all_32_0 % 78.41/11.52 | | | % 78.41/11.52 | | | GROUND_INST: instantiating (9) with all_32_0, simplifying with (22), (26), % 78.41/11.52 | | | (58) gives: % 78.41/11.52 | | | (62) ilf_type(all_32_0, binary_relation_type) % 78.41/11.52 | | | % 78.41/11.52 | | | GROUND_INST: instantiating (1) with all_32_1, all_32_0, simplifying with % 78.41/11.52 | | | (18), (21), (22), (25), (62) gives: % 78.41/11.52 | | | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = % 78.41/11.52 | | | v2 & $i(v2) & $i(v1) & $i(v0) & member(v2, all_32_1) & % 78.41/11.52 | | | ilf_type(v1, set_type) & ilf_type(v0, set_type) & ~ member(v2, % 78.41/11.52 | | | all_32_0)) % 78.41/11.52 | | | % 78.41/11.52 | | | DELTA: instantiating (63) with fresh symbols all_118_0, all_118_1, % 78.41/11.52 | | | all_118_2 gives: % 78.41/11.52 | | | (64) ordered_pair(all_118_2, all_118_1) = all_118_0 & $i(all_118_0) & % 78.41/11.52 | | | $i(all_118_1) & $i(all_118_2) & member(all_118_0, all_32_1) & % 78.41/11.52 | | | ilf_type(all_118_1, set_type) & ilf_type(all_118_2, set_type) & ~ % 78.41/11.52 | | | member(all_118_0, all_32_0) % 78.41/11.52 | | | % 78.41/11.52 | | | ALPHA: (64) implies: % 78.41/11.52 | | | (65) ~ member(all_118_0, all_32_0) % 78.41/11.52 | | | (66) ilf_type(all_118_2, set_type) % 78.41/11.52 | | | (67) ilf_type(all_118_1, set_type) % 78.41/11.52 | | | (68) member(all_118_0, all_32_1) % 78.41/11.52 | | | (69) $i(all_118_2) % 78.41/11.52 | | | (70) $i(all_118_1) % 78.41/11.52 | | | (71) ordered_pair(all_118_2, all_118_1) = all_118_0 % 78.41/11.52 | | | % 78.41/11.52 | | | GROUND_INST: instantiating (7) with all_32_2, all_32_1, all_118_2, % 78.41/11.52 | | | all_118_1, all_118_0, simplifying with (19), (20), (23), % 78.41/11.52 | | | (66), (67), (68), (69), (70), (71) gives: % 78.41/11.52 | | | (72) all_118_1 = all_118_2 % 78.41/11.52 | | | % 78.41/11.52 | | | GROUND_INST: instantiating (6) with all_32_2, all_32_1, all_118_2, % 78.41/11.52 | | | all_118_1, all_118_0, simplifying with (19), (20), (23), % 78.41/11.52 | | | (66), (67), (68), (69), (70), (71) gives: % 78.41/11.52 | | | (73) member(all_118_2, all_32_2) % 78.41/11.52 | | | % 78.41/11.52 | | | REDUCE: (71), (72) imply: % 78.41/11.52 | | | (74) ordered_pair(all_118_2, all_118_2) = all_118_0 % 78.41/11.52 | | | % 78.41/11.52 | | | GROUND_INST: instantiating (2) with all_118_2, all_118_2, all_118_0, % 78.41/11.52 | | | all_32_2, all_32_2, all_32_0, simplifying with (19), (20), % 78.41/11.52 | | | (24), (65), (66), (69), (73), (74) gives: % 78.41/11.52 | | | (75) $false % 78.41/11.52 | | | % 78.41/11.52 | | | CLOSE: (75) is inconsistent. % 78.41/11.52 | | | % 78.41/11.52 | | End of split % 78.41/11.52 | | % 78.41/11.52 | End of split % 78.41/11.52 | % 78.41/11.52 End of proof % 78.41/11.52 % SZS output end Proof for theBenchmark % 78.41/11.52 % 78.41/11.52 10891ms %------------------------------------------------------------------------------