%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LAT297+1 : TPTP v8.1.2. Released v3.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n001.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 06:24:31 EDT 2023 % Result : Theorem 66.14s 9.62s % Output : Proof 67.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : LAT297+1 : TPTP v8.1.2. Released v3.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n001.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Aug 24 06:43:55 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.07/1.31 Prover 1: Preprocessing ... % 4.07/1.31 Prover 4: Preprocessing ... % 4.61/1.35 Prover 0: Preprocessing ... % 4.61/1.35 Prover 5: Preprocessing ... % 4.61/1.35 Prover 3: Preprocessing ... % 4.61/1.35 Prover 6: Preprocessing ... % 4.61/1.35 Prover 2: Preprocessing ... % 11.19/2.27 Prover 1: Warning: ignoring some quantifiers % 11.87/2.32 Prover 3: Warning: ignoring some quantifiers % 11.87/2.33 Prover 5: Proving ... % 12.07/2.35 Prover 2: Proving ... % 12.07/2.36 Prover 3: Constructing countermodel ... % 12.07/2.37 Prover 6: Proving ... % 12.07/2.37 Prover 1: Constructing countermodel ... % 14.87/2.82 Prover 4: Warning: ignoring some quantifiers % 15.91/2.94 Prover 4: Constructing countermodel ... % 18.32/3.23 Prover 0: Proving ... % 25.65/4.45 Prover 3: gave up % 25.65/4.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 29.18/4.66 Prover 7: Preprocessing ... % 31.53/5.00 Prover 7: Warning: ignoring some quantifiers % 32.32/5.04 Prover 7: Constructing countermodel ... % 64.67/9.30 Prover 2: stopped % 65.11/9.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 65.11/9.33 Prover 7: Found proof (size 130) % 65.11/9.33 Prover 7: proved (4857ms) % 65.11/9.33 Prover 5: stopped % 65.11/9.33 Prover 4: stopped % 65.11/9.33 Prover 1: stopped % 65.11/9.33 Prover 6: stopped % 65.11/9.34 Prover 0: stopped % 65.31/9.40 Prover 8: Preprocessing ... % 66.14/9.60 Prover 8: Warning: ignoring some quantifiers % 66.14/9.62 Prover 8: Constructing countermodel ... % 66.14/9.62 Prover 8: stopped % 66.14/9.62 % 66.14/9.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 66.14/9.62 % 66.14/9.64 % SZS output start Proof for theBenchmark % 66.14/9.65 Assumptions after simplification: % 66.14/9.65 --------------------------------- % 66.14/9.65 % 66.14/9.65 (antisymmetry_r2_hidden) % 66.14/9.65 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v1, v0) | ~ % 66.14/9.66 r2_hidden(v0, v1)) % 66.14/9.66 % 66.14/9.66 (cc1_lattices) % 66.14/9.66 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | % 66.14/9.66 v9_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 66.14/9.66 l3_lattices(v0) | ~ v10_lattices(v0) | v8_lattices(v0) | v3_struct_0(v0)) & % 66.14/9.66 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | % 66.14/9.66 v7_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 66.14/9.66 l3_lattices(v0) | ~ v10_lattices(v0) | v6_lattices(v0) | v3_struct_0(v0)) & % 66.14/9.66 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | % 66.14/9.66 v5_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 66.14/9.66 l3_lattices(v0) | ~ v10_lattices(v0) | v4_lattices(v0) | v3_struct_0(v0)) % 66.14/9.66 % 66.14/9.66 (commutativity_k3_lattices) % 66.49/9.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0, % 66.49/9.70 v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) | % 66.49/9.70 ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 % 66.49/9.70 & k3_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & % 66.49/9.70 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) & ! [v0: % 66.49/9.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0, v1, v2) % 66.49/9.70 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) | ~ % 66.49/9.70 v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & % 66.49/9.70 k3_lattices(v0, v2, v1) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) % 66.49/9.70 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) % 66.49/9.70 % 66.49/9.70 (d10_lattice4) % 66.49/9.71 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 66.49/9.71 l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] : % 66.49/9.71 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 66.49/9.71 ! [v6: $i] : ( ~ (k4_lattices(v0, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | % 66.49/9.71 ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3) | ~ % 66.49/9.71 r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | ~ % 66.49/9.71 m1_subset_1(v3, v2) | r2_hidden(v6, v3)) & ! [v3: $i] : ! [v4: $i] : % 66.49/9.71 ! [v5: $i] : ! [v6: $i] : ( ~ (k4_lattices(v0, v4, v5) = v6) | ~ $i(v5) % 66.49/9.71 | ~ $i(v4) | ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3) % 66.49/9.71 | ~ r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) % 66.49/9.71 | ~ m1_subset_1(v3, v2) | ? [v7: $i] : (k3_lattices(v0, v4, v5) = v7 & % 66.49/9.71 $i(v7) & r2_hidden(v7, v3))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 66.49/9.71 : ! [v6: $i] : ( ~ (k3_lattices(v0, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) % 66.49/9.71 | ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3) | ~ % 66.49/9.71 r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | ~ % 66.49/9.71 m1_subset_1(v3, v2) | r2_hidden(v6, v3)) & ! [v3: $i] : ! [v4: $i] : % 66.49/9.71 ! [v5: $i] : ! [v6: $i] : ( ~ (k3_lattices(v0, v4, v5) = v6) | ~ $i(v5) % 66.49/9.71 | ~ $i(v4) | ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3) % 66.49/9.71 | ~ r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) % 66.49/9.71 | ~ m1_subset_1(v3, v2) | ? [v7: $i] : (k4_lattices(v0, v4, v5) = v7 & % 66.49/9.71 $i(v7) & r2_hidden(v7, v3))) & ! [v3: $i] : ( ~ $i(v3) | ~ % 66.49/9.71 m1_subset_1(v3, v2) | m2_lattice4(v3, v0) | ? [v4: $i] : ? [v5: $i] : % 66.49/9.71 ? [v6: $i] : ? [v7: $i] : ($i(v5) & $i(v4) & r2_hidden(v5, v3) & % 66.49/9.71 r2_hidden(v4, v3) & m1_subset_1(v5, v1) & m1_subset_1(v4, v1) & % 66.49/9.71 ((k4_lattices(v0, v4, v5) = v6 & $i(v6) & ~ r2_hidden(v6, v3)) | % 66.49/9.71 (k3_lattices(v0, v4, v5) = v7 & $i(v7) & ~ r2_hidden(v7, v3))))))) % 66.49/9.71 % 66.49/9.71 (d1_lattices) % 66.49/9.71 ! [v0: $i] : ! [v1: $i] : ( ~ (u2_lattices(v0) = v1) | ~ $i(v0) | ~ % 66.49/9.71 l2_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & % 66.49/9.71 $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k2_binop_1(v2, v2, % 66.49/9.71 v2, v1, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ m1_subset_1(v4, % 66.49/9.71 v2) | ~ m1_subset_1(v3, v2) | (k1_lattices(v0, v3, v4) = v5 & % 66.49/9.71 $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 66.49/9.71 (k1_lattices(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 66.49/9.71 m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2) | (k2_binop_1(v2, v2, v2, % 66.49/9.71 v1, v3, v4) = v5 & $i(v5))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 66.49/9.71 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l2_lattices(v0) | v3_struct_0(v0) | % 66.49/9.71 ? [v2: $i] : (u2_lattices(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! % 66.49/9.71 [v5: $i] : ( ~ (k2_binop_1(v1, v1, v1, v2, v3, v4) = v5) | ~ $i(v4) | ~ % 66.49/9.71 $i(v3) | ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3, v1) | % 66.49/9.71 (k1_lattices(v0, v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : % 66.49/9.71 ! [v5: $i] : ( ~ (k1_lattices(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 66.49/9.71 ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3, v1) | (k2_binop_1(v1, v1, v1, % 66.49/9.71 v2, v3, v4) = v5 & $i(v5))))) % 66.49/9.71 % 66.49/9.71 (d9_lattices) % 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 66.49/9.72 (k1_lattices(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~ % 66.49/9.72 $i(v2) | ~ $i(v0) | ~ v9_lattices(v0) | ~ m1_subset_1(v3, v1) | ~ % 66.49/9.72 m1_subset_1(v2, v1) | ~ l3_lattices(v0) | k2_lattices(v0, v2, v4) = v2 | % 66.49/9.72 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | % 66.49/9.72 ~ $i(v0) | ~ l3_lattices(v0) | v9_lattices(v0) | v3_struct_0(v0) | ? [v2: % 66.49/9.72 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v2) & % 66.49/9.72 k2_lattices(v0, v2, v4) = v5 & k1_lattices(v0, v2, v3) = v4 & $i(v5) & % 66.49/9.72 $i(v4) & $i(v3) & $i(v2) & m1_subset_1(v3, v1) & m1_subset_1(v2, v1))) % 66.49/9.72 % 66.49/9.72 (dt_k3_lattices) % 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0, % 66.49/9.72 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) | % 66.49/9.72 ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : (u1_struct_0(v0) = v4 & % 66.49/9.72 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4) | % 66.49/9.72 m1_subset_1(v3, v4)))) % 66.49/9.72 % 66.49/9.72 (dt_l3_lattices) % 66.49/9.72 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l1_lattices(v0)) & ! [v0: $i] % 66.49/9.72 : ( ~ $i(v0) | ~ l3_lattices(v0) | l2_lattices(v0)) % 66.49/9.72 % 66.49/9.72 (dt_m2_lattice4) % 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 66.49/9.72 l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] : % 66.49/9.72 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ % 66.49/9.72 m2_lattice4(v3, v0) | m1_subset_1(v3, v2)))) % 66.49/9.72 % 66.49/9.72 (redefinition_k3_lattices) % 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_lattices(v0, % 66.49/9.72 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) | % 66.49/9.72 ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 % 66.49/9.72 & k3_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & % 66.49/9.72 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) & ! [v0: % 66.49/9.72 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0, v1, v2) % 66.49/9.72 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) | ~ % 66.49/9.72 v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & % 66.49/9.72 k1_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) % 66.49/9.72 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) % 66.49/9.72 % 66.49/9.72 (redefinition_k4_lattices) % 66.49/9.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k2_lattices(v0, % 66.49/9.73 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_lattices(v0) | % 66.49/9.73 ~ v6_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 % 66.49/9.73 & k4_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & % 66.49/9.73 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) & ! [v0: % 66.49/9.73 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k4_lattices(v0, v1, v2) % 66.49/9.73 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_lattices(v0) | ~ % 66.49/9.73 v6_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & % 66.49/9.73 k2_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) % 66.49/9.73 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) % 66.49/9.73 % 66.49/9.73 (t13_filter_2) % 66.49/9.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (u1_struct_0(v0) = v1 % 66.49/9.73 & k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & m1_subset_1(v3, % 66.49/9.73 v2) & l3_lattices(v0) & v10_lattices(v0) & ~ m2_lattice4(v3, v0) & ~ % 66.49/9.73 v3_struct_0(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 66.49/9.73 (k4_lattices(v0, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ r2_hidden(v6, % 66.49/9.73 v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | r2_hidden(v5, % 66.49/9.73 v3)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (k4_lattices(v0, % 66.49/9.73 v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ r2_hidden(v6, v3) | ~ % 66.49/9.73 m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | r2_hidden(v4, v3)) & ! % 66.49/9.73 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (k4_lattices(v0, v4, v5) = v6) | % 66.49/9.73 ~ $i(v5) | ~ $i(v4) | ~ r2_hidden(v5, v3) | ~ r2_hidden(v4, v3) | ~ % 66.49/9.73 m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | r2_hidden(v6, v3))) % 66.49/9.73 % 66.49/9.73 (t4_subset) % 66.49/9.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_zfmisc_1(v2) = % 66.49/9.73 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v0, v1) | ~ % 66.49/9.73 m1_subset_1(v1, v3) | m1_subset_1(v0, v2)) % 66.49/9.73 % 66.49/9.73 (function-axioms) % 67.02/9.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 67.02/9.74 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (k2_binop_1(v7, v6, v5, v4, % 67.02/9.74 v3, v2) = v1) | ~ (k2_binop_1(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 67.02/9.74 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 67.02/9.74 (k2_lattices(v4, v3, v2) = v1) | ~ (k2_lattices(v4, v3, v2) = v0)) & ! % 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 67.02/9.74 ~ (k1_lattices(v4, v3, v2) = v1) | ~ (k1_lattices(v4, v3, v2) = v0)) & ! % 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 67.02/9.74 ~ (k1_binop_1(v4, v3, v2) = v1) | ~ (k1_binop_1(v4, v3, v2) = v0)) & ! % 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 67.02/9.74 ~ (k4_lattices(v4, v3, v2) = v1) | ~ (k4_lattices(v4, v3, v2) = v0)) & ! % 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 67.02/9.74 ~ (k3_lattices(v4, v3, v2) = v1) | ~ (k3_lattices(v4, v3, v2) = v0)) & ! % 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 67.02/9.74 (k4_tarski(v3, v2) = v1) | ~ (k4_tarski(v3, v2) = v0)) & ! [v0: $i] : ! % 67.02/9.74 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1) % 67.02/9.74 | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 67.02/9.74 ! [v3: $i] : (v1 = v0 | ~ (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) = % 67.02/9.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 67.02/9.74 ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] % 67.02/9.74 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~ % 67.02/9.74 (k1_tarski(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 67.02/9.74 ~ (u1_lattices(v2) = v1) | ~ (u1_lattices(v2) = v0)) & ! [v0: $i] : ! % 67.02/9.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u2_lattices(v2) = v1) | ~ % 67.02/9.74 (u2_lattices(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 67.02/9.74 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! % 67.02/9.