%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU189+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 : n015.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 17:43:09 EDT 2023 % Result : Theorem 24.34s 4.19s % Output : Proof 29.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU189+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n015.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Wed Aug 23 16:46:35 EDT 2023 % 0.15/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.67/1.47 Prover 4: Preprocessing ... % 4.67/1.47 Prover 1: Preprocessing ... % 5.35/1.51 Prover 3: Preprocessing ... % 5.35/1.51 Prover 0: Preprocessing ... % 5.35/1.51 Prover 2: Preprocessing ... % 5.35/1.51 Prover 5: Preprocessing ... % 5.35/1.51 Prover 6: Preprocessing ... % 16.02/2.98 Prover 1: Warning: ignoring some quantifiers % 17.00/3.08 Prover 6: Proving ... % 17.00/3.09 Prover 5: Proving ... % 17.00/3.10 Prover 3: Warning: ignoring some quantifiers % 17.00/3.14 Prover 3: Constructing countermodel ... % 17.00/3.15 Prover 1: Constructing countermodel ... % 18.25/3.32 Prover 2: Proving ... % 18.25/3.40 Prover 4: Warning: ignoring some quantifiers % 18.25/3.40 Prover 0: Proving ... % 20.39/3.55 Prover 4: Constructing countermodel ... % 24.34/4.19 Prover 3: proved (3534ms) % 24.34/4.19 % 24.34/4.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.34/4.19 % 24.34/4.19 Prover 6: stopped % 24.34/4.19 Prover 5: stopped % 24.34/4.19 Prover 2: stopped % 24.34/4.19 Prover 0: stopped % 24.34/4.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.34/4.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.34/4.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 24.34/4.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.34/4.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.27/4.35 Prover 1: Found proof (size 43) % 26.27/4.35 Prover 1: proved (3709ms) % 26.27/4.36 Prover 4: stopped % 27.26/4.48 Prover 10: Preprocessing ... % 27.26/4.49 Prover 7: Preprocessing ... % 27.26/4.49 Prover 8: Preprocessing ... % 27.26/4.49 Prover 11: Preprocessing ... % 27.26/4.50 Prover 13: Preprocessing ... % 28.53/4.63 Prover 10: stopped % 28.53/4.66 Prover 7: stopped % 28.99/4.71 Prover 11: stopped % 28.99/4.74 Prover 13: stopped % 28.99/4.81 Prover 8: Warning: ignoring some quantifiers % 28.99/4.83 Prover 8: Constructing countermodel ... % 28.99/4.84 Prover 8: stopped % 28.99/4.84 % 28.99/4.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 28.99/4.84 % 28.99/4.85 % SZS output start Proof for theBenchmark % 28.99/4.86 Assumptions after simplification: % 28.99/4.86 --------------------------------- % 28.99/4.86 % 28.99/4.86 (t60_relat_1) % 29.66/4.89 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 29.66/4.89 $i(empty_set) % 29.66/4.89 % 29.66/4.89 (t64_relat_1) % 29.66/4.89 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ % 29.66/4.89 (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 29.66/4.89 (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ~ (v3 % 29.66/4.89 = empty_set) & ~ (v1 = empty_set))))) % 29.66/4.89 % 29.66/4.89 (t65_relat_1) % 29.66/4.90 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = % 29.66/4.90 v2 & relation_dom(v0) = v1 & relation(v0) = 0 & $i(v2) & $i(v1) & $i(v0) & % 29.66/4.90 ((v2 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v2 = % 29.66/4.90 empty_set)))) % 29.66/4.90 % 29.66/4.90 (function-axioms) % 29.66/4.