%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU180+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 : n025.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 17:43:05 EDT 2023 % Result : Theorem 23.79s 4.10s % Output : Proof 41.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU180+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.35 % Computer : n025.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Wed Aug 23 17:06:50 EDT 2023 % 0.12/0.35 % CPUTime : % 0.19/0.64 ________ _____ % 0.19/0.64 ___ __ \_________(_)________________________________ % 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.64 % 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.64 (2023-06-19) % 0.19/0.64 % 0.19/0.64 (c) Philipp Rümmer, 2009-2023 % 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.64 Amanda Stjerna. % 0.19/0.64 Free software under BSD-3-Clause. % 0.19/0.64 % 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.64 % 0.19/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.66 Running up to 7 provers in parallel. % 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.70/1.43 Prover 1: Preprocessing ... % 4.70/1.44 Prover 4: Preprocessing ... % 5.15/1.48 Prover 6: Preprocessing ... % 5.15/1.48 Prover 3: Preprocessing ... % 5.15/1.48 Prover 0: Preprocessing ... % 5.15/1.48 Prover 5: Preprocessing ... % 5.15/1.49 Prover 2: Preprocessing ... % 13.27/2.55 Prover 1: Warning: ignoring some quantifiers % 13.27/2.73 Prover 1: Constructing countermodel ... % 13.27/2.74 Prover 3: Warning: ignoring some quantifiers % 13.27/2.76 Prover 5: Proving ... % 14.48/2.79 Prover 3: Constructing countermodel ... % 15.32/2.84 Prover 6: Proving ... % 16.54/3.00 Prover 2: Proving ... % 17.31/3.08 Prover 4: Warning: ignoring some quantifiers % 17.62/3.20 Prover 4: Constructing countermodel ... % 18.85/3.31 Prover 0: Proving ... % 23.79/4.09 Prover 0: proved (3429ms) % 23.79/4.10 % 23.79/4.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.79/4.10 % 23.79/4.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.79/4.10 Prover 3: stopped % 23.79/4.10 Prover 5: stopped % 23.79/4.10 Prover 2: stopped % 23.79/4.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.79/4.10 Prover 6: stopped % 23.79/4.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.79/4.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.79/4.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.38/4.32 Prover 11: Preprocessing ... % 26.38/4.33 Prover 7: Preprocessing ... % 26.38/4.33 Prover 8: Preprocessing ... % 26.38/4.35 Prover 10: Preprocessing ... % 