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ % 67.02/9.74 (k1_zfmisc_1(v2) = v0)) % 67.02/9.74 % 67.02/9.74 Further assumptions not needed in the proof: % 67.02/9.74 -------------------------------------------- % 67.02/9.74 cc1_funct_1, cc1_realset1, cc1_relset_1, cc2_funct_1, cc2_lattices, % 67.02/9.74 commutativity_k2_tarski, commutativity_k4_lattices, d1_binop_1, d2_lattices, % 67.02/9.74 d5_tarski, dt_k1_binop_1, dt_k1_funct_1, dt_k1_lattices, dt_k1_tarski, % 67.02/9.74 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_binop_1, dt_k2_lattices, dt_k2_tarski, % 67.02/9.74 dt_k2_zfmisc_1, dt_k4_lattices, dt_k4_tarski, dt_l1_lattices, dt_l1_struct_0, % 67.02/9.74 dt_l2_lattices, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_lattices, % 67.02/9.74 dt_u1_struct_0, dt_u2_lattices, existence_l1_lattices, existence_l1_struct_0, % 67.02/9.74 existence_l2_lattices, existence_l3_lattices, existence_m1_relset_1, % 67.02/9.74 existence_m1_subset_1, existence_m2_lattice4, existence_m2_relset_1, % 67.02/9.74 fc1_struct_0, fc1_subset_1, fc1_xboole_0, fc2_lattice2, fc2_subset_1, % 67.02/9.74 fc3_lattice2, fc3_realset1, fc3_subset_1, fc4_lattice2, fc4_subset_1, % 67.02/9.74 fc5_lattice2, rc1_funct_1, rc1_lattice4, rc1_realset1, rc1_subset_1, % 67.02/9.74 rc1_xboole_0, rc2_funct_1, rc2_realset1, rc2_subset_1, rc2_xboole_0, % 67.02/9.74 rc3_funct_1, rc3_struct_0, rc5_struct_0, redefinition_k2_binop_1, % 67.02/9.74 redefinition_m2_relset_1, reflexivity_r1_tarski, t1_subset, t2_subset, % 67.02/9.74 t3_subset, t5_subset, t6_boole, t7_boole, t8_boole % 67.02/9.74 % 67.02/9.74 Those formulas are unsatisfiable: % 67.02/9.74 --------------------------------- % 67.02/9.74 % 67.02/9.74 Begin of proof % 67.02/9.74 | % 67.02/9.74 | ALPHA: (cc1_lattices) implies: % 67.02/9.74 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | % 67.02/9.74 | v4_lattices(v0) | v3_struct_0(v0)) % 67.02/9.74 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | % 67.02/9.74 | v6_lattices(v0) | v3_struct_0(v0)) % 67.02/9.74 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | % 67.02/9.74 | v9_lattices(v0) | v3_struct_0(v0)) % 67.02/9.74 | % 67.02/9.74 | ALPHA: (commutativity_k3_lattices) implies: % 67.02/9.75 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 67.02/9.75 | (k3_lattices(v0, v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 67.02/9.75 | ~ l2_lattices(v0) | ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: % 67.02/9.75 | $i] : ? [v5: $i] : ((v5 = v3 & k3_lattices(v0, v1, v2) = v3 & % 67.02/9.75 | $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2, % 67.02/9.75 | v4) | ~ m1_subset_1(v1, v4))))) % 67.02/9.75 | % 67.02/9.75 | ALPHA: (d1_lattices) implies: % 67.02/9.75 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ % 67.02/9.75 | l2_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] : (u2_lattices(v0) = % 67.02/9.75 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 67.02/9.75 | (k2_binop_1(v1, v1, v1, v2, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) % 67.02/9.75 | | ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3, v1) | % 67.02/9.75 | (k1_lattices(v0, v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: % 67.02/9.75 | $i] : ! [v5: $i] : ( ~ (k1_lattices(v0, v3, v4) = v5) | ~ % 67.02/9.75 | $i(v4) | ~ $i(v3) | ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3, % 67.02/9.75 | v1) | (k2_binop_1(v1, v1, v1, v2, v3, v4) = v5 & $i(v5))))) % 67.02/9.75 | % 67.02/9.75 | ALPHA: (d9_lattices) implies: % 67.02/9.75 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 67.02/9.75 | ~ (k1_lattices(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ % 67.02/9.75 | $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ v9_lattices(v0) | ~ % 67.02/9.75 | m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | % 67.02/9.75 | k2_lattices(v0, v2, v4) = v2 | v3_struct_0(v0)) % 67.02/9.75 | % 67.02/9.75 | ALPHA: (dt_l3_lattices) implies: % 67.02/9.75 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l2_lattices(v0)) % 67.02/9.75 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l1_lattices(v0)) % 67.02/9.75 | % 67.02/9.75 | ALPHA: (redefinition_k3_lattices) implies: % 67.02/9.75 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 67.02/9.75 | (k3_lattices(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 67.02/9.75 | ~ l2_lattices(v0) | ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: % 67.02/9.75 | $i] : ? [v5: $i] : ((v5 = v3 & k1_lattices(v0, v1, v2) = v3 & % 67.02/9.75 | $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2, % 67.02/9.75 | v4) | ~ m1_subset_1(v1, v4))))) % 67.02/9.75 | % 67.02/9.75 | ALPHA: (redefinition_k4_lattices) implies: % 67.02/9.75 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 67.02/9.75 | (k2_lattices(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 67.02/9.75 | ~ l1_lattices(v0) | ~ v6_lattices(v0) | v3_struct_0(v0) | ? [v4: % 67.02/9.75 | $i] : ? [v5: $i] : ((v5 = v3 & k4_lattices(v0, v1, v2) = v3 & % 67.02/9.75 | $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2, % 67.02/9.75 | v4) | ~ m1_subset_1(v1, v4))))) % 67.02/9.75 | % 67.02/9.75 | ALPHA: (function-axioms) implies: % 67.02/9.75 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 67.02/9.76 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 67.02/9.76 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 67.02/9.76 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) % 67.02/9.76 | % 67.02/9.76 | DELTA: instantiating (t13_filter_2) with fresh symbols all_87_0, all_87_1, % 67.02/9.76 | all_87_2, all_87_3 gives: % 67.02/9.76 | (13) u1_struct_0(all_87_3) = all_87_2 & k1_zfmisc_1(all_87_2) = all_87_1 & % 67.02/9.76 | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) & % 67.02/9.76 | m1_subset_1(all_87_0, all_87_1) & l3_lattices(all_87_3) & % 67.02/9.76 | v10_lattices(all_87_3) & ~ m2_lattice4(all_87_0, all_87_3) & ~ % 67.02/9.76 | v3_struct_0(all_87_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 67.02/9.76 | (k4_lattices(all_87_3, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 67.02/9.76 | r2_hidden(v2, all_87_0) | ~ m1_subset_1(v1, all_87_2) | ~ % 67.02/9.76 | m1_subset_1(v0, all_87_2) | r2_hidden(v1, all_87_0)) & ! [v0: $i] : % 67.02/9.76 | ! [v1: $i] : ! [v2: $i] : ( ~ (k4_lattices(all_87_3, v0, v1) = v2) | % 67.02/9.76 | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v2, all_87_0) | ~ % 67.02/9.76 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_87_2) | % 67.02/9.76 | r2_hidden(v0, all_87_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 67.02/9.76 | ( ~ (k4_lattices(all_87_3, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 67.02/9.76 | r2_hidden(v1, all_87_0) | ~ r2_hidden(v0, all_87_0) | ~ % 67.02/9.76 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_87_2) | % 67.02/9.76 | r2_hidden(v2, all_87_0)) % 67.02/9.76 | % 67.02/9.76 | ALPHA: (13) implies: % 67.02/9.76 | (14) ~ v3_struct_0(all_87_3) % 67.02/9.76 | (15) ~ m2_lattice4(all_87_0, all_87_3) % 67.02/9.76 | (16) v10_lattices(all_87_3) % 67.02/9.76 | (17) l3_lattices(all_87_3) % 67.02/9.76 | (18) m1_subset_1(all_87_0, all_87_1) % 67.02/9.76 | (19) $i(all_87_3) % 67.02/9.76 | (20) $i(all_87_2) % 67.02/9.76 | (21) $i(all_87_0) % 67.02/9.76 | (22) k1_zfmisc_1(all_87_2) = all_87_1 % 67.02/9.76 | (23) u1_struct_0(all_87_3) = all_87_2 % 67.02/9.76 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k4_lattices(all_87_3, % 67.02/9.76 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v1, % 67.02/9.76 | all_87_0) | ~ r2_hidden(v0, all_87_0) | ~ m1_subset_1(v1, % 67.02/9.76 | all_87_2) | ~ m1_subset_1(v0, all_87_2) | r2_hidden(v2, % 67.02/9.76 | all_87_0)) % 67.02/9.76 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k4_lattices(all_87_3, % 67.02/9.76 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v2, % 67.02/9.76 | all_87_0) | ~ m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, % 67.02/9.76 | all_87_2) | r2_hidden(v1, all_87_0)) % 67.02/9.76 | % 67.02/9.77 | GROUND_INST: instantiating (3) with all_87_3, simplifying with (14), (16), % 67.02/9.77 | (17), (19) gives: % 67.02/9.77 | (26) v9_lattices(all_87_3) % 67.02/9.77 | % 67.02/9.77 | GROUND_INST: instantiating (2) with all_87_3, simplifying with (14), (16), % 67.02/9.77 | (17), (19) gives: % 67.02/9.77 | (27) v6_lattices(all_87_3) % 67.02/9.77 | % 67.02/9.77 | GROUND_INST: instantiating (1) with all_87_3, simplifying with (14), (16), % 67.02/9.77 | (17), (19) gives: % 67.02/9.77 | (28) v4_lattices(all_87_3) % 67.02/9.77 | % 67.02/9.77 | GROUND_INST: instantiating (8) with all_87_3, simplifying with (17), (19) % 67.02/9.77 | gives: % 67.19/9.77 | (29) l1_lattices(all_87_3) % 67.19/9.77 | % 67.19/9.77 | GROUND_INST: instantiating (7) with all_87_3, simplifying with (17), (19) % 67.19/9.77 | gives: % 67.19/9.77 | (30) l2_lattices(all_87_3) % 67.19/9.77 | % 67.19/9.77 | GROUND_INST: instantiating (d10_lattice4) with all_87_3, all_87_2, simplifying % 67.19/9.77 | with (14), (16), (17), (19), (23) gives: % 67.19/9.77 | (31) ? [v0: $i] : (k1_zfmisc_1(all_87_2) = v0 & $i(v0) & ! [v1: $i] : ! % 67.19/9.77 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (k4_lattices(all_87_3, % 67.19/9.77 | v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 67.19/9.77 | m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) | ~ % 67.19/9.77 | r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~ % 67.19/9.77 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | r2_hidden(v4, % 67.19/9.77 | v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 67.19/9.77 | ~ (k4_lattices(all_87_3, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 67.19/9.77 | ~ $i(v1) | ~ m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) | % 67.19/9.77 | ~ r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~ % 67.19/9.77 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | ? [v5: $i] : % 67.19/9.78 | (k3_lattices(all_87_3, v2, v3) = v5 & $i(v5) & r2_hidden(v5, v1))) % 67.19/9.78 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 67.19/9.78 | (k3_lattices(all_87_3, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 67.19/9.78 | $i(v1) | ~ m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) | ~ % 67.19/9.78 | r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~ % 67.19/9.78 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | r2_hidden(v4, % 67.19/9.78 | v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 67.19/9.78 | ~ (k3_lattices(all_87_3, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 67.19/9.78 | ~ $i(v1) | ~ m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) | % 67.19/9.78 | ~ r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~ % 67.19/9.78 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | ? [v5: $i] : % 67.19/9.78 | (k4_lattices(all_87_3, v2, v3) = v5 & $i(v5) & r2_hidden(v5, v1))) % 67.19/9.78 | & ! [v1: $i] : ( ~ $i(v1) | ~ m1_subset_1(v1, v0) | % 67.19/9.78 | m2_lattice4(v1, all_87_3) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 67.19/9.78 | $i] : ? [v5: $i] : ($i(v3) & $i(v2) & r2_hidden(v3, v1) & % 67.19/9.78 | r2_hidden(v2, v1) & m1_subset_1(v3, all_87_2) & m1_subset_1(v2, % 67.19/9.78 | all_87_2) & ((k4_lattices(all_87_3, v2, v3) = v4 & $i(v4) & ~ % 67.19/9.78 | r2_hidden(v4, v1)) | (k3_lattices(all_87_3, v2, v3) = v5 & % 67.19/9.78 | $i(v5) & ~ r2_hidden(v5, v1)))))) % 67.19/9.78 | % 67.19/9.78 | GROUND_INST: instantiating (dt_m2_lattice4) with all_87_3, all_87_2, % 67.19/9.78 | simplifying with (14), (16), (17), (19), (23) gives: % 67.19/9.78 | (32) ? [v0: $i] : (k1_zfmisc_1(all_87_2) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 67.19/9.78 | $i(v1) | ~ m2_lattice4(v1, all_87_3) | m1_subset_1(v1, v0))) % 67.19/9.78 | % 67.19/9.78 | DELTA: instantiating (32) with fresh symbol all_106_0 gives: % 67.19/9.78 | (33) k1_zfmisc_1(all_87_2) = all_106_0 & $i(all_106_0) & ! [v0: $i] : ( ~ % 67.19/9.78 | $i(v0) | ~ m2_lattice4(v0, all_87_3) | m1_subset_1(v0, all_106_0)) % 67.19/9.78 | % 67.19/9.78 | ALPHA: (33) implies: % 67.19/9.78 | (34) k1_zfmisc_1(all_87_2) = all_106_0 % 67.19/9.78 | % 67.19/9.78 | DELTA: instantiating (31) with fresh symbol all_109_0 gives: % 67.19/9.78 | (35) k1_zfmisc_1(all_87_2) = all_109_0 & $i(all_109_0) & ! [v0: $i] : ! % 67.19/9.78 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k4_lattices(all_87_3, v1, % 67.19/9.78 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 67.19/9.78 | m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2, v0) | ~ r2_hidden(v1, % 67.19/9.78 | v0) | ~ m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, all_87_2) % 67.19/9.78 | | ~ m1_subset_1(v0, all_109_0) | r2_hidden(v3, v0)) & ! [v0: $i] : % 67.19/9.78 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k4_lattices(all_87_3, % 67.19/9.78 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 67.19/9.78 | m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2, v0) | ~ r2_hidden(v1, % 67.19/9.78 | v0) | ~ m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, all_87_2) % 67.19/9.78 | | ~ m1_subset_1(v0, all_109_0) | ? [v4: $i] : % 67.19/9.78 | (k3_lattices(all_87_3, v1, v2) = v4 & $i(v4) & r2_hidden(v4, v0))) & % 67.19/9.78 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 67.19/9.78 | (k3_lattices(all_87_3, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 67.19/9.78 | $i(v0) | ~ m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2, v0) | ~ % 67.19/9.78 | r2_hidden(v1, v0) | ~ m1_subset_1(v2, all_87_2) | ~ % 67.19/9.78 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_109_0) | % 67.19/9.78 | r2_hidden(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 67.19/9.78 | [v3: $i] : ( ~ (k3_lattices(all_87_3, v1, v2) = v3) | ~ $i(v2) | ~ % 67.19/9.79 | $i(v1) | ~ $i(v0) | ~ m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2, % 67.19/9.79 | v0) | ~ r2_hidden(v1, v0) | ~ m1_subset_1(v2, all_87_2) | ~ % 67.19/9.79 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_109_0) | ? [v4: % 67.19/9.79 | $i] : (k4_lattices(all_87_3, v1, v2) = v4 & $i(v4) & r2_hidden(v4, % 67.19/9.79 | v0))) & ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_109_0) % 67.19/9.79 | | m2_lattice4(v0, all_87_3) | ? [v1: $i] : ? [v2: $i] : ? [v3: % 67.19/9.79 | $i] : ? [v4: $i] : ($i(v2) & $i(v1) & r2_hidden(v2, v0) & % 