%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU174+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:03 EDT 2023 % Result : Theorem 33.79s 5.42s % Output : Proof 34.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SEU174+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n002.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Wed Aug 23 19:58:46 EDT 2023 % 0.15/0.36 % CPUTime : % 0.21/0.68 ________ _____ % 0.21/0.68 ___ __ \_________(_)________________________________ % 0.21/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.68 % 0.21/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.68 (2023-06-19) % 0.21/0.68 % 0.21/0.68 (c) Philipp Rümmer, 2009-2023 % 0.21/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.68 Amanda Stjerna. % 0.21/0.68 Free software under BSD-3-Clause. % 0.21/0.68 % 0.21/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.68 % 0.21/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.70 Running up to 7 provers in parallel. % 0.21/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.59/1.48 Prover 4: Preprocessing ... % 4.59/1.50 Prover 1: Preprocessing ... % 4.59/1.51 Prover 5: Preprocessing ... % 4.59/1.51 Prover 0: Preprocessing ... % 4.59/1.51 Prover 6: Preprocessing ... % 4.59/1.51 Prover 3: Preprocessing ... % 4.59/1.52 Prover 2: Preprocessing ... % 12.36/2.58 Prover 1: Warning: ignoring some quantifiers % 12.99/2.62 Prover 5: Proving ... % 12.99/2.70 Prover 3: Warning: ignoring some quantifiers % 12.99/2.72 Prover 1: Constructing countermodel ... % 12.99/2.72 Prover 6: Proving ... % 12.99/2.73 Prover 3: Constructing countermodel ... % 13.86/2.80 Prover 4: Warning: ignoring some quantifiers % 13.86/2.86 Prover 2: Proving ... % 15.09/2.92 Prover 4: Constructing countermodel ... % 15.14/3.00 Prover 0: Proving ... % 33.79/5.40 Prover 1: Found proof (size 187) % 33.79/5.42 Prover 1: proved (4692ms) % 33.79/5.42 Prover 0: stopped % 33.79/5.42 Prover 2: stopped % 33.79/5.42 Prover 6: stopped % 33.79/5.42 Prover 5: stopped % 33.79/5.42 Prover 4: stopped % 33.79/5.42 Prover 3: stopped % 33.79/5.42 % 33.79/5.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 33.79/5.42 % 33.79/5.44 % SZS output start Proof for theBenchmark % 33.79/5.44 Assumptions after simplification: % 33.79/5.44 --------------------------------- % 33.79/5.44 % 33.79/5.44 (d2_subset_1) % 34.29/5.47 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~ % 34.29/5.47 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & in(v1, % 34.29/5.47 v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 34.29/5.47 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = % 34.29/5.47 v2) | ~ (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 34.29/5.47 (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 34.29/5.47 % 34.29/5.47 (d4_xboole_0) % 34.29/5.48 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 34.29/5.48 (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 34.29/5.48 $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 34.29/5.48 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) | % 34.29/5.48 v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: % 34.29/5.48 $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v2) | ~ % 34.29/5.48 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | % 34.29/5.48 ~ $i(v3) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = % 34.29/5.48 v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ % 34.29/5.48 (in(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 34.29/5.48 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 34.29/5.48 % 34.29/5.48 (d5_subset_1) % 34.29/5.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) | ~ % 34.29/5.48 (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 34.29/5.48 (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 & $i(v3))) % 34.29/5.48 % 34.29/5.48 (d8_setfam_1) % 34.29/5.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 34.29/5.48 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 34.29/5.48 $i(v0) | ? [v4: $i] : (complements_of_subsets(v0, v1) = v4 & $i(v4) & ! % 34.29/5.48 [v5: $i] : ( ~ (element(v5, v3) = 0) | ~ $i(v5) | (( ~ (v5 = v4) | ! % 34.29/5.48 [v6: $i] : ( ~ (element(v6, v2) = 0) | ~ $i(v6) | ? [v7: any] : ? % 34.29/5.48 [v8: $i] : ? [v9: any] : (subset_complement(v0, v6) = v8 & in(v8, % 34.29/5.48 v1) = v9 & in(v6, v4) = v7 & $i(v8) & ( ~ (v9 = 0) | v7 = 0) & % 34.29/5.48 ( ~ (v7 = 0) | v9 = 0)))) & (v5 = v4 | ? [v6: $i] : ? [v7: % 34.29/5.48 any] : ? [v8: $i] : ? [v9: any] : (subset_complement(v0, v6) = % 34.29/5.48 v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & % 34.29/5.48 $i(v8) & $i(v6) & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = % 34.29/5.48 0))))))) % 34.29/5.48 % 34.29/5.48 (fc1_subset_1) % 34.29/5.48 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] % 34.29/5.48 : ( ~ (v2 = 0) & empty(v1) = v2)) % 34.29/5.48 % 34.29/5.48 (involutiveness_k7_setfam_1) % 34.29/5.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 34.29/5.48 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 34.37/5.48 $i(v0) | ? [v4: $i] : (complements_of_subsets(v0, v4) = v1 & % 34.37/5.48 complements_of_subsets(v0, v1) = v4 & $i(v4))) % 34.37/5.48 % 34.37/5.48 (rc1_subset_1) % 34.37/5.48 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 34.37/5.48 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~ % 34.37/5.48 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3)))) % 34.37/5.48 % 34.37/5.48 (rc1_xboole_0) % 34.37/5.49 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 34.37/5.49 % 34.37/5.49 (rc2_subset_1) % 34.37/5.49 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 34.37/5.49 : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2))) % 34.37/5.49 % 34.37/5.49 (rc2_xboole_0) % 34.37/5.49 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 34.37/5.49 % 34.37/5.49 (t1_zfmisc_1) % 34.37/5.49 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) % 34.37/5.49 = v0 & $i(v0)) % 34.37/5.49 % 34.37/5.49 (t3_boole) % 34.37/5.49 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0, % 34.37/5.49 empty_set) = v1) | ~ $i(v0)) % 34.37/5.49 % 34.37/5.49 (t43_subset_1) % 34.37/5.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) | ~ % 34.37/5.49 (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (element(v3, % 34.37/5.49 v2) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 34.37/5.49 (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) = % 34.37/5.49 v6 & $i(v5) & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))) % 34.37/5.49 % 34.37/5.49 (t46_setfam_1) % 34.37/5.49 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ % 34.37/5.49 (v1 = empty_set) & complements_of_subsets(v0, v1) = empty_set & element(v1, % 34.37/5.49 v3) = 0 & powerset(v2) = v3 & powerset(v0) = v2 & $i(v3) & $i(v2) & $i(v1) % 34.37/5.49 & $i(v0)) % 34.37/5.49 % 34.37/5.49 (t6_boole) % 34.37/5.49 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 34.37/5.49 $i(v0)) % 34.37/5.49 % 34.37/5.49 (t8_boole) % 34.37/5.49 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 34.37/5.49 | ~ $i(v1) | ~ $i(v0)) % 34.37/5.49 % 34.37/5.49 (function-axioms) % 34.37/5.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 34.37/5.49 [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 34.37/5.49 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.37/5.49 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 34.37/5.49 (complements_of_subsets(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 34.37/5.49 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.37/5.49 (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! % 34.37/5.