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 29.66/4.91 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 29.66/4.91 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 29.66/4.91 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 29.66/4.91 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.66/4.91 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 29.66/4.91 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.66/4.91 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 29.66/4.91 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.66/4.91 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 29.66/4.91 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.66/4.91 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ % 29.66/4.91 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.66/4.91 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 29.66/4.91 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.66/4.91 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 29.66/4.91 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.66/4.91 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 29.66/4.91 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.66/4.91 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 29.66/4.91 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.66/4.91 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 29.66/4.91 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.66/4.91 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 29.66/4.91 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.66/4.91 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 29.66/4.91 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.66/4.91 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 29.66/4.91 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.66/4.91 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 29.66/4.91 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 29.66/4.91 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 29.66/4.91 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 29.66/4.91 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, % 29.66/4.91 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 29.66/4.91 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 29.66/4.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 29.66/4.91 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 29.66/4.91 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ % 29.66/4.91 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 29.66/4.91 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] % 29.66/4.91 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 29.66/4.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 29.66/4.91 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 29.66/4.91 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 29.66/4.91 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 29.66/4.91 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 29.66/4.91 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 29.66/4.91 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 29.66/4.91 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: % 29.66/4.91 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 29.66/4.91 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 29.66/4.91 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 29.66/4.91 (relation(v2) = v0)) % 29.66/4.91 % 29.66/4.91 Further assumptions not needed in the proof: % 29.66/4.91 -------------------------------------------- % 29.66/4.91 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1, % 29.66/4.91 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0, % 29.66/4.91 d10_xboole_0, d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, % 29.66/4.91 d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski, d3_xboole_0, % 29.66/4.91 d4_relat_1, d4_subset_1, d4_tarski, d4_xboole_0, d5_relat_1, d5_subset_1, % 29.66/4.91 d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, % 29.66/4.91 