67.19/9.79 | r2_hidden(v1, v0) & m1_subset_1(v2, all_87_2) & m1_subset_1(v1, % 67.19/9.79 | all_87_2) & ((k4_lattices(all_87_3, v1, v2) = v3 & $i(v3) & ~ % 67.19/9.79 | r2_hidden(v3, v0)) | (k3_lattices(all_87_3, v1, v2) = v4 & % 67.19/9.79 | $i(v4) & ~ r2_hidden(v4, v0))))) % 67.19/9.79 | % 67.19/9.79 | ALPHA: (35) implies: % 67.19/9.79 | (36) k1_zfmisc_1(all_87_2) = all_109_0 % 67.19/9.79 | (37) ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_109_0) | % 67.19/9.79 | m2_lattice4(v0, all_87_3) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 67.19/9.79 | : ? [v4: $i] : ($i(v2) & $i(v1) & r2_hidden(v2, v0) & r2_hidden(v1, % 67.19/9.79 | v0) & m1_subset_1(v2, all_87_2) & m1_subset_1(v1, all_87_2) & % 67.19/9.79 | ((k4_lattices(all_87_3, v1, v2) = v3 & $i(v3) & ~ r2_hidden(v3, % 67.19/9.79 | v0)) | (k3_lattices(all_87_3, v1, v2) = v4 & $i(v4) & ~ % 67.19/9.79 | r2_hidden(v4, v0))))) % 67.19/9.79 | % 67.19/9.79 | GROUND_INST: instantiating (37) with all_87_0, simplifying with (15), (21) % 67.19/9.79 | gives: % 67.19/9.79 | (38) ~ m1_subset_1(all_87_0, all_109_0) | ? [v0: $i] : ? [v1: $i] : ? % 67.19/9.79 | [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) & r2_hidden(v1, all_87_0) & % 67.19/9.79 | r2_hidden(v0, all_87_0) & m1_subset_1(v1, all_87_2) & % 67.19/9.79 | m1_subset_1(v0, all_87_2) & ((k4_lattices(all_87_3, v0, v1) = v2 & % 67.19/9.79 | $i(v2) & ~ r2_hidden(v2, all_87_0)) | (k3_lattices(all_87_3, % 67.19/9.79 | v0, v1) = v3 & $i(v3) & ~ r2_hidden(v3, all_87_0)))) % 67.19/9.79 | % 67.19/9.79 | GROUND_INST: instantiating (11) with all_87_1, all_109_0, all_87_2, % 67.19/9.79 | simplifying with (22), (36) gives: % 67.19/9.79 | (39) all_109_0 = all_87_1 % 67.19/9.79 | % 67.19/9.79 | GROUND_INST: instantiating (11) with all_106_0, all_109_0, all_87_2, % 67.19/9.79 | simplifying with (34), (36) gives: % 67.19/9.79 | (40) all_109_0 = all_106_0 % 67.19/9.79 | % 67.19/9.79 | COMBINE_EQS: (39), (40) imply: % 67.19/9.79 | (41) all_106_0 = all_87_1 % 67.19/9.79 | % 67.19/9.79 | BETA: splitting (38) gives: % 67.19/9.79 | % 67.19/9.79 | Case 1: % 67.19/9.79 | | % 67.19/9.79 | | (42) ~ m1_subset_1(all_87_0, all_109_0) % 67.19/9.79 | | % 67.19/9.79 | | REDUCE: (39), (42) imply: % 67.19/9.79 | | (43) ~ m1_subset_1(all_87_0, all_87_1) % 67.19/9.79 | | % 67.19/9.79 | | PRED_UNIFY: (18), (43) imply: % 67.19/9.79 | | (44) $false % 67.19/9.79 | | % 67.19/9.79 | | CLOSE: (44) is inconsistent. % 67.19/9.79 | | % 67.19/9.79 | Case 2: % 67.19/9.79 | | % 67.19/9.80 | | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & % 67.19/9.80 | | $i(v0) & r2_hidden(v1, all_87_0) & r2_hidden(v0, all_87_0) & % 67.19/9.80 | | m1_subset_1(v1, all_87_2) & m1_subset_1(v0, all_87_2) & % 67.19/9.80 | | ((k4_lattices(all_87_3, v0, v1) = v2 & $i(v2) & ~ r2_hidden(v2, % 67.19/9.80 | | all_87_0)) | (k3_lattices(all_87_3, v0, v1) = v3 & $i(v3) & % 67.19/9.80 | | ~ r2_hidden(v3, all_87_0)))) % 67.19/9.80 | | % 67.19/9.80 | | DELTA: instantiating (45) with fresh symbols all_120_0, all_120_1, % 67.19/9.80 | | all_120_2, all_120_3 gives: % 67.19/9.80 | | (46) $i(all_120_2) & $i(all_120_3) & r2_hidden(all_120_2, all_87_0) & % 67.19/9.80 | | r2_hidden(all_120_3, all_87_0) & m1_subset_1(all_120_2, all_87_2) & % 67.19/9.80 | | m1_subset_1(all_120_3, all_87_2) & ((k4_lattices(all_87_3, % 67.19/9.80 | | all_120_3, all_120_2) = all_120_1 & $i(all_120_1) & ~ % 67.19/9.80 | | r2_hidden(all_120_1, all_87_0)) | (k3_lattices(all_87_3, % 67.19/9.80 | | all_120_3, all_120_2) = all_120_0 & $i(all_120_0) & ~ % 67.19/9.80 | | r2_hidden(all_120_0, all_87_0))) % 67.19/9.80 | | % 67.19/9.80 | | ALPHA: (46) implies: % 67.19/9.80 | | (47) m1_subset_1(all_120_3, all_87_2) % 67.19/9.80 | | (48) m1_subset_1(all_120_2, all_87_2) % 67.19/9.80 | | (49) r2_hidden(all_120_3, all_87_0) % 67.19/9.80 | | (50) r2_hidden(all_120_2, all_87_0) % 67.19/9.80 | | (51) $i(all_120_3) % 67.19/9.80 | | (52) $i(all_120_2) % 67.19/9.80 | | (53) (k4_lattices(all_87_3, all_120_3, all_120_2) = all_120_1 & % 67.19/9.80 | | $i(all_120_1) & ~ r2_hidden(all_120_1, all_87_0)) | % 67.19/9.80 | | (k3_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 & % 67.19/9.80 | | $i(all_120_0) & ~ r2_hidden(all_120_0, all_87_0)) % 67.19/9.80 | | % 67.19/9.80 | | GROUND_INST: instantiating (5) with all_87_3, all_87_2, simplifying with % 67.19/9.80 | | (14), (19), (23), (30) gives: % 67.19/9.80 | | (54) ? [v0: $i] : (u2_lattices(all_87_3) = v0 & $i(v0) & ! [v1: $i] : % 67.19/9.80 | | ! [v2: $i] : ! [v3: $i] : ( ~ (k2_binop_1(all_87_2, all_87_2, % 67.19/9.80 | | all_87_2, v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 67.19/9.80 | | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, all_87_2) | % 67.19/9.80 | | (k1_lattices(all_87_3, v1, v2) = v3 & $i(v3))) & ! [v1: $i] : % 67.19/9.80 | | ! [v2: $i] : ! [v3: $i] : ( ~ (k1_lattices(all_87_3, v1, v2) = % 67.19/9.80 | | v3) | ~ $i(v2) | ~ $i(v1) | ~ m1_subset_1(v2, all_87_2) | % 67.19/9.80 | | ~ m1_subset_1(v1, all_87_2) | (k2_binop_1(all_87_2, all_87_2, % 67.19/9.80 | | all_87_2, v0, v1, v2) = v3 & $i(v3)))) % 67.19/9.80 | | % 67.19/9.80 | | DELTA: instantiating (54) with fresh symbol all_140_0 gives: % 67.19/9.80 | | (55) u2_lattices(all_87_3) = all_140_0 & $i(all_140_0) & ! [v0: $i] : ! % 67.19/9.80 | | [v1: $i] : ! [v2: $i] : ( ~ (k2_binop_1(all_87_2, all_87_2, % 67.19/9.80 | | all_87_2, all_140_0, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 67.19/9.80 | | ~ m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_87_2) | % 67.19/9.80 | | (k1_lattices(all_87_3, v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 67.19/9.80 | | [v1: $i] : ! [v2: $i] : ( ~ (k1_lattices(all_87_3, v0, v1) = v2) | % 67.19/9.80 | | ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1, all_87_2) | ~ % 67.19/9.80 | | m1_subset_1(v0, all_87_2) | (k2_binop_1(all_87_2, all_87_2, % 67.19/9.80 | | all_87_2, all_140_0, v0, v1) = v2 & $i(v2))) % 67.19/9.80 | | % 67.19/9.80 | | ALPHA: (55) implies: % 67.19/9.80 | | (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_lattices(all_87_3, % 67.19/9.80 | | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1, % 67.19/9.80 | | all_87_2) | ~ m1_subset_1(v0, all_87_2) | (k2_binop_1(all_87_2, % 67.19/9.80 | | all_87_2, all_87_2, all_140_0, v0, v1) = v2 & $i(v2))) % 67.19/9.80 | | % 67.19/9.80 | | BETA: splitting (53) gives: % 67.19/9.80 | | % 67.19/9.80 | | Case 1: % 67.19/9.80 | | | % 67.19/9.80 | | | (57) k4_lattices(all_87_3, all_120_3, all_120_2) = all_120_1 & % 67.19/9.80 | | | $i(all_120_1) & ~ r2_hidden(all_120_1, all_87_0) % 67.19/9.81 | | | % 67.19/9.81 | | | ALPHA: (57) implies: % 67.19/9.81 | | | (58) ~ r2_hidden(all_120_1, all_87_0) % 67.19/9.81 | | | (59) k4_lattices(all_87_3, all_120_3, all_120_2) = all_120_1 % 67.19/9.81 | | | % 67.19/9.81 | | | GROUND_INST: instantiating (24) with all_120_3, all_120_2, all_120_1, % 67.19/9.81 | | | simplifying with (47), (48), (49), (50), (51), (52), (58), % 67.19/9.81 | | | (59) gives: % 67.19/9.81 | | | (60) $false % 67.19/9.81 | | | % 67.19/9.81 | | | CLOSE: (60) is