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, % 34.37/5.49 v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 34.37/5.49 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = % 34.37/5.49 v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 34.37/5.49 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 34.37/5.49 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 34.37/5.49 : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 34.37/5.49 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.37/5.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 34.37/5.49 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 34.37/5.50 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.37/5.50 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 34.37/5.50 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = % 34.37/5.50 v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 34.37/5.50 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ % 34.37/5.50 (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 34.37/5.50 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 34.37/5.50 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.37/5.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.37/5.50 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 34.37/5.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 34.37/5.50 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 34.37/5.50 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 34.37/5.50 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 34.37/5.50 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: % 34.37/5.50 $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = % 34.37/5.50 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.37/5.50 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 34.37/5.50 % 34.37/5.50 Further assumptions not needed in the proof: % 34.37/5.50 -------------------------------------------- % 34.37/5.50 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 34.37/5.50 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, % 34.37/5.50 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski, % 34.37/5.50 d3_xboole_0, d4_tarski, d5_tarski, d7_xboole_0, d8_xboole_0, dt_k1_tarski, % 34.37/5.50 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, % 34.37/5.50 dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, % 34.37/5.50 dt_k7_setfam_1, dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, % 34.37/5.50 fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 34.37/5.50 idempotence_k3_xboole_0, involutiveness_k3_subset_1, irreflexivity_r2_xboole_0, % 34.37/5.50 l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, % 34.37/5.50 l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, % 34.37/5.50 l71_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, % 34.37/5.50 t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, % 34.37/5.50 t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t26_xboole_1, % 34.37/5.50 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t33_xboole_1, % 34.37/5.50 t33_zfmisc_1, t36_xboole_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, % 34.37/5.50 t39_xboole_1, t39_zfmisc_1, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, % 34.37/5.50 t45_xboole_1, t46_zfmisc_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, % 34.37/5.50 t50_subset_1, t54_subset_1, t5_subset, t60_xboole_1, t63_xboole_1, t65_zfmisc_1, % 34.37/5.50 t69_enumset1, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_xboole_1, % 34.37/5.50 t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 34.37/5.50 % 34.37/5.50 Those formulas are unsatisfiable: % 34.37/5.50 --------------------------------- % 34.37/5.50 % 34.37/5.50 Begin of proof % 34.37/5.50 | % 34.37/5.50 | ALPHA: (d2_subset_1) implies: % 34.37/5.50 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = v2) | ~ % 34.37/5.50 | (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : (element(v1, % 34.37/5.50 | v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 34.37/5.50 | % 34.37/5.50 | ALPHA: (d4_xboole_0) implies: % 34.37/5.50 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = % 34.37/5.50 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: % 34.37/5.50 | any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: % 34.37/5.50 | any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 % 34.37/5.50 | = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 34.37/5.50 | | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 34.37/5.50 | in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 34.37/5.50 | % 34.37/5.50 | ALPHA: (t1_zfmisc_1) implies: % 34.37/5.50 | (3) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 & % 34.37/5.50 | $i(v0)) % 34.37/5.50 | % 34.37/5.50 | ALPHA: (t3_boole) implies: % 34.37/5.50 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (set_difference(v0, % 34.37/5.50 | empty_set) = v1) | ~ $i(v0)) % 34.37/5.50 | % 34.37/5.50 | ALPHA: (t6_boole) implies: % 34.37/5.50 | (5) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 34.37/5.50 | % 34.37/5.50 | ALPHA: (t46_setfam_1) implies: % 34.37/5.50 | (6) $i(empty_set) % 34.37/5.50 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = % 34.37/5.50 | empty_set) & complements_of_subsets(v0, v1) = empty_set & % 34.37/5.50 | element(v1, v3) = 0 & powerset(v2) = v3 & powerset(v0) = v2 & $i(v3) % 34.37/5.50 | & $i(v2) & $i(v1) & $i(v0)) % 34.37/5.50 | % 34.37/5.50 | ALPHA: (function-axioms) implies: % 34.37/5.50 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 34.37/5.50 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 34.37/5.50 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.37/5.50 | (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = % 34.37/5.50 | v0)) % 34.37/5.51 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 34.37/5.51 | (complements_of_subsets(v3, v2) = v1) | ~ % 34.37/5.51 | (complements_of_subsets(v3, v2) = v0)) % 34.37/5.51 | % 34.37/5.51 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_102_0 gives: % 34.37/5.51 | (11) empty(all_102_0) = 0 & $i(all_102_0) % 34.37/5.51 | % 34.37/5.51 | ALPHA: (11) implies: % 34.37/5.51 | (12) $i(all_102_0) % 34.37/5.51 | (13) empty(all_102_0) = 0 % 34.37/5.51 | % 34.37/5.51 | DELTA: instantiating (3) with fresh symbol all_104_0 gives: % 34.37/5.51 | (14) powerset(empty_set) = all_104_0 & singleton(empty_set) = all_104_0 & % 34.37/5.51 | $i(all_104_0) % 34.37/5.51 | % 34.37/5.51 | ALPHA: (14) implies: % 34.37/5.51 | (15) $i(all_104_0) % 34.37/5.51 | (16) powerset(empty_set) = all_104_0 % 34.37/5.51 | % 34.37/5.51 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_106_0, all_106_1 % 34.37/5.51 | gives: % 34.37/5.51 | (17) ~ (all_106_0 = 0) & empty(all_106_1) = all_106_0 & $i(all_106_1) % 34.37/5.51 | % 34.37/5.51 | ALPHA: (17) implies: % 34.37/5.51 | (18) ~ (all_106_0 = 0) % 34.37/5.51 | (19) $i(all_106_1) % 34.37/5.51 | (20) empty(all_106_1) = all_106_0 % 34.37/5.51 | % 34.37/5.51 | DELTA: instantiating (7) with fresh symbols all_118_0, all_118_1, all_118_2, % 34.37/5.51 | all_118_3 gives: % 34.37/5.51 | (21) ~ (all_118_2 = empty_set) & complements_of_subsets(all_118_3, % 34.37/5.51 | all_118_2) = empty_set & element(all_118_2, all_118_0) = 0 & % 34.37/5.51 | powerset(all_118_1) = all_118_0 & powerset(all_118_3) = all_118_1 & % 34.37/5.51 | $i(all_118_0) & $i(all_118_1) & $i(all_118_2) & $i(all_118_3) % 34.37/5.51 | % 34.37/5.51 | ALPHA: (21) implies: % 34.37/5.51 | (22) ~ (all_118_2 = empty_set) % 34.37/5.51 | (23) $i(all_118_3) % 34.37/5.51 | (24) $i(all_118_2) % 34.37/5.51 | (25) $i(all_118_1) % 34.37/5.51 | (26) powerset(all_118_3) = all_118_1 % 34.37/5.51 | (27) powerset(all_118_1) = all_118_0 % 34.37/5.51 | (28) element(all_118_2, all_118_0) = 0 % 34.37/5.51 | (29) complements_of_subsets(all_118_3, all_118_2) = empty_set % 34.37/5.51 | % 34.37/5.51 | GROUND_INST: instantiating (fc1_subset_1) with empty_set, all_104_0, % 34.37/5.51 | simplifying with (6), (16) gives: % 34.37/5.51 | (30) ? [v0: int] : ( ~ (v0 = 0) & empty(all_104_0) = v0) % 34.37/5.51 | % 34.37/5.51 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_104_0, % 34.37/5.51 | simplifying with (6), (16) gives: % 34.37/5.51 | (31) ? [v0: $i] : (element(v0, all_104_0) = 0 & empty(v0) = 0 & $i(v0)) % 34.37/5.51 | % 34.37/5.51 | GROUND_INST: instantiating (fc1_subset_1) with all_118_3, all_118_1, % 34.37/5.51 | simplifying with (23), (26) gives: % 34.37/5.51 | (32) ? [v0: int] : ( ~ (v0 = 0) & empty(all_118_1) = v0) % 34.37/5.51 | % 34.37/5.51 | GROUND_INST: instantiating (rc2_subset_1) with all_118_3, all_118_1, % 34.37/5.51 | simplifying with (23), (26) gives: % 34.37/5.51 | (33) ? [v0: $i] : (element(v0, all_118_1) = 0 & empty(v0) = 0 & $i(v0)) % 34.37/5.51 | % 34.37/5.51 | GROUND_INST: instantiating (rc2_subset_1) with all_118_1, all_118_0, % 34.37/5.51 | simplifying with (25), (27) gives: % 34.37/5.51 | (34) ? [v0: $i] : (element(v0, all_118_0) = 0 & empty(v0) = 0 & $i(v0)) % 34.37/5.51 | % 34.37/5.51 | GROUND_INST: instantiating (1) with all_102_0, all_106_1, all_106_0, % 34.37/5.51 | simplifying with (12), (13), (19), (20) gives: % 34.37/5.51 | (35) ? [v0: any] : (element(all_106_1, all_102_0) = v0 & ( ~ (v0 = 0) | % 34.37/5.51 | all_106_0 = 0) & ( ~ (all_106_0 = 0) | v0 = 0)) % 34.37/5.51 | % 34.37/5.51 | GROUND_INST: instantiating (involutiveness_k7_setfam_1) with all_118_3, % 34.37/5.51 | all_118_2, all_118_1, all_118_0, simplifying with (23), (24), % 34.37/5.51 | (26), (27), (28) gives: % 34.37/5.52 | (36) ? [v0: $i] : (complements_of_subsets(all_118_3, v0) = all_118_2 & % 34.37/5.52 | complements_of_subsets(all_118_3, all_118_2) = v0 & $i(v0)) % 34.37/5.52 | % 34.37/5.52 | GROUND_INST: instantiating (d8_setfam_1) with all_118_3, all_118_2, all_118_1, % 34.37/5.52 | all_118_0, simplifying with (23), (24), (26), (27), (28) gives: % 34.37/5.52 | (37) ? [v0: $i] : (complements_of_subsets(all_118_3, all_118_2) = v0 & % 34.37/5.52 | $i(v0) & ! [v1: $i] : ( ~ (element(v1, all_118_0) = 0) | ~ $i(v1) % 34.37/5.52 | | (( ~ (v1 = v0) | ! [v2: $i] : ( ~ (element(v2, all_118_1) = 0) % 34.37/5.52 | | ~ $i(v2) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 34.37/5.52 | (subset_complement(all_118_3, v2) = v4 & in(v4, all_118_2) = % 34.37/5.52 | v5 & in(v2, v0) = v3 & $i(v4) & ( ~ (v5 = 0) | v3 = 0) & ( % 34.37/5.52 | ~ (v3 = 0) | v5 = 0)))) & (v1 = v0 | ? [v2: $i] : ? % 34.37/5.52 | [v3: any] : ? [v4: $i] : ? [v5: any] : % 34.37/5.52 | (subset_complement(all_118_3, v2) = v4 & element(v2, % 34.37/5.52 | all_118_1) = 0 & in(v4, all_118_2) = v5 & in(v2, v1) = v3 % 34.37/5.52 | & $i(v4) & $i(v2) & ( ~ (v5 = 0) | ~ (v3 = 0)) & (v5 = 0 | % 34.37/5.52 | v3 = 0)))))) % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (32) with fresh symbol all_151_0 gives: % 34.37/5.52 | (38) ~ (all_151_0 = 0) & empty(all_118_1) = all_151_0 % 34.37/5.52 | % 34.37/5.52 | ALPHA: (38) implies: % 34.37/5.52 | (39) ~ (all_151_0 = 0) % 34.37/5.52 | (40) empty(all_118_1) = all_151_0 % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (30) with fresh symbol all_155_0 gives: % 34.37/5.52 | (41) ~ (all_155_0 = 0) & empty(all_104_0) = all_155_0 % 34.37/5.52 | % 34.37/5.52 | ALPHA: (41) implies: % 34.37/5.52 | (42) ~ (all_155_0 = 0) % 34.37/5.52 | (43) empty(all_104_0) = all_155_0 % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (31) with fresh symbol all_157_0 gives: % 34.37/5.52 | (44) element(all_157_0, all_104_0) = 0 & empty(all_157_0) = 0 & % 34.37/5.52 | $i(all_157_0) % 34.37/5.52 | % 34.37/5.52 | ALPHA: (44) implies: % 34.37/5.52 | (45) $i(all_157_0) % 34.37/5.52 | (46) empty(all_157_0) = 0 % 34.37/5.52 | (47) element(all_157_0, all_104_0) = 0 % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (33) with fresh symbol all_159_0 gives: % 34.37/5.52 | (48) element(all_159_0, all_118_1) = 0 & empty(all_159_0) = 0 & % 34.37/5.52 | $i(all_159_0) % 34.37/5.52 | % 34.37/5.52 | ALPHA: (48) implies: % 34.37/5.52 | (49) $i(all_159_0) % 34.37/5.52 | (50) empty(all_159_0) = 0 % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (36) with fresh symbol all_163_0 gives: % 34.37/5.52 | (51) complements_of_subsets(all_118_3, all_163_0) = all_118_2 & % 34.37/5.52 | complements_of_subsets(all_118_3, all_118_2) = all_163_0 & % 34.37/5.52 | $i(all_163_0) % 34.37/5.52 | % 34.37/5.52 | ALPHA: (51) implies: % 34.37/5.52 | (52) $i(all_163_0) % 34.37/5.52 | (53) complements_of_subsets(all_118_3, all_118_2) = all_163_0 % 34.37/5.52 | (54) complements_of_subsets(all_118_3, all_163_0) = all_118_2 % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (34) with fresh symbol all_165_0 gives: % 34.37/5.52 | (55) element(all_165_0, all_118_0) = 0 & empty(all_165_0) = 0 & % 34.37/5.52 | $i(all_165_0) % 34.37/5.52 | % 34.37/5.52 | ALPHA: (55) implies: % 34.37/5.52 | (56) $i(all_165_0) % 34.37/5.52 | (57) empty(all_165_0) = 0 % 34.37/5.52 | (58) element(all_165_0, all_118_0) = 0 % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (35) with fresh symbol all_171_0 gives: % 34.37/5.52 | (59) element(all_106_1, all_102_0) = all_171_0 & ( ~ (all_171_0 = 0) | % 34.37/5.52 | all_106_0 = 0) & ( ~ (all_106_0 = 0) | all_171_0 = 0) % 34.37/5.52 | % 34.37/5.52 | ALPHA: (59) implies: % 34.37/5.52 | (60) ~ (all_171_0 = 0) | all_106_0 = 0 % 34.37/5.52 | % 34.37/5.52 | DELTA: instantiating (37) with fresh symbol all_175_0 gives: % 34.37/5.52 | (61) complements_of_subsets(all_118_3, all_118_2) = all_175_0 & % 34.37/5.52 | $i(all_175_0) & ! [v0: $i] : ( ~ (element(v0, all_118_0) = 0) | ~ % 34.37/5.52 | $i(v0) | (( ~ (v0 = all_175_0) | ! [v1: $i] : ( ~ (element(v1, % 34.37/5.52 | all_118_1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : % 34.37/5.52 | ? [v4: any] : (subset_complement(all_118_3, v1) = v3 & in(v3, % 34.37/5.52 | all_118_2) = v4 & in(v1, all_175_0) = v2 & $i(v3) & ( ~ % 34.37/5.52 | (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))) & (v0 = % 34.37/5.52 | all_175_0 | ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 34.37/5.52 | any] : (subset_complement(all_118_3, v1) = v3 & element(v1, % 34.37/5.52 | all_118_1) = 0 & in(v3, all_118_2) = v4 & in(v1, v0) = v2 & % 34.37/5.52 | $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = % 34.37/5.52 | 0))))) % 34.37/5.52 | % 34.37/5.52 | ALPHA: (61) implies: % 34.37/5.53 | (62) complements_of_subsets(all_118_3, all_118_2) = all_175_0 % 34.37/5.53 | (63) ! [v0: $i] : ( ~ (element(v0, all_118_0) = 0) | ~ $i(v0) | (( ~ (v0 % 34.37/5.53 | = all_175_0) | ! [v1: $i] : ( ~ (element(v1, all_118_1) = 0) % 34.37/5.53 | | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 34.37/5.53 | (subset_complement(all_118_3, v1) = v3 & in(v3, all_118_2) = % 34.37/5.53 | v4 & in(v1, all_175_0) = v2 & $i(v3) & ( ~ (v4 = 0) | v2 = % 34.37/5.53 | 0) & ( ~ (v2 = 0) | v4 = 0)))) & (v0 = all_175_0 | ? [v1: % 34.37/5.53 | $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 34.37/5.53 | (subset_complement(all_118_3, v1) = v3 & element(v1, all_118_1) % 34.37/5.53 | = 0 & in(v3, all_118_2) = v4 & in(v1, v0) = v2 & $i(v3) & % 