d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, % 29.66/4.91 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, % 29.66/4.91 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, % 29.66/4.91 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, % 29.66/4.91 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, dt_m1_subset_1, % 29.66/4.91 existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, % 29.66/4.91 fc2_subset_1, fc2_xboole_0, fc3_subset_1, fc3_xboole_0, fc4_relat_1, % 29.66/4.91 fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, % 29.66/4.91 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1, % 29.66/4.91 involutiveness_k4_relat_1, involutiveness_k7_setfam_1, % 29.66/4.91 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 29.66/4.91 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, % 29.66/4.91 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_relat_1, rc1_subset_1, % 29.66/4.91 rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0, redefinition_k5_setfam_1, % 29.66/4.91 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski, % 29.66/4.91 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, % 29.66/4.91 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, % 29.66/4.91 t1_xboole_1, t1_zfmisc_1, t20_relat_1, t21_relat_1, t25_relat_1, t26_xboole_1, % 29.66/4.91 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, % 29.66/4.91 t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_relat_1, t37_xboole_1, % 29.66/4.91 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, % 29.66/4.91 t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1, % 29.66/4.91 t45_xboole_1, t46_relat_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1, % 29.66/4.91 t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, % 29.66/4.91 t50_subset_1, t54_subset_1, t56_relat_1, t5_subset, t60_xboole_1, t63_xboole_1, % 29.66/4.91 t65_zfmisc_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1, % 29.66/4.91 t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1, % 29.66/4.91 t9_tarski, t9_zfmisc_1 % 29.66/4.91 % 29.66/4.91 Those formulas are unsatisfiable: % 29.66/4.91 --------------------------------- % 29.66/4.91 % 29.66/4.91 Begin of proof % 29.66/4.92 | % 29.66/4.92 | ALPHA: (t60_relat_1) implies: % 29.66/4.92 | (1) relation_dom(empty_set) = empty_set % 29.66/4.92 | (2) relation_rng(empty_set) = empty_set % 29.66/4.92 | % 29.66/4.92 | ALPHA: (t64_relat_1) implies: % 29.66/4.92 | (3) ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ (relation_rng(v0) = % 29.66/4.92 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = % 29.66/4.92 | v3 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ~ (v3 = % 29.66/4.92 | empty_set) & ~ (v1 = empty_set))))) % 29.66/4.92 | % 29.66/4.92 | ALPHA: (t65_relat_1) implies: % 29.66/4.92 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = v2 & % 29.66/4.92 | relation_dom(v0) = v1 & relation(v0) = 0 & $i(v2) & $i(v1) & $i(v0) & % 29.66/4.92 | ((v2 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v2 = % 29.66/4.92 | empty_set)))) % 29.66/4.92 | % 29.66/4.92 | ALPHA: (function-axioms) implies: % 29.66/4.92 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 29.66/4.92 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 29.66/4.92 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 29.66/4.92 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 29.66/4.92 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 29.66/4.92 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 29.66/4.92 | % 29.66/4.92 | DELTA: instantiating (4) with fresh symbols all_167_0, all_167_1, all_167_2 % 29.66/4.92 | gives: % 29.66/4.92 | (8) relation_rng(all_167_2) = all_167_0 & relation_dom(all_167_2) = % 29.66/4.92 | all_167_1 & relation(all_167_2) = 0 & $i(all_167_0) & $i(all_167_1) & % 29.66/4.92 | $i(all_167_2) & ((all_167_0 = empty_set & ~ (all_167_1 = empty_set)) | % 29.66/4.92 | (all_167_1 = empty_set & ~ (all_167_0 = empty_set))) % 29.66/4.92 | % 29.66/4.92 | ALPHA: (8) implies: % 29.66/4.92 | (9) $i(all_167_2) % 29.66/4.92 | (10) relation(all_167_2) = 0 % 29.66/4.92 | (11) relation_dom(all_167_2) = all_167_1 % 29.66/4.92 | (12) relation_rng(all_167_2) = all_167_0 % 29.66/4.92 | (13) (all_167_0 = empty_set & ~ (all_167_1 = empty_set)) | (all_167_1 = % 29.66/4.92 | empty_set & ~ (all_167_0 = empty_set)) % 29.66/4.92 | % 29.66/4.92 | GROUND_INST: instantiating (3) with all_167_2, all_167_0, simplifying with % 29.66/4.92 | (9), (12) gives: % 29.66/4.92 | (14) all_167_2 = empty_set | ? [v0: any] : ? [v1: $i] : % 29.66/4.92 | (relation_dom(all_167_2) = v1 & relation(all_167_2) = v0 & $i(v1) & ( % 29.66/4.92 | ~ (v0 = 0) | ( ~ (v1 = empty_set) & ~ (all_167_0 = empty_set)))) % 29.66/4.92 | % 29.66/4.92 | BETA: splitting (13) gives: % 29.66/4.93 | % 29.66/4.93 | Case 1: % 29.66/4.93 | | % 29.66/4.93 | | (15) all_167_0 = empty_set & ~ (all_167_1 = empty_set) % 29.66/4.93 | | % 29.66/4.93 | | ALPHA: (15) implies: % 29.66/4.93 | | (16) all_167_0 = empty_set % 29.66/4.93 | | (17) ~ (all_167_1 = empty_set) % 29.66/4.93 | | % 29.66/4.93 | | BETA: splitting (14) gives: % 29.66/4.93 | | % 29.66/4.93 | | Case 1: % 29.66/4.93 | | | % 29.66/4.93 | | | (18) all_167_2 = empty_set % 29.66/4.93 | | | % 29.66/4.93 | | | REDUCE: (11), (18) imply: % 29.66/4.93 | | | (19) relation_dom(empty_set) = all_167_1 % 29.66/4.93 | | | % 29.66/4.93 | | | GROUND_INST: instantiating (6) with empty_set, all_167_1, empty_set, % 29.66/4.93 | | | simplifying with (1), (19) gives: % 29.66/4.93 | | | (20) all_167_1 = empty_set % 29.66/4.93 | | | % 29.66/4.93 | | | REDUCE: (17), (20) imply: % 29.66/4.93 | | | (21) $false % 29.66/4.93 | | | % 29.66/4.93 | | | CLOSE: (21) is inconsistent. % 29.66/4.93 | | | % 29.66/4.93 | | Case 2: % 29.66/4.93 | | | % 29.66/4.93 | | | (22) ? [v0: any] : ? [v1: $i] : (relation_dom(all_167_2) = v1 & % 29.66/4.93 | | | relation(all_167_2) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ~ (v1 = % 29.66/4.93 | | | empty_set) & ~ (all_167_0 = empty_set)))) % 29.66/4.93 | | | % 29.66/4.93 | | | DELTA: instantiating (22) with fresh symbols all_509_0, all_509_1 gives: % 29.66/4.93 | | | (23) relation_dom(all_167_2) = all_509_0 & relation(all_167_2) = % 29.66/4.93 | | | all_509_1 & $i(all_509_0) & ( ~ (all_509_1 = 0) | ( ~ (all_509_0 = % 29.66/4.93 | | | empty_set) & ~ (all_167_0 = empty_set))) % 29.66/4.93 | | | % 29.66/4.93 | | | ALPHA: (23) implies: % 29.66/4.93 | | | (24) relation(all_167_2) = all_509_1 % 29.66/4.93 | | | (25) ~ (all_509_1 = 0) | ( ~ (all_509_0 = empty_set) & ~ (all_167_0 = % 29.66/4.93 | | | empty_set)) % 29.66/4.93 | | | % 29.66/4.93 | | | BETA: splitting (25) gives: % 29.66/4.93 | | | % 29.66/4.93 | | | Case 1: % 29.66/4.93 | | | | % 29.66/4.93 | | | | (26) ~ (all_509_1 = 0) % 29.66/4.93 | | | | % 29.66/4.93 | | | | GROUND_INST: instantiating (5) with 0, all_509_1, all_167_2, simplifying % 29.66/4.93 | | | | with (10), (24) gives: % 29.66/4.93 | | | | (27) all_509_1 = 0 % 29.66/4.93 | | | | % 29.66/4.93 | | | | REDUCE: (26), (27) imply: % 29.66/4.93 | | | | (28) $false % 29.66/4.93 | | | | % 29.66/4.93 | | | | CLOSE: (28) is inconsistent. % 29.66/4.93 | | | | % 29.66/4.93 | | | Case 2: % 29.66/4.93 | | | | % 29.66/4.93 | | | | (29) ~ (all_509_0 = empty_set) & ~ (all_167_0 = empty_set) % 29.66/4.93 | | | | % 29.66/4.93 | | | | ALPHA: (29) implies: % 29.66/4.93 | | | | (30) ~ (all_167_0 = empty_set) % 29.66/4.93 | | | | % 29.66/4.93 | | | | REDUCE: (16), (30) imply: % 29.66/4.93 | | | | (31) $false % 29.66/4.93 | | | | % 29.66/4.93 | | | | CLOSE: (31) is inconsistent. % 29.66/4.93 | | | | % 29.66/4.93 | | | End of split % 29.66/4.93 | | | % 29.66/4.93 | | End of split % 29.66/4.93 | | % 29.66/4.93 | Case 2: % 29.66/4.93 | | % 29.66/4.93 | | (32) all_167_1 = empty_set & ~ (all_167_0 = empty_set) % 29.66/4.93 | | % 29.66/4.93 | | ALPHA: (32) implies: % 29.66/4.93 | | (33) all_167_1 = empty_set % 29.66/4.93 | | (34) ~ (all_167_0 = empty_set) % 29.66/4.93 | | % 29.66/4.93 | | REDUCE: (11), (33) imply: % 29.66/4.93 | | (35) relation_dom(all_167_2) = empty_set % 29.66/4.93 | | % 29.66/4.93 | | BETA: splitting (14) gives: % 29.66/4.93 | | % 29.66/4.93 | | Case 1: % 29.66/4.93 | | | % 29.66/4.93 | | | (36) all_167_2 = empty_set % 29.66/4.93 | | | % 29.66/4.93 | | | REDUCE: (12), (36) imply: % 29.66/4.93 | | | (37) relation_rng(empty_set) = all_167_0 % 29.66/4.93 | | | % 29.66/4.93 | | | GROUND_INST: instantiating (7) with empty_set, all_167_0, empty_set, % 29.66/4.93 | | | simplifying with (2), (37) gives: % 29.66/4.93 | | | (38) all_167_0 = empty_set % 29.66/4.93 | | | % 29.66/4.93 | | | REDUCE: (34), (38) imply: % 29.66/4.93 | | | (39) $false % 29.66/4.93 | | | % 29.66/4.93 | | | CLOSE: (39) is inconsistent. % 29.66/4.93 | | | % 29.66/4.93 | | Case 2: % 29.66/4.93 | | | % 29.66/4.93 | | | (40) ? [v0: any] : ? [v1: $i] : (relation_dom(all_167_2) = v1 & % 29.66/4.93 | | | relation(all_167_2) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ~ (v1 = % 29.66/4.93 | | | empty_set) & ~ (all_167_0 = empty_set)))) % 29.66/4.93 | | | % 29.66/4.93 | | | DELTA: instantiating (40) with fresh symbols all_509_0, all_509_1 gives: % 29.66/4.93 | | | (41) relation_dom(all_167_2) = all_509_0 & relation(all_167_2) = % 29.66/4.93 | | | all_509_1 & $i(all_509_0) & ( ~ (all_509_1 = 0) | ( ~ (all_509_0 = % 29.66/4.93 | | | empty_set) & ~ (all_167_0 = empty_set))) % 29.66/4.93 | | | % 29.66/4.93 | | | ALPHA: (41) implies: % 29.66/4.93 | | | (42) relation(all_167_2) = all_509_1 % 29.66/4.93 | | | (43) relation_dom(all_167_2) = all_509_0 % 29.66/4.93 | | | (44) ~ (all_509_1 = 0) | ( ~ (all_509_0 = empty_set) & ~ (all_167_0 = % 29.66/4.93 | | | empty_set)) % 29.66/4.93 | | | % 29.66/4.93 | | | GROUND_INST: instantiating (5) with 0, all_509_1, all_167_2, simplifying % 29.66/4.93 | | | with (10), (42) gives: % 29.66/4.94 | | | (45) all_509_1 = 0 % 29.66/4.94 | | | % 29.66/4.94 | | | GROUND_INST: instantiating (6) with empty_set, all_509_0, all_167_2, % 29.66/4.94 | | | simplifying with (35), (43) gives: % 29.66/4.94 | | | (46) all_509_0 = empty_set % 29.66/4.94 | | | % 29.66/4.94 | | | BETA: splitting (44) gives: % 29.66/4.94 | | | % 29.66/4.94 | | | Case 1: % 29.66/4.94 | | | | % 29.66/4.94 | | | | (47) ~ (all_509_1 = 0) % 29.66/4.94 | | | | % 29.66/4.94 | | | | REDUCE: (45), (47) imply: % 29.66/4.94 | | | | (48) $false % 29.66/4.94 | | | | % 29.66/4.94 | | | | CLOSE: (48) is inconsistent. % 29.66/4.94 | | | | % 29.66/4.94 | | | Case 2: % 29.66/4.94 | | | | % 29.66/4.94 | | | | (49) ~ (all_509_0 = empty_set) & ~ (all_167_0 = empty_set) % 29.66/4.94 | | | | % 29.66/4.94 | | | | ALPHA: (49) implies: % 29.66/4.94 | | | | (50) ~ (all_509_0 = empty_set) % 29.66/4.94 | | | | % 29.66/4.94 | | | | REDUCE: (46), (50) imply: % 29.66/4.94 | | | | (51) $false % 29.66/4.94 | | | | % 29.66/4.94 | | | | CLOSE: (51) is inconsistent. % 29.66/4.94 | | | | % 29.66/4.94 | | | End of split % 29.66/4.94 | | | % 29.66/4.94 | | End of split % 29.66/4.94 | | % 29.66/4.94 | End of split % 29.66/4.94 | % 29.66/4.94 End of proof % 29.66/4.94 % SZS output end Proof for theBenchmark % 29.66/4.94 % 29.66/4.94 4310ms %------------------------------------------------------------------------------