inconsistent. % 67.19/9.81 | | | % 67.19/9.81 | | Case 2: % 67.19/9.81 | | | % 67.19/9.81 | | | (61) k3_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 & % 67.19/9.81 | | | $i(all_120_0) & ~ r2_hidden(all_120_0, all_87_0) % 67.19/9.81 | | | % 67.19/9.81 | | | ALPHA: (61) implies: % 67.19/9.81 | | | (62) ~ r2_hidden(all_120_0, all_87_0) % 67.19/9.81 | | | (63) k3_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 % 67.19/9.81 | | | % 67.19/9.81 | | | GROUND_INST: instantiating (t4_subset) with all_87_2, all_87_2, all_87_2, % 67.19/9.81 | | | all_87_1, simplifying with (20), (22) gives: % 67.19/9.81 | | | (64) ~ r2_hidden(all_87_2, all_87_2) | ~ m1_subset_1(all_87_2, % 67.19/9.81 | | | all_87_1) | m1_subset_1(all_87_2, all_87_2) % 67.19/9.81 | | | % 67.19/9.81 | | | GROUND_INST: instantiating (4) with all_87_3, all_120_2, all_120_3, % 67.19/9.81 | | | all_120_0, simplifying with (14), (19), (28), (30), (51), % 67.19/9.81 | | | (52), (63) gives: % 67.19/9.81 | | | (65) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_0 & % 67.19/9.81 | | | k3_lattices(all_87_3, all_120_2, all_120_3) = all_120_0 & % 67.19/9.81 | | | $i(all_120_0)) | (u1_struct_0(all_87_3) = v0 & $i(v0) & ( ~ % 67.19/9.81 | | | m1_subset_1(all_120_2, v0) | ~ m1_subset_1(all_120_3, % 67.19/9.81 | | | v0)))) % 67.19/9.81 | | | % 67.19/9.81 | | | GROUND_INST: instantiating (9) with all_87_3, all_120_3, all_120_2, % 67.19/9.81 | | | all_120_0, simplifying with (14), (19), (28), (30), (51), % 67.19/9.81 | | | (52), (63) gives: % 67.19/9.81 | | | (66) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_0 & % 67.19/9.81 | | | k1_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 & % 67.19/9.81 | | | $i(all_120_0)) | (u1_struct_0(all_87_3) = v0 & $i(v0) & ( ~ % 67.19/9.81 | | | m1_subset_1(all_120_2, v0) | ~ m1_subset_1(all_120_3, % 67.19/9.81 | | | v0)))) % 67.19/9.81 | | | % 67.19/9.81 | | | GROUND_INST: instantiating (dt_k3_lattices) with all_87_3, all_120_3, % 67.19/9.81 | | | all_120_2, all_120_0, simplifying with (14), (19), (28), % 67.19/9.81 | | | (30), (51), (52), (63) gives: % 67.19/9.81 | | | (67) ? [v0: $i] : (u1_struct_0(all_87_3) = v0 & $i(v0) & ( ~ % 67.19/9.81 | | | m1_subset_1(all_120_2, v0) | ~ m1_subset_1(all_120_3, v0) | % 67.19/9.81 | | | m1_subset_1(all_120_0, v0))) % 67.19/9.81 | | | % 67.19/9.81 | | | DELTA: instantiating (67) with fresh symbol all_492_0 gives: % 67.19/9.81 | | | (68) u1_struct_0(all_87_3) = all_492_0 & $i(all_492_0) & ( ~ % 67.19/9.81 | | | m1_subset_1(all_120_2, all_492_0) | ~ m1_subset_1(all_120_3, % 67.19/9.81 | | | all_492_0) | m1_subset_1(all_120_0, all_492_0)) % 67.19/9.81 | | | % 67.19/9.81 | | | ALPHA: (68) implies: % 67.19/9.82 | | | (69) $i(all_492_0) % 67.19/9.82 | | | (70) u1_struct_0(all_87_3) = all_492_0 % 67.19/9.82 | | | (71) ~ m1_subset_1(all_120_2, all_492_0) | ~ m1_subset_1(all_120_3, % 67.19/9.82 | | | all_492_0) | m1_subset_1(all_120_0, all_492_0) % 67.19/9.82 | | | % 67.19/9.82 | | | DELTA: instantiating (66) with fresh symbols all_494_0, all_494_1 gives: % 67.19/9.82 | | | (72) (all_494_0 = all_120_0 & k1_lattices(all_87_3, all_120_3, % 67.19/9.82 | | | all_120_2) = all_120_0 & $i(all_120_0)) | % 67.19/9.82 | | | (u1_struct_0(all_87_3) = all_494_1 & $i(all_494_1) & ( ~ % 67.19/9.82 | | | m1_subset_1(all_120_2, all_494_1) | ~ m1_subset_1(all_120_3, % 67.19/9.82 | | | all_494_1))) % 67.19/9.82 | | | % 67.19/9.82 | | | DELTA: instantiating (65) with fresh symbols all_495_0, all_495_1 gives: % 67.19/9.82 | | | (73) (all_495_0 = all_120_0 & k3_lattices(all_87_3, all_120_2, % 67.19/9.82 | | | all_120_3) = all_120_0 & $i(all_120_0)) | % 67.19/9.82 | | | (u1_struct_0(all_87_3) = all_495_1 & $i(all_495_1) & ( ~ % 67.19/9.82 | | | m1_subset_1(all_120_2, all_495_1) | ~ m1_subset_1(all_120_3, % 67.19/9.82 | | | all_495_1))) % 67.19/9.82 | | | % 67.19/9.82 | | | BETA: splitting (73) gives: % 67.19/9.82 | | | % 67.19/9.82 | | | Case 1: % 67.19/9.82 | | | | % 67.19/9.82 | | | | (74) all_495_0 = all_120_0 & k3_lattices(all_87_3, all_120_2, % 67.19/9.82 | | | | all_120_3) = all_120_0 & $i(all_120_0) % 67.19/9.82 | | | | % 67.19/9.82 | | | | ALPHA: (74) implies: % 67.19/9.82 | | | | (75) k3_lattices(all_87_3, all_120_2, all_120_3) = all_120_0 % 67.19/9.82 | | | | % 67.19/9.82 | | | | GROUND_INST: instantiating (12) with all_87_2, all_492_0, all_87_3, % 67.19/9.82 | | | | simplifying with (23), (70) gives: % 67.19/9.82 | | | | (76) all_492_0 = all_87_2 % 67.19/9.82 | | | | % 67.19/9.82 | | | | BETA: splitting (71) gives: % 67.19/9.82 | | | | % 67.19/9.82 | | | | Case 1: % 67.19/9.82 | | | | | % 67.19/9.82 | | | | | (77) ~ m1_subset_1(all_120_2, all_492_0) % 67.19/9.82 | | | | | % 67.19/9.82 | | | | | REDUCE: (76), (77) imply: % 67.19/9.82 | | | | | (78) ~ m1_subset_1(all_120_2, all_87_2) % 67.19/9.82 | | | | | % 67.19/9.82 | | | | | PRED_UNIFY: (48), (78) imply: % 67.19/9.82 | | | | | (79) $false % 67.19/9.82 | | | | | % 67.19/9.82 | | | | | CLOSE: (79) is inconsistent. % 67.19/9.82 | | | | | % 67.19/9.82 | | | | Case 2: % 67.19/9.82 | | | | | % 67.19/9.82 | | | | | (80) m1_subset_1(all_120_2, all_492_0) % 67.19/9.82 | | | | | (81) ~ m1_subset_1(all_120_3, all_492_0) | m1_subset_1(all_120_0, % 67.19/9.82 | | | | | all_492_0) % 67.19/9.82 | | | | | % 67.19/9.82 | | | | | BETA: splitting (81) gives: % 67.19/9.82 | | | | | % 67.19/9.82 | | | | | Case 1: % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | | (82) ~ m1_subset_1(all_120_3, all_492_0) % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | | REDUCE: (76), (82) imply: % 67.19/9.82 | | | | | | (83) ~ m1_subset_1(all_120_3, all_87_2) % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | | PRED_UNIFY: (47), (83) imply: % 67.19/9.82 | | | | | | (84) $false % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | | CLOSE: (84) is inconsistent. % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | Case 2: % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | | (85) m1_subset_1(all_120_3, all_492_0) % 67.19/9.82 | | | | | | (86) m1_subset_1(all_120_0, all_492_0) % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | | REDUCE: (76), (86) imply: % 67.19/9.82 | | | | | | (87) m1_subset_1(all_120_0, all_87_2) % 67.19/9.82 | | | | | | % 67.19/9.82 | | | | | | BETA: splitting (72) gives: % 67.19/9.82 | | | | | | % 67.19/9.83 | | | | | | Case 1: % 67.19/9.83 | | | | | | | % 67.19/9.83 | | | | | | | (88) all_494_0 = all_120_0 & k1_lattices(all_87_3, all_120_3, % 67.19/9.83 | | | | | | | all_120_2) = all_120_0 & $i(all_120_0) % 67.19/9.83 | | | | | | | % 67.19/9.83 | | | | | | | ALPHA: (88) implies: % 67.19/9.83 | | | | | | | (89) k1_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 % 67.19/9.83 | | | | | | | % 67.19/9.83 | | | | | | | GROUND_INST: instantiating (9) with all_87_3, all_120_2, % 67.19/9.83 | | | | | | | all_120_3, all_120_0, simplifying with (14), (19), % 67.19/9.83 | | | | | | | (28), (30), (51), (52), (75) gives: % 67.19/9.83 | | | | | | | (90) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_0 & % 67.19/9.83 | | | | | | | k1_lattices(all_87_3, all_120_2, all_120_3) = % 67.19/9.83 | | | | | | | all_120_0 & $i(all_120_0)) | (u1_struct_0(all_87_3) = % 67.19/9.83 | | | | | | | v0 & $i(v0) & ( ~ m1_subset_1(all_120_2, v0) | ~ % 67.19/9.83 | | | | | | | m1_subset_1(all_120_3, v0)))) % 67.19/9.83 | | | | | | | % 67.48/9.83 | | | | | | | GROUND_INST: instantiating (6) with all_87_3, all_87_2, all_120_3, % 67.48/9.83 | | | | | | | all_120_2, all_120_0, simplifying with (14), (17), % 67.48/9.83 | | | | | | | (19), (23), (26), (47), (48), (51), (52), (89) gives: % 67.48/9.83 | | | | | | | (91) k2_lattices(all_87_3, all_120_3, all_120_0) = all_120_3 % 67.48/9.83 | | | | | | | % 67.48/9.83 | | | | | | | DELTA: instantiating (90) with fresh symbols all_677_0, all_677_1 % 67.48/9.83 | | | | | | | gives: % 67.48/9.83 | | | | | | | (92) (all_677_0 = all_120_0 & k1_lattices(all_87_3, all_120_2, % 67.48/9.83 | | | | | | | all_120_3) = all_120_0 & $i(all_120_0)) | % 67.48/9.83 | | | | | | | (u1_struct_0(all_87_3) = all_677_1 & $i(all_677_1) & ( ~ % 67.48/9.83 | | | | | | | m1_subset_1(all_120_2, all_677_1) | ~ % 67.48/9.83 | | | | | | | m1_subset_1(all_120_3, all_677_1))) % 67.48/9.83 | | | | | | | % 67.48/9.83 | | | | | | | BETA: splitting (92) gives: % 67.48/9.83 | | | | | | | % 67.48/9.83 | | | | | | | Case 1: % 67.48/9.83 | | | | | | | | % 67.48/9.83 | | | | | | | | (93) all_677_0 = all_120_0 & k1_lattices(all_87_3, all_120_2, % 67.48/9.83 | | | | | | | | all_120_3) = all_120_0 & $i(all_120_0) % 67.48/9.83 | | | | | | | | % 67.48/9.83 | | | | | | | | ALPHA: (93) implies: % 67.48/9.83 | | | | | | | | (94) k1_lattices(all_87_3, all_120_2, all_120_3) = all_120_0 % 67.48/9.83 | | | | | | | | % 67.48/9.83 | | | | | | | | BETA: splitting (64) gives: % 67.48/9.83 | | | | | | | | % 67.48/9.83 | | | | | | | | Case 1: % 67.48/9.83 | | | | | | | | | % 67.48/9.83 | | | | | | | | | % 67.48/9.83 | | | | | | | | | GROUND_INST: instantiating (56) with all_120_2, all_120_3, % 67.48/9.83 | | | | | | | | | all_120_0, simplifying with (47), (48), (51), % 67.48/9.83 | | | | | | | | | (52), (94) gives: % 67.48/9.83 | | | | | | | | | (95) k2_binop_1(all_87_2, all_87_2, all_87_2, all_140_0, % 67.48/9.83 | | | | | | | | | all_120_2, all_120_3) = all_120_0 & $i(all_120_0) % 67.48/9.83 | | | | | | | | | % 67.48/9.83 | | | | | | | | | ALPHA: (95) implies: % 67.48/9.83 | | | | | | | | | (96) $i(all_120_0) % 67.48/9.83 | | | | | | | | | % 67.48/9.84 | | | | | | | | | GROUND_INST: instantiating (10) with all_87_3, all_120_3, % 67.48/9.84 | | | | | | | | | all_120_0, all_120_3, simplifying with (14), (19), % 67.48/9.84 | | | | | | | | | (27), (29), (51), (91), (96) gives: % 67.48/9.84 | | | | | | | | | (97) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_3 & % 67.48/9.84 | | | | | | | | | k4_lattices(all_87_3, all_120_3, all_120_0) = % 67.48/9.84 | | | | | | | | | all_120_3) | (u1_struct_0(all_87_3) = v0 & $i(v0) % 67.48/9.84 | | | | | | | | | & ( ~ m1_subset_1(all_120_0, v0) | ~ % 67.48/9.84 | | | | | | | | | m1_subset_1(all_120_3, v0)))) % 67.48/9.84 | | | | | | | | | % 67.48/9.84 | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_742_0, % 67.48/9.84 | | | | | | | | | all_742_1 gives: % 67.48/9.84 | | | | | | | | | (98) (all_742_0 = all_120_3 & k4_lattices(all_87_3, % 67.48/9.84 | | | | | | | | | all_120_3, all_120_0) = all_120_3) | % 67.48/9.84 | | | | | | | | | (u1_struct_0(all_87_3) = all_742_1 & $i(all_742_1) & ( % 67.48/9.84 | | | | | | | | | ~ m1_subset_1(all_120_0, all_742_1) | ~ % 67.48/9.84 | | | | | | | | | m1_subset_1(all_120_3, all_742_1))) % 67.48/9.84 | | | | | | | | | % 67.48/9.84 | | | | | | | | | BETA: splitting (98) gives: % 67.48/9.84 | | | | | | | | | % 67.48/9.84 | | | | | | | | | Case 1: % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | (99) all_742_0 = all_120_3 & k4_lattices(all_87_3, % 67.48/9.84 | | | | | | | | | | all_120_3, all_120_0) = all_120_3 % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | ALPHA: (99) implies: % 67.48/9.84 | | | | | | | | | | (100) k4_lattices(all_87_3, all_120_3, all_120_0) = % 67.48/9.84 | | | | | | | | | | all_120_3 % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | GROUND_INST: instantiating (25) with all_120_3, all_120_0, % 67.48/9.84 | | | | | | | | | | all_120_3, simplifying with (47), (49), (51), % 67.48/9.84 | | | | | | | | | | (62), (87), (96), (100) gives: % 67.48/9.84 | | | | | | | | | | (101) $false % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | CLOSE: (101) is inconsistent. % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | Case 2: % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | (102) u1_struct_0(all_87_3) = all_742_1 & $i(all_742_1) & % 67.48/9.84 | | | | | | | | | | ( ~ m1_subset_1(all_120_0, all_742_1) | ~ % 67.48/9.84 | | | | | | | | | | m1_subset_1(all_120_3, all_742_1)) % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | ALPHA: (102) implies: % 67.48/9.84 | | | | | | | | | | (103) u1_struct_0(all_87_3) = all_742_1 % 67.48/9.84 | | | | | | | | | | (104) ~ m1_subset_1(all_120_0, all_742_1) | ~ % 67.48/9.84 | | | | | | | | | | m1_subset_1(all_120_3, all_742_1) % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | GROUND_INST: instantiating (12) with all_87_2, all_742_1, % 67.48/9.84 | | | | | | | | | | all_87_3, simplifying with (23), (103) gives: % 67.48/9.84 | | | | | | | | | | (105) all_742_1 = all_87_2 % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | BETA: splitting (104) gives: % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | Case 1: % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | (106) ~ m1_subset_1(all_120_0, all_742_1) % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | REDUCE: (105), (106) imply: % 67.48/9.84 | | | | | | | | | | | (107) ~ m1_subset_1(all_120_0, all_87_2) % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | PRED_UNIFY: (87), (107) imply: % 67.48/9.84 | | | | | | | | | | | (108) $false % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | CLOSE: (108) is inconsistent. % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | Case 2: % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | (109) ~ m1_subset_1(all_120_3, all_742_1) % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | REDUCE: (105), (109) imply: % 67.48/9.84 | | | | | | | | | | | (110) ~ m1_subset_1(all_120_3, all_87_2) % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | PRED_UNIFY: (47), (110) imply: % 67.48/9.84 | | | | | | | | | | | (111) $false % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | | CLOSE: (111) is inconsistent. % 67.48/9.84 | | | | | | | | | | | % 67.48/9.84 | | | | | | | | | | End of split % 67.48/9.84 | | | | | | | | | | % 67.48/9.84 | | | | | | | | | End of split % 67.48/9.84 | | | | | | | | | % 67.48/9.84 | | | | | | | | Case 2: % 67.48/9.84 | | | | | | | | | % 67.48/9.84 | | | | | | | | | (112) r2_hidden(all_87_2, all_87_2) % 67.48/9.84 | | | | | | | | | % 67.48/9.84 | | | | | | | | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with % 67.48/9.84 | | | | | | | | | all_87_2, all_87_2, simplifying with (20), (112) % 67.48/9.84 | | | | | | | | | gives: % 67.48/9.85 | | | | | | | | | (113) $false % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | CLOSE: (113) is inconsistent. % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | End of split % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | Case 2: % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | (114) u1_struct_0(all_87_3) = all_677_1 & $i(all_677_1) & ( ~ % 67.48/9.85 | | | | | | | | m1_subset_1(all_120_2, all_677_1) | ~ % 67.48/9.85 | | | | | | | | m1_subset_1(all_120_3, all_677_1)) % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | ALPHA: (114) implies: % 67.48/9.85 | | | | | | | | (115) u1_struct_0(all_87_3) = all_677_1 % 67.48/9.85 | | | | | | | | (116) ~ m1_subset_1(all_120_2, all_677_1) | ~ % 67.48/9.85 | | | | | | | | m1_subset_1(all_120_3, all_677_1) % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | GROUND_INST: instantiating (12) with all_87_2, all_677_1, % 67.48/9.85 | | | | | | | | all_87_3, simplifying with (23), (115) gives: % 67.48/9.85 | | | | | | | | (117) all_677_1 = all_87_2 % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | BETA: splitting (116) gives: % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | Case 1: % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | (118) ~ m1_subset_1(all_120_2, all_677_1) % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | REDUCE: (117), (118) imply: % 67.48/9.85 | | | | | | | | | (119) ~ m1_subset_1(all_120_2, all_87_2) % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | PRED_UNIFY: (48), (119) imply: % 67.48/9.85 | | | | | | | | | (120) $false % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | CLOSE: (120) is inconsistent. % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | Case 2: % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | (121) ~ m1_subset_1(all_120_3, all_677_1) % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | REDUCE: (117), (121) imply: % 67.48/9.85 | | | | | | | | | (122) ~ m1_subset_1(all_120_3, all_87_2) % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | PRED_UNIFY: (47), (122) imply: % 67.48/9.85 | | | | | | | | | (123) $false % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | | CLOSE: (123) is inconsistent. % 67.48/9.85 | | | | | | | | | % 67.48/9.85 | | | | | | | | End of split % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | End of split % 67.48/9.85 | | | | | | | % 67.48/9.85 | | | | | | Case 2: % 67.48/9.85 | | | | | | | % 67.48/9.85 | | | | | | | (124) u1_struct_0(all_87_3) = all_494_1 & $i(all_494_1) & ( ~ % 67.48/9.85 | | | | | | | m1_subset_1(all_120_2, all_494_1) | ~ % 67.48/9.85 | | | | | | | m1_subset_1(all_120_3, all_494_1)) % 67.48/9.85 | | | | | | | % 67.48/9.85 | | | | | | | ALPHA: (124) implies: % 67.48/9.85 | | | | | | | (125) u1_struct_0(all_87_3) = all_494_1 % 67.48/9.85 | | | | | | | (126) ~ m1_subset_1(all_120_2, all_494_1) | ~ % 67.48/9.85 | | | | | | | m1_subset_1(all_120_3, all_494_1) % 67.48/9.85 | | | | | | | % 67.48/9.85 | | | | | | | GROUND_INST: instantiating (12) with all_87_2, all_494_1, % 67.48/9.85 | | | | | | | all_87_3, simplifying with (23), (125) gives: % 67.48/9.85 | | | | | | | (127) all_494_1 = all_87_2 % 67.48/9.85 | | | | | | | % 67.48/9.85 | | | | | | | BETA: splitting (126) gives: % 67.48/9.85 | | | | | | | % 67.48/9.85 | | | | | | | Case 1: % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | (128) ~ m1_subset_1(all_120_2, all_494_1) % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | REDUCE: (127), (128) imply: % 67.48/9.85 | | | | | | | | (129) ~ m1_subset_1(all_120_2, all_87_2) % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | PRED_UNIFY: (48), (129) imply: % 67.48/9.85 | | | | | | | | (130) $false % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | CLOSE: (130) is inconsistent. % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | Case 2: % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | (131) ~ m1_subset_1(all_120_3, all_494_1) % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | REDUCE: (127), (131) imply: % 67.48/9.85 | | | | | | | | (132) ~ m1_subset_1(all_120_3, all_87_2) % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | PRED_UNIFY: (47), (132) imply: % 67.48/9.85 | | | | | | | | (133) $false % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | | CLOSE: (133) is inconsistent. % 67.48/9.85 | | | | | | | | % 67.48/9.85 | | | | | | | End of split % 67.48/9.85 | | | | | | | % 67.48/9.85 | | | | | | End of split % 67.48/9.85 | | | | | | % 67.48/9.85 | | | | | End of split % 67.48/9.85 | | | | | % 67.48/9.85 | | | | End of split % 67.48/9.85 | | | | % 67.48/9.85 | | | Case 2: % 67.48/9.86 | | | | % 67.48/9.86 | | | | (134) u1_struct_0(all_87_3) = all_495_1 & $i(all_495_1) & ( ~ % 67.48/9.86 | | | | m1_subset_1(all_120_2, all_495_1) | ~ m1_subset_1(all_120_3, % 67.48/9.86 | | | | all_495_1)) % 67.48/9.86 | | | | % 67.48/9.86 | | | | ALPHA: (134) implies: % 67.48/9.86 | | | | (135) u1_struct_0(all_87_3) = all_495_1 % 67.48/9.86 | | | | (136) ~ m1_subset_1(all_120_2, all_495_1) | ~ % 67.48/9.86 | | | | m1_subset_1(all_120_3, all_495_1) % 67.48/9.86 | | | | % 67.48/9.86 | | | | GROUND_INST: instantiating (12) with all_87_2, all_495_1, all_87_3, % 67.48/9.86 | | | | simplifying with (23), (135) gives: % 67.48/9.86 | | | | (137) all_495_1 = all_87_2 % 67.48/9.86 | | | | % 67.48/9.86 | | | | GROUND_INST: instantiating (12) with all_492_0, all_495_1, all_87_3, % 67.48/9.86 | | | | simplifying with (70), (135) gives: % 67.48/9.86 | | | | (138) all_495_1 = all_492_0 % 67.48/9.86 | | | | % 67.48/9.86 | | | | COMBINE_EQS: (137), (138) imply: % 67.48/9.86 | | | | (139) all_492_0 = all_87_2 % 67.48/9.86 | | | | % 67.48/9.86 | | | | BETA: splitting (136) gives: % 67.48/9.86 | | | | % 67.48/9.86 | | | | Case 1: % 67.48/9.86 | | | | | % 67.48/9.86 | | | | | (140) ~ m1_subset_1(all_120_2, all_495_1) % 67.48/9.86 | | | | | % 67.48/9.86 | | | | | REDUCE: (137), (140) imply: % 67.48/9.86 | | | | | (141) ~ m1_subset_1(all_120_2, all_87_2) % 67.48/9.86 | | | | | % 67.61/9.86 | | | | | PRED_UNIFY: (48), (141) imply: % 67.61/9.86 | | | | | (142) $false % 67.61/9.86 | | | | | % 67.61/9.86 | | | | | CLOSE: (142) is inconsistent. % 67.61/9.86 | | | | | % 67.61/9.86 | | | | Case 2: % 67.61/9.86 | | | | | % 67.61/9.86 | | | | | (143) ~ m1_subset_1(all_120_3, all_495_1) % 67.61/9.86 | | | | | % 67.61/9.86 | | | | | REDUCE: (137), (143) imply: % 67.61/9.86 | | | | | (144) ~ m1_subset_1(all_120_3, all_87_2) % 67.61/9.86 | | | | | % 67.61/9.86 | | | | | PRED_UNIFY: (47), (144) imply: % 67.61/9.86 | | | | | (145) $false % 67.61/9.86 | | | | | % 67.61/9.86 | | | | | CLOSE: (145) is inconsistent. % 67.61/9.86 | | | | | % 67.61/9.86 | | | | End of split % 67.61/9.86 | | | | % 67.61/9.86 | | | End of split % 67.61/9.86 | | | % 67.61/9.86 | | End of split % 67.61/9.86 | | % 67.61/9.86 | End of split % 67.61/9.86 | % 67.61/9.86 End of proof % 67.61/9.86 % SZS output end Proof for theBenchmark % 67.61/9.86 % 67.61/9.86 9235ms %------------------------------------------------------------------------------