34.37/5.53 | $i(v1) & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0))))) % 34.37/5.53 | % 34.37/5.53 | GROUND_INST: instantiating (63) with all_118_2, simplifying with (24), (28) % 34.37/5.53 | gives: % 34.37/5.53 | (64) ( ~ (all_175_0 = all_118_2) | ! [v0: $i] : ( ~ (element(v0, % 34.37/5.53 | all_118_1) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? % 34.37/5.53 | [v3: any] : (subset_complement(all_118_3, v0) = v2 & in(v2, % 34.37/5.53 | all_118_2) = v3 & in(v0, all_118_2) = v1 & $i(v2) & ( ~ (v3 = % 34.37/5.53 | 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))) & (all_175_0 = % 34.37/5.53 | all_118_2 | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] % 34.37/5.53 | : (subset_complement(all_118_3, v0) = v2 & element(v0, all_118_1) = % 34.37/5.53 | 0 & in(v2, all_118_2) = v3 & in(v0, all_118_2) = v1 & $i(v2) & % 34.37/5.53 | $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 34.37/5.53 | % 34.37/5.53 | ALPHA: (64) implies: % 34.37/5.53 | (65) all_175_0 = all_118_2 | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 34.37/5.53 | [v3: any] : (subset_complement(all_118_3, v0) = v2 & element(v0, % 34.37/5.53 | all_118_1) = 0 & in(v2, all_118_2) = v3 & in(v0, all_118_2) = v1 & % 34.37/5.53 | $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0)) % 34.37/5.53 | % 34.37/5.53 | BETA: splitting (60) gives: % 34.37/5.53 | % 34.37/5.53 | Case 1: % 34.37/5.53 | | % 34.37/5.53 | | % 34.37/5.53 | | GROUND_INST: instantiating (10) with empty_set, all_175_0, all_118_2, % 34.37/5.53 | | all_118_3, simplifying with (29), (62) gives: % 34.37/5.53 | | (66) all_175_0 = empty_set % 34.37/5.53 | | % 34.37/5.53 | | GROUND_INST: instantiating (10) with all_163_0, all_175_0, all_118_2, % 34.37/5.53 | | all_118_3, simplifying with (53), (62) gives: % 34.37/5.53 | | (67) all_175_0 = all_163_0 % 34.37/5.53 | | % 34.37/5.53 | | COMBINE_EQS: (66), (67) imply: % 34.37/5.53 | | (68) all_163_0 = empty_set % 34.37/5.53 | | % 34.37/5.53 | | REDUCE: (54), (68) imply: % 34.37/5.53 | | (69) complements_of_subsets(all_118_3, empty_set) = all_118_2 % 34.37/5.53 | | % 34.37/5.53 | | BETA: splitting (65) gives: % 34.37/5.53 | | % 34.37/5.53 | | Case 1: % 34.37/5.53 | | | % 34.37/5.53 | | | (70) all_175_0 = all_118_2 % 34.37/5.53 | | | % 34.37/5.53 | | | COMBINE_EQS: (66), (70) imply: % 34.37/5.53 | | | (71) all_118_2 = empty_set % 34.37/5.53 | | | % 34.37/5.53 | | | SIMP: (71) implies: % 34.37/5.53 | | | (72) all_118_2 = empty_set % 34.37/5.53 | | | % 34.37/5.53 | | | REDUCE: (22), (72) imply: % 34.37/5.53 | | | (73) $false % 34.37/5.53 | | | % 34.37/5.53 | | | CLOSE: (73) is inconsistent. % 34.37/5.53 | | | % 34.37/5.53 | | Case 2: % 34.37/5.53 | | | % 34.37/5.53 | | | (74) ~ (all_175_0 = all_118_2) % 34.37/5.53 | | | % 34.37/5.53 | | | REDUCE: (66), (74) imply: % 34.37/5.53 | | | (75) ~ (all_118_2 = empty_set) % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (rc1_subset_1) with all_118_1, all_151_0, % 34.37/5.54 | | | simplifying with (25), (40) gives: % 34.37/5.54 | | | (76) all_151_0 = 0 | ? [v0: $i] : (powerset(all_118_1) = v0 & $i(v0) & % 34.37/5.54 | | | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 % 34.37/5.54 | | | & empty(v1) = v2 & $i(v1))) % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (1) with all_159_0, all_104_0, all_155_0, % 34.37/5.54 | | | simplifying with (15), (43), (49), (50) gives: % 34.37/5.54 | | | (77) ? [v0: any] : (element(all_104_0, all_159_0) = v0 & ( ~ (v0 = 0) % 34.37/5.54 | | | | all_155_0 = 0) & ( ~ (all_155_0 = 0) | v0 = 0)) % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (5) with all_159_0, simplifying with (49), (50) % 34.37/5.54 | | | gives: % 34.37/5.54 | | | (78) all_159_0 = empty_set % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (t8_boole) with all_159_0, all_165_0, % 34.37/5.54 | | | simplifying with (49), (50), (56), (57) gives: % 34.37/5.54 | | | (79) all_165_0 = all_159_0 % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (t8_boole) with all_157_0, all_165_0, % 34.37/5.54 | | | simplifying with (45), (46), (56), (57) gives: % 34.37/5.54 | | | (80) all_165_0 = all_157_0 % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (d5_subset_1) with empty_set, all_157_0, % 34.37/5.54 | | | all_104_0, simplifying with (6), (16), (45), (47) gives: % 34.37/5.54 | | | (81) ? [v0: $i] : (subset_complement(empty_set, all_157_0) = v0 & % 34.37/5.54 | | | set_difference(empty_set, all_157_0) = v0 & $i(v0)) % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (t43_subset_1) with empty_set, all_157_0, % 34.37/5.54 | | | all_104_0, simplifying with (6), (16), (45), (47) gives: % 34.37/5.54 | | | (82) ! [v0: $i] : ( ~ (element(v0, all_104_0) = 0) | ~ $i(v0) | ? % 34.37/5.54 | | | [v1: any] : ? [v2: $i] : ? [v3: any] : (disjoint(all_157_0, % 34.37/5.54 | | | v0) = v1 & subset_complement(empty_set, v0) = v2 & % 34.37/5.54 | | | subset(all_157_0, v2) = v3 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) & % 34.37/5.54 | | | ( ~ (v1 = 0) | v3 = 0))) % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (d8_setfam_1) with all_118_3, all_165_0, % 34.37/5.54 | | | all_118_1, all_118_0, simplifying with (23), (26), (27), % 34.37/5.54 | | | (56), (58) gives: % 34.37/5.54 | | | (83) ? [v0: $i] : (complements_of_subsets(all_118_3, all_165_0) = v0 & % 34.37/5.54 | | | $i(v0) & ! [v1: $i] : ( ~ (element(v1, all_118_0) = 0) | ~ % 34.37/5.54 | | | $i(v1) | (( ~ (v1 = v0) | ! [v2: $i] : ( ~ (element(v2, % 34.37/5.54 | | | all_118_1) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4: % 34.37/5.54 | | | $i] : ? [v5: any] : (subset_complement(all_118_3, v2) % 34.37/5.54 | | | = v4 & in(v4, all_165_0) = v5 & in(v2, v0) = v3 & % 34.37/5.54 | | | $i(v4) & ( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = % 34.37/5.54 | | | 0)))) & (v1 = v0 | ? [v2: $i] : ? [v3: any] : ? % 34.37/5.54 | | | [v4: $i] : ? [v5: any] : (subset_complement(all_118_3, % 34.37/5.54 | | | v2) = v4 & element(v2, all_118_1) = 0 & in(v4, % 34.37/5.54 | | | all_165_0) = v5 & in(v2, v1) = v3 & $i(v4) & $i(v2) & % 34.37/5.54 | | | ( ~ (v5 = 0) | ~ (v3 = 0)) & (v5 = 0 | v3 = 0)))))) % 34.37/5.54 | | | % 34.37/5.54 | | | GROUND_INST: instantiating (63) with all_165_0, simplifying with (56), % 34.37/5.54 | | | (58) gives: % 34.37/5.54 | | | (84) ( ~ (all_175_0 = all_165_0) | ! [v0: $i] : ( ~ (element(v0, % 34.37/5.54 | | | all_118_1) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : % 34.37/5.54 | | | ? [v3: any] : (subset_complement(all_118_3, v0) = v2 & in(v2, % 34.37/5.54 | | | all_118_2) = v3 & in(v0, all_165_0) = v1 & $i(v2) & ( ~ % 34.37/5.54 | | | (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))) & % 34.37/5.54 | | | (all_175_0 = all_165_0 | ? [v0: $i] : ? [v1: any] : ? [v2: $i] % 34.37/5.54 | | | : ? [v3: any] : (subset_complement(all_118_3, v0) = v2 & % 34.37/5.54 | | | element(v0, all_118_1) = 0 & in(v2, all_118_2) = v3 & in(v0, % 34.37/5.54 | | | all_165_0) = v1 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = % 34.37/5.54 | | | 0)) & (v3 = 0 | v1 = 0))) % 34.37/5.54 | | | % 34.37/5.54 | | | ALPHA: (84) implies: % 34.37/5.54 | | | (85) ~ (all_175_0 = all_165_0) | ! [v0: $i] : ( ~ (element(v0, % 34.37/5.54 | | | all_118_1) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : % 34.37/5.54 | | | ? [v3: any] : (subset_complement(all_118_3, v0) = v2 & in(v2, % 34.37/5.54 | | | all_118_2) = v3 & in(v0, all_165_0) = v1 & $i(v2) & ( ~ (v3 % 34.37/5.54 | | | = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))) % 34.37/5.54 | | | % 34.37/5.55 | | | COMBINE_EQS: (79), (80) imply: % 34.37/5.55 | | | (86) all_159_0 = all_157_0 % 34.37/5.55 | | | % 34.37/5.55 | | | SIMP: (86) implies: % 34.37/5.55 | | | (87) all_159_0 = all_157_0 % 34.37/5.55 | | | % 34.37/5.55 | | | COMBINE_EQS: (78), (87) imply: % 34.37/5.55 | | | (88) all_157_0 = empty_set % 34.37/5.55 | | | % 34.37/5.55 | | | SIMP: (88) implies: % 34.37/5.55 | | | (89) all_157_0 = empty_set % 34.37/5.55 | | | % 34.37/5.55 | | | COMBINE_EQS: (80), (89) imply: % 34.37/5.55 | | | (90) all_165_0 = empty_set % 34.37/5.55 | | | % 34.37/5.55 | | | GROUND_INST: instantiating (82) with all_157_0, simplifying with (45), % 34.37/5.55 | | | (47) gives: % 34.37/5.55 | | | (91) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (disjoint(all_157_0, % 34.37/5.55 | | | all_157_0) = v0 & subset_complement(empty_set, all_157_0) = v1 % 34.37/5.55 | | | & subset(all_157_0, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 34.37/5.55 | | | ( ~ (v0 = 0) | v2 = 0)) % 34.37/5.55 | | | % 34.37/5.55 | | | DELTA: instantiating (81) with fresh symbol all_235_0 gives: % 34.37/5.55 | | | (92) subset_complement(empty_set, all_157_0) = all_235_0 & % 34.37/5.55 | | | set_difference(empty_set, all_157_0) = all_235_0 & $i(all_235_0) % 34.37/5.55 | | | % 34.37/5.55 | | | ALPHA: (92) implies: % 34.37/5.55 | | | (93) set_difference(empty_set, all_157_0) = all_235_0 % 34.37/5.55 | | | (94) subset_complement(empty_set, all_157_0) = all_235_0 % 34.37/5.55 | | | % 34.37/5.55 | | | DELTA: instantiating (77) with fresh symbol all_265_0 gives: % 34.37/5.55 | | | (95) element(all_104_0, all_159_0) = all_265_0 & ( ~ (all_265_0 = 0) | % 34.37/5.55 | | | all_155_0 = 0) & ( ~ (all_155_0 = 0) | all_265_0 = 0) % 34.37/5.55 | | | % 34.37/5.55 | | | ALPHA: (95) implies: % 34.37/5.55 | | | (96) ~ (all_265_0 = 0) | all_155_0 = 0 % 34.37/5.55 | | | % 34.37/5.55 | | | DELTA: instantiating (91) with fresh symbols all_301_0, all_301_1, % 34.37/5.55 | | | all_301_2 gives: % 34.37/5.55 | | | (97) disjoint(all_157_0, all_157_0) = all_301_2 & % 34.37/5.55 | | | subset_complement(empty_set, all_157_0) = all_301_1 & % 34.37/5.55 | | | subset(all_157_0, all_301_1) = all_301_0 & $i(all_301_1) & ( ~ % 34.37/5.55 | | | (all_301_0 = 0) | all_301_2 = 0) & ( ~ (all_301_2 = 0) | % 34.37/5.55 | | | all_301_0 = 0) % 34.37/5.55 | | | % 34.37/5.55 | | | ALPHA: (97) implies: % 34.37/5.55 | | | (98) $i(all_301_1) % 34.37/5.55 | | | (99) subset_complement(empty_set, all_157_0) = all_301_1 % 34.37/5.55 | | | % 34.37/5.55 | | | DELTA: instantiating (83) with fresh symbol all_317_0 gives: % 34.37/5.55 | | | (100) complements_of_subsets(all_118_3, all_165_0) = all_317_0 & % 34.37/5.55 | | | $i(all_317_0) & ! [v0: $i] : ( ~ (element(v0, all_118_0) = 0) | % 34.37/5.55 | | | ~ $i(v0) | (( ~ (v0 = all_317_0) | ! [v1: $i] : ( ~ % 34.37/5.55 | | | (element(v1, all_118_1) = 0) | ~ $i(v1) | ? [v2: any] : % 34.37/5.55 | | | ? [v3: $i] : ? [v4: any] : % 34.37/5.55 | | | (subset_complement(all_118_3, v1) = v3 & in(v3, % 34.37/5.55 | | | all_165_0) = v4 & in(v1, all_317_0) = v2 & $i(v3) & ( % 34.37/5.55 | | | ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))) & % 34.37/5.55 | | | (v0 = all_317_0 | ? [v1: $i] : ? [v2: any] : ? [v3: $i] : % 34.37/5.55 | | | ? [v4: any] : (subset_complement(all_118_3, v1) = v3 & % 34.37/5.55 | | | element(v1, all_118_1) = 0 & in(v3, all_165_0) = v4 & % 34.37/5.55 | | | in(v1, v0) = v2 & $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v2 % 34.37/5.55 | | | = 0)) & (v4 = 0 | v2 = 0))))) % 34.37/5.55 | | | % 34.37/5.55 | | | ALPHA: (100) implies: % 34.37/5.55 | | | (101) complements_of_subsets(all_118_3, all_165_0) = all_317_0 % 34.37/5.55 | | | (102) ! [v0: $i] : ( ~ (element(v0, all_118_0) = 0) | ~ $i(v0) | (( ~ % 34.37/5.55 | | | (v0 = all_317_0) | ! [v1: $i] : ( ~ (element(v1, % 34.37/5.55 | | | all_118_1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: % 34.37/5.55 | | | $i] : ? [v4: any] : (subset_complement(all_118_3, v1) % 34.37/5.55 | | | = v3 & in(v3, all_165_0) = v4 & in(v1, all_317_0) = v2 % 34.37/5.55 | | | & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 34.37/5.55 | | | 0)))) & (v0 = all_317_0 | ? [v1: $i] : ? [v2: any] % 34.37/5.55 | | | : ? [v3: $i] : ? [v4: any] : % 34.37/5.55 | | | (subset_complement(all_118_3, v1) = v3 & element(v1, % 34.37/5.55 | | | all_118_1) = 0 & in(v3, all_165_0) = v4 & in(v1, v0) = % 34.37/5.55 | | | v2 & $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 % 34.37/5.55 | | | = 0 | v2 = 0))))) % 34.37/5.55 | | | % 34.37/5.55 | | | GROUND_INST: instantiating (102) with all_165_0, simplifying with (56), % 34.37/5.55 | | | (58) gives: % 34.37/5.55 | | | (103) ( ~ (all_317_0 = all_165_0) | ! [v0: $i] : ( ~ (element(v0, % 34.37/5.55 | | | all_118_1) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 34.37/5.55 | | | : ? [v3: any] : (subset_complement(all_118_3, v0) = v2 & % 34.37/5.55 | | | in(v2, all_165_0) = v3 & in(v0, all_165_0) = v1 & $i(v2) & % 34.37/5.55 | | | ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))) & % 34.37/5.55 | | | (all_317_0 = all_165_0 | ? [v0: $i] : ? [v1: any] : ? [v2: $i] % 34.37/5.55 | | | : ? [v3: any] : (subset_complement(all_118_3, v0) = v2 & % 34.37/5.55 | | | element(v0, all_118_1) = 0 & in(v2, all_165_0) = v3 & in(v0, % 34.37/5.55 | | | all_165_0) = v1 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = % 34.37/5.55 | | | 0)) & (v3 = 0 | v1 = 0))) % 34.37/5.55 | | | % 34.37/5.55 | | | ALPHA: (103) implies: % 34.37/5.55 | | | (104) all_317_0 = all_165_0 | ? [v0: $i] : ? [v1: any] : ? [v2: $i] % 34.37/5.55 | | | : ? [v3: any] : (subset_complement(all_118_3, v0) = v2 & % 34.37/5.55 | | | element(v0, all_118_1) = 0 & in(v2, all_165_0) = v3 & in(v0, % 34.37/5.55 | | | all_165_0) = v1 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = % 34.37/5.55 | | | 0)) & (v3 = 0 | v1 = 0)) % 34.37/5.55 | | | % 34.37/5.55 | | | REDUCE: (90), (101) imply: % 34.37/5.55 | | | (105) complements_of_subsets(all_118_3, empty_set) = all_317_0 % 34.37/5.55 | | | % 34.37/5.55 | | | REDUCE: (89), (99) imply: % 34.37/5.55 | | | (106) subset_complement(empty_set, empty_set) = all_301_1 % 34.37/5.55 | | | % 34.37/5.55 | | | REDUCE: (89), (94) imply: % 34.37/5.55 | | | (107) subset_complement(empty_set, empty_set) = all_235_0 % 34.37/5.55 | | | % 34.37/5.55 | | | REDUCE: (89), (93) imply: % 34.37/5.55 | | | (108) set_difference(empty_set, empty_set) = all_235_0 % 34.37/5.55 | | | % 34.37/5.55 | | | REDUCE: (58), (90) imply: % 34.37/5.55 | | | (109) element(empty_set, all_118_0) = 0 % 34.37/5.55 | | | % 34.37/5.55 | | | BETA: splitting (76) gives: % 34.37/5.55 | | | % 34.37/5.55 | | | Case 1: % 34.37/5.55 | | | | % 34.37/5.55 | | | | (110) all_151_0 = 0 % 34.37/5.55 | | | | % 34.37/5.55 | | | | REDUCE: (39), (110) imply: % 34.37/5.55 | | | | (111) $false % 34.37/5.55 | | | | % 34.37/5.55 | | | | CLOSE: (111) is inconsistent. % 34.37/5.55 | | | | % 34.37/5.55 | | | Case 2: % 34.37/5.55 | | | | % 34.37/5.55 | | | | (112) ? [v0: $i] : (powerset(all_118_1) = v0 & $i(v0) & ? [v1: $i] % 34.37/5.55 | | | | : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & % 34.37/5.55 | | | | empty(v1) = v2 & $i(v1))) % 34.37/5.55 | | | | % 34.37/5.55 | | | | DELTA: instantiating (112) with fresh symbol all_359_0 gives: % 34.37/5.55 | | | | (113) powerset(all_118_1) = all_359_0 & $i(all_359_0) & ? [v0: $i] : % 34.37/5.55 | | | | ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_359_0) = 0 & % 34.37/5.55 | | | | empty(v0) = v1 & $i(v0)) % 34.37/5.55 | | | | % 34.37/5.55 | | | | ALPHA: (113) implies: % 34.37/5.56 | | | | (114) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, % 34.37/5.56 | | | | all_359_0) = 0 & empty(v0) = v1 & $i(v0)) % 34.37/5.56 | | | | % 34.37/5.56 | | | | DELTA: instantiating (114) with fresh symbols all_361_0, all_361_1 % 34.37/5.56 | | | | gives: % 34.37/5.56 | | | | (115) ~ (all_361_0 = 0) & element(all_361_1, all_359_0) = 0 & % 34.37/5.56 | | | | empty(all_361_1) = all_361_0 & $i(all_361_1) % 34.37/5.56 | | | | % 34.37/5.56 | | | | ALPHA: (115) implies: % 34.37/5.56 | | | | (116) ~ (all_361_0 = 0) % 34.37/5.56 | | | | (117) $i(all_361_1) % 34.37/5.56 | | | | (118) empty(all_361_1) = all_361_0 % 34.37/5.56 | | | | % 34.37/5.56 | | | | BETA: splitting (85) gives: % 34.37/5.56 | | | | % 34.37/5.56 | | | | Case 1: % 34.37/5.56 | | | | | % 34.37/5.56 | | | | | (119) ~ (all_175_0 = all_165_0) % 34.37/5.56 | | | | | % 34.37/5.56 | | | | | REDUCE: (66), (90), (119) imply: % 34.37/5.56 | | | | | (120) $false % 34.37/5.56 | | | | | % 34.37/5.56 | | | | | CLOSE: (120) is inconsistent. % 34.37/5.56 | | | | | % 34.37/5.56 | | | | Case 2: % 34.37/5.56 | | | | | % 34.37/5.56 | | | | | (121) all_175_0 = all_165_0 % 34.37/5.56 | | | | | (122) ! [v0: $i] : ( ~ (element(v0, all_118_1) = 0) | ~ $i(v0) | % 34.37/5.56 | | | | | ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 34.37/5.56 | | | | | (subset_complement(all_118_3, v0) = v2 & in(v2, all_118_2) % 34.37/5.56 | | | | | = v3 & in(v0, all_165_0) = v1 & $i(v2) & ( ~ (v3 = 0) | % 34.37/5.56 | | | | | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))) % 34.37/5.56 | | | | | % 34.37/5.56 | | | | | COMBINE_EQS: (66), (121) imply: % 34.37/5.56 | | | | | (123) all_165_0 = empty_set % 34.37/5.56 | | | | | % 34.37/5.56 | | | | | BETA: splitting (96) gives: % 34.37/5.56 | | | | | % 34.37/5.56 | | | | | Case 1: % 34.37/5.56 | | | | | | % 34.37/5.56 | | | | | | % 34.37/5.56 | | | | | | GROUND_INST: instantiating (9) with all_235_0, all_301_1, empty_set, % 34.37/5.56 | | | | | | empty_set, simplifying with (106), (107) gives: % 34.37/5.56 | | | | | | (124) all_301_1 = all_235_0 % 34.37/5.56 | | | | | | % 34.37/5.56 | | | | | | GROUND_INST: instantiating (10) with all_118_2, all_317_0, % 34.37/5.56 | | | | | | empty_set, all_118_3, simplifying with (69), (105) % 34.37/5.56 | | | | | | gives: % 34.37/5.56 | | | | | | (125) all_317_0 = all_118_2 % 34.37/5.56 | | | | | | % 34.37/5.56 | | | | | | REDUCE: (98), (124) imply: % 34.37/5.56 | | | | | | (126) $i(all_235_0) % 34.37/5.56 | | | | | | % 34.37/5.56 | | | | | | BETA: splitting (104) gives: % 34.37/5.56 | | | | | | % 34.37/5.56 | | | | | | Case 1: % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | (127) all_317_0 = all_165_0 % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | COMBINE_EQS: (125), (127) imply: % 34.37/5.56 | | | | | | | (128) all_165_0 = all_118_2 % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | SIMP: (128) implies: % 34.37/5.56 | | | | | | | (129) all_165_0 = all_118_2 % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | COMBINE_EQS: (90), (129) imply: % 34.37/5.56 | | | | | | | (130) all_118_2 = empty_set % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | REDUCE: (22), (130) imply: % 34.37/5.56 | | | | | | | (131) $false % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | CLOSE: (131) is inconsistent. % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | Case 2: % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | (132) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 34.37/5.56 | | | | | | | (subset_complement(all_118_3, v0) = v2 & element(v0, % 34.37/5.56 | | | | | | | all_118_1) = 0 & in(v2, all_165_0) = v3 & in(v0, % 34.37/5.56 | | | | | | | all_165_0) = v1 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ % 34.37/5.56 | | | | | | | (v1 = 0)) & (v3 = 0 | v1 = 0)) % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | DELTA: instantiating (132) with fresh symbols all_466_0, % 34.37/5.56 | | | | | | | all_466_1, all_466_2, all_466_3 gives: % 34.37/5.56 | | | | | | | (133) subset_complement(all_118_3, all_466_3) = all_466_1 & % 34.37/5.56 | | | | | | | element(all_466_3, all_118_1) = 0 & in(all_466_1, % 34.37/5.56 | | | | | | | all_165_0) = all_466_0 & in(all_466_3, all_165_0) = % 34.37/5.56 | | | | | | | all_466_2 & $i(all_466_1) & $i(all_466_3) & ( ~ % 34.37/5.56 | | | | | | | (all_466_0 = 0) | ~ (all_466_2 = 0)) & (all_466_0 = 0 % 34.37/5.56 | | | | | | | | all_466_2 = 0) % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | ALPHA: (133) implies: % 34.37/5.56 | | | | | | | (134) $i(all_466_3) % 34.37/5.56 | | | | | | | (135) $i(all_466_1) % 34.37/5.56 | | | | | | | (136) in(all_466_3, all_165_0) = all_466_2 % 34.37/5.56 | | | | | | | (137) in(all_466_1, all_165_0) = all_466_0 % 34.37/5.56 | | | | | | | (138) element(all_466_3, all_118_1) = 0 % 34.37/5.56 | | | | | | | (139) all_466_0 = 0 | all_466_2 = 0 % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | REDUCE: (90), (137) imply: % 34.37/5.56 | | | | | | | (140) in(all_466_1, empty_set) = all_466_0 % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | REDUCE: (90), (136) imply: % 34.37/5.56 | | | | | | | (141) in(all_466_3, empty_set) = all_466_2 % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_361_1, % 34.37/5.56 | | | | | | | all_361_0, simplifying with (117), (118) gives: % 34.37/5.56 | | | | | | | (142) all_361_0 = 0 | ? [v0: $i] : (powerset(all_361_1) = v0 & % 34.37/5.56 | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 34.37/5.56 | | | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1))) % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | GROUND_INST: instantiating (63) with empty_set, simplifying with % 34.37/5.56 | | | | | | | (6), (109) gives: % 34.37/5.56 | | | | | | | (143) ( ~ (all_175_0 = empty_set) | ! [v0: $i] : ( ~ % 34.37/5.56 | | | | | | | (element(v0, all_118_1) = 0) | ~ $i(v0) | ? [v1: % 34.37/5.56 | | | | | | | any] : ? [v2: $i] : ? [v3: any] : % 34.37/5.56 | | | | | | | (subset_complement(all_118_3, v0) = v2 & in(v2, % 34.37/5.56 | | | | | | | all_118_2) = v3 & in(v0, empty_set) = v1 & $i(v2) % 34.37/5.56 | | | | | | | & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = % 34.37/5.56 | | | | | | | 0)))) & (all_175_0 = empty_set | ? [v0: $i] : ? % 34.37/5.56 | | | | | | | [v1: any] : ? [v2: $i] : ? [v3: any] : % 34.37/5.56 | | | | | | | (subset_complement(all_118_3, v0) = v2 & element(v0, % 34.37/5.56 | | | | | | | all_118_1) = 0 & in(v2, all_118_2) = v3 & in(v0, % 34.37/5.56 | | | | | | | empty_set) = v1 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | % 34.37/5.56 | | | | | | | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | ALPHA: (143) implies: % 34.37/5.56 | | | | | | | (144) ~ (all_175_0 = empty_set) | ! [v0: $i] : ( ~ % 34.37/5.56 | | | | | | | (element(v0, all_118_1) = 0) | ~ $i(v0) | ? [v1: any] % 34.37/5.56 | | | | | | | : ? [v2: $i] : ? [v3: any] : % 34.37/5.56 | | | | | | | (subset_complement(all_118_3, v0) = v2 & in(v2, % 34.37/5.56 | | | | | | | all_118_2) = v3 & in(v0, empty_set) = v1 & $i(v2) & % 34.37/5.56 | | | | | | | ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))) % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | GROUND_INST: instantiating (122) with all_466_3, simplifying with % 34.37/5.56 | | | | | | | (134), (138) gives: % 34.37/5.56 | | | | | | | (145) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 34.37/5.56 | | | | | | | (subset_complement(all_118_3, all_466_3) = v1 & in(v1, % 34.37/5.56 | | | | | | | all_118_2) = v2 & in(all_466_3, all_165_0) = v0 & % 34.37/5.56 | | | | | | | $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = % 34.37/5.56 | | | | | | | 0)) % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | GROUND_INST: instantiating (4) with empty_set, all_235_0, % 34.37/5.56 | | | | | | | simplifying with (6), (108) gives: % 34.37/5.56 | | | | | | | (146) all_235_0 = empty_set % 34.37/5.56 | | | | | | | % 34.37/5.56 | | | | | | | GROUND_INST: instantiating (2) with empty_set, empty_set, % 34.37/5.56 | | | | | | | all_235_0, simplifying with (6), (108), (126) gives: % 34.37/5.57 | | | | | | | (147) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, empty_set) = v1) % 34.37/5.57 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, % 34.37/5.57 | | | | | | | all_235_0) = v2 & in(v0, empty_set) = v3 & ( ~ (v2 % 34.37/5.57 | | | | | | | = 0) | (v1 = 0 & ~ (v3 = 0))))) & ! [v0: $i] : % 34.37/5.57 | | | | | | | ( ~ (in(v0, empty_set) = 0) | ~ $i(v0) | ? [v1: any] : % 34.37/5.57 | | | | | | | ? [v2: any] : (in(v0, all_235_0) = v2 & in(v0, % 34.37/5.57 | | | | | | | empty_set) = v1 & (v2 = 0 | v1 = 0))) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | ALPHA: (147) implies: % 34.37/5.57 | | | | | | | (148) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, empty_set) = v1) % 34.37/5.57 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, % 34.37/5.57 | | | | | | | all_235_0) = v2 & in(v0, empty_set) = v3 & ( ~ (v2 % 34.37/5.57 | | | | | | | = 0) | (v1 = 0 & ~ (v3 = 0))))) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | GROUND_INST: instantiating (148) with all_466_3, all_466_2, % 34.37/5.57 | | | | | | | simplifying with (134), (141) gives: % 34.37/5.57 | | | | | | | (149) ? [v0: any] : ? [v1: any] : (in(all_466_3, all_235_0) = % 34.37/5.57 | | | | | | | v0 & in(all_466_3, empty_set) = v1 & ( ~ (v0 = 0) | % 34.37/5.57 | | | | | | | (all_466_2 = 0 & ~ (v1 = 0)))) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | GROUND_INST: instantiating (148) with all_466_1, all_466_0, % 34.37/5.57 | | | | | | | simplifying with (135), (140) gives: % 34.37/5.57 | | | | | | | (150) ? [v0: any] : ? [v1: any] : (in(all_466_1, all_235_0) = % 34.37/5.57 | | | | | | | v0 & in(all_466_1, empty_set) = v1 & ( ~ (v0 = 0) | % 34.37/5.57 | | | | | | | (all_466_0 = 0 & ~ (v1 = 0)))) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | DELTA: instantiating (145) with fresh symbols all_635_0, % 34.37/5.57 | | | | | | | all_635_1, all_635_2 gives: % 34.37/5.57 | | | | | | | (151) subset_complement(all_118_3, all_466_3) = all_635_1 & % 34.37/5.57 | | | | | | | in(all_635_1, all_118_2) = all_635_0 & in(all_466_3, % 34.37/5.57 | | | | | | | all_165_0) = all_635_2 & $i(all_635_1) & ( ~ (all_635_0 % 34.37/5.57 | | | | | | | = 0) | all_635_2 = 0) & ( ~ (all_635_2 = 0) | % 34.37/5.57 | | | | | | | all_635_0 = 0) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | ALPHA: (151) implies: % 34.37/5.57 | | | | | | | (152) in(all_466_3, all_165_0) = all_635_2 % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | DELTA: instantiating (150) with fresh symbols all_647_0, all_647_1 % 34.37/5.57 | | | | | | | gives: % 34.37/5.57 | | | | | | | (153) in(all_466_1, all_235_0) = all_647_1 & in(all_466_1, % 34.37/5.57 | | | | | | | empty_set) = all_647_0 & ( ~ (all_647_1 = 0) | % 34.37/5.57 | | | | | | | (all_466_0 = 0 & ~ (all_647_0 = 0))) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | ALPHA: (153) implies: % 34.37/5.57 | | | | | | | (154) in(all_466_1, empty_set) = all_647_0 % 34.37/5.57 | | | | | | | (155) in(all_466_1, all_235_0) = all_647_1 % 34.37/5.57 | | | | | | | (156) ~ (all_647_1 = 0) | (all_466_0 = 0 & ~ (all_647_0 = 0)) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | DELTA: instantiating (149) with fresh symbols all_651_0, all_651_1 % 34.37/5.57 | | | | | | | gives: % 34.37/5.57 | | | | | | | (157) in(all_466_3, all_235_0) = all_651_1 & in(all_466_3, % 34.37/5.57 | | | | | | | empty_set) = all_651_0 & ( ~ (all_651_1 = 0) | % 34.37/5.57 | | | | | | | (all_466_2 = 0 & ~ (all_651_0 = 0))) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | ALPHA: (157) implies: % 34.37/5.57 | | | | | | | (158) in(all_466_3, empty_set) = all_651_0 % 34.37/5.57 | | | | | | | (159) in(all_466_3, all_235_0) = all_651_1 % 34.37/5.57 | | | | | | | (160) ~ (all_651_1 = 0) | (all_466_2 = 0 & ~ (all_651_0 = 0)) % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | REDUCE: (146), (155) imply: % 34.37/5.57 | | | | | | | (161) in(all_466_1, empty_set) = all_647_1 % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | REDUCE: (146), (159) imply: % 34.37/5.57 | | | | | | | (162) in(all_466_3, empty_set) = all_651_1 % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | REDUCE: (90), (152) imply: % 34.37/5.57 | | | | | | | (163) in(all_466_3, empty_set) = all_635_2 % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | BETA: splitting (144) gives: % 34.37/5.57 | | | | | | | % 34.37/5.57 | | | | | | | Case 1: % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | (164) ~ (all_175_0 = empty_set) % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | REDUCE: (66), (164) imply: % 34.37/5.57 | | | | | | | | (165) $false % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | CLOSE: (165) is inconsistent. % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | Case 2: % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | (166) ! [v0: $i] : ( ~ (element(v0, all_118_1) = 0) | ~ % 34.37/5.57 | | | | | | | | $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 34.37/5.57 | | | | | | | | (subset_complement(all_118_3, v0) = v2 & in(v2, % 34.37/5.57 | | | | | | | | all_118_2) = v3 & in(v0, empty_set) = v1 & $i(v2) % 34.37/5.57 | | | | | | | | & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))) % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | GROUND_INST: instantiating (166) with all_466_3, simplifying % 34.37/5.57 | | | | | | | | with (134), (138) gives: % 34.37/5.57 | | | | | | | | (167) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 34.37/5.57 | | | | | | | | (subset_complement(all_118_3, all_466_3) = v1 & in(v1, % 34.37/5.57 | | | | | | | | all_118_2) = v2 & in(all_466_3, empty_set) = v0 & % 34.37/5.57 | | | | | | | | $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = % 34.37/5.57 | | | | | | | | 0)) % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | DELTA: instantiating (167) with fresh symbols all_721_0, % 34.37/5.57 | | | | | | | | all_721_1, all_721_2 gives: % 34.37/5.57 | | | | | | | | (168) subset_complement(all_118_3, all_466_3) = all_721_1 & % 34.37/5.57 | | | | | | | | in(all_721_1, all_118_2) = all_721_0 & in(all_466_3, % 34.37/5.57 | | | | | | | | empty_set) = all_721_2 & $i(all_721_1) & ( ~ % 34.37/5.57 | | | | | | | | (all_721_0 = 0) | all_721_2 = 0) & ( ~ (all_721_2 = % 34.37/5.57 | | | | | | | | 0) | all_721_0 = 0) % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | ALPHA: (168) implies: % 34.37/5.57 | | | | | | | | (169) in(all_466_3, empty_set) = all_721_2 % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | BETA: splitting (142) gives: % 34.37/5.57 | | | | | | | | % 34.37/5.57 | | | | | | | | Case 1: % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | (170) all_361_0 = 0 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | REDUCE: (116), (170) imply: % 34.37/5.57 | | | | | | | | | (171) $false % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | CLOSE: (171) is inconsistent. % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | Case 2: % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | GROUND_INST: instantiating (8) with all_466_2, all_651_1, % 34.37/5.57 | | | | | | | | | empty_set, all_466_3, simplifying with (141), % 34.37/5.57 | | | | | | | | | (162) gives: % 34.37/5.57 | | | | | | | | | (172) all_651_1 = all_466_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | GROUND_INST: instantiating (8) with all_651_1, all_651_0, % 34.37/5.57 | | | | | | | | | empty_set, all_466_3, simplifying with (158), % 34.37/5.57 | | | | | | | | | (162) gives: % 34.37/5.57 | | | | | | | | | (173) all_651_0 = all_651_1 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | GROUND_INST: instantiating (8) with all_651_0, all_721_2, % 34.37/5.57 | | | | | | | | | empty_set, all_466_3, simplifying with (158), % 34.37/5.57 | | | | | | | | | (169) gives: % 34.37/5.57 | | | | | | | | | (174) all_721_2 = all_651_0 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | GROUND_INST: instantiating (8) with all_635_2, all_721_2, % 34.37/5.57 | | | | | | | | | empty_set, all_466_3, simplifying with (163), % 34.37/5.57 | | | | | | | | | (169) gives: % 34.37/5.57 | | | | | | | | | (175) all_721_2 = all_635_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | GROUND_INST: instantiating (8) with all_466_0, all_647_0, % 34.37/5.57 | | | | | | | | | empty_set, all_466_1, simplifying with (140), % 34.37/5.57 | | | | | | | | | (154) gives: % 34.37/5.57 | | | | | | | | | (176) all_647_0 = all_466_0 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | GROUND_INST: instantiating (8) with all_647_1, all_647_0, % 34.37/5.57 | | | | | | | | | empty_set, all_466_1, simplifying with (154), % 34.37/5.57 | | | | | | | | | (161) gives: % 34.37/5.57 | | | | | | | | | (177) all_647_0 = all_647_1 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | COMBINE_EQS: (174), (175) imply: % 34.37/5.57 | | | | | | | | | (178) all_651_0 = all_635_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | SIMP: (178) implies: % 34.37/5.57 | | | | | | | | | (179) all_651_0 = all_635_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | COMBINE_EQS: (173), (179) imply: % 34.37/5.57 | | | | | | | | | (180) all_651_1 = all_635_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | SIMP: (180) implies: % 34.37/5.57 | | | | | | | | | (181) all_651_1 = all_635_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | COMBINE_EQS: (172), (181) imply: % 34.37/5.57 | | | | | | | | | (182) all_635_2 = all_466_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | COMBINE_EQS: (176), (177) imply: % 34.37/5.57 | | | | | | | | | (183) all_647_1 = all_466_0 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | COMBINE_EQS: (179), (182) imply: % 34.37/5.57 | | | | | | | | | (184) all_651_0 = all_466_2 % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | BETA: splitting (160) gives: % 34.37/5.57 | | | | | | | | | % 34.37/5.57 | | | | | | | | | Case 1: % 34.37/5.57 | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | (185) ~ (all_651_1 = 0) % 34.37/5.57 | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | REDUCE: (172), (185) imply: % 34.37/5.57 | | | | | | | | | | (186) ~ (all_466_2 = 0) % 34.37/5.57 | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | BETA: splitting (139) gives: % 34.37/5.57 | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | Case 1: % 34.37/5.57 | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | (187) all_466_0 = 0 % 34.37/5.57 | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | COMBINE_EQS: (183), (187) imply: % 34.37/5.57 | | | | | | | | | | | (188) all_647_1 = 0 % 34.37/5.57 | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | COMBINE_EQS: (176), (187) imply: % 34.37/5.57 | | | | | | | | | | | (189) all_647_0 = 0 % 34.37/5.57 | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | BETA: splitting (156) gives: % 34.37/5.57 | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | Case 1: % 34.37/5.57 | | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | | (190) ~ (all_647_1 = 0) % 34.37/5.57 | | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | | REDUCE: (188), (190) imply: % 34.37/5.57 | | | | | | | | | | | | (191) $false % 34.37/5.57 | | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 34.37/5.57 | | | | | | | | | | | | % 34.37/5.57 | | | | | | | | | | | Case 2: % 34.37/5.57 | | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | | (192) all_466_0 = 0 & ~ (all_647_0 = 0) % 34.37/5.58 | | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | | ALPHA: (192) implies: % 34.37/5.58 | | | | | | | | | | | | (193) ~ (all_647_0 = 0) % 34.37/5.58 | | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | | REDUCE: (189), (193) imply: % 34.37/5.58 | | | | | | | | | | | | (194) $false % 34.37/5.58 | | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | | CLOSE: (194) is inconsistent. % 34.37/5.58 | | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | End of split % 34.37/5.58 | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | Case 2: % 34.37/5.58 | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | (195) all_466_2 = 0 % 34.37/5.58 | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | REDUCE: (186), (195) imply: % 34.37/5.58 | | | | | | | | | | | (196) $false % 34.37/5.58 | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | | CLOSE: (196) is inconsistent. % 34.37/5.58 | | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | End of split % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | Case 2: % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | (197) all_651_1 = 0 % 34.37/5.58 | | | | | | | | | | (198) all_466_2 = 0 & ~ (all_651_0 = 0) % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | ALPHA: (198) implies: % 34.37/5.58 | | | | | | | | | | (199) ~ (all_651_0 = 0) % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | COMBINE_EQS: (172), (197) imply: % 34.37/5.58 | | | | | | | | | | (200) all_466_2 = 0 % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | COMBINE_EQS: (184), (200) imply: % 34.37/5.58 | | | | | | | | | | (201) all_651_0 = 0 % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | REDUCE: (199), (201) imply: % 34.37/5.58 | | | | | | | | | | (202) $false % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | | CLOSE: (202) is inconsistent. % 34.37/5.58 | | | | | | | | | | % 34.37/5.58 | | | | | | | | | End of split % 34.37/5.58 | | | | | | | | | % 34.37/5.58 | | | | | | | | End of split % 34.37/5.58 | | | | | | | | % 34.37/5.58 | | | | | | | End of split % 34.37/5.58 | | | | | | | % 34.37/5.58 | | | | | | End of split % 34.37/5.58 | | | | | | % 34.37/5.58 | | | | | Case 2: % 34.37/5.58 | | | | | | % 34.37/5.58 | | | | | | (203) all_155_0 = 0 % 34.37/5.58 | | | | | | % 34.37/5.58 | | | | | | REDUCE: (42), (203) imply: % 34.37/5.58 | | | | | | (204) $false % 34.37/5.58 | | | | | | % 34.37/5.58 | | | | | | CLOSE: (204) is inconsistent. % 34.37/5.58 | | | | | | % 34.37/5.58 | | | | | End of split % 34.37/5.58 | | | | | % 34.37/5.58 | | | | End of split % 34.37/5.58 | | | | % 34.37/5.58 | | | End of split % 34.37/5.58 | | | % 34.37/5.58 | | End of split % 34.37/5.58 | | % 34.37/5.58 | Case 2: % 34.37/5.58 | | % 34.37/5.58 | | (205) all_106_0 = 0 % 34.37/5.58 | | % 34.37/5.58 | | REDUCE: (18), (205) imply: % 34.37/5.58 | | (206) $false % 34.37/5.58 | | % 34.37/5.58 | | CLOSE: (206) is inconsistent. % 34.37/5.58 | | % 34.37/5.58 | End of split % 34.37/5.58 | % 34.37/5.58 End of proof % 34.37/5.58 % SZS output end Proof for theBenchmark % 34.37/5.58 % 34.37/5.58 4894ms %------------------------------------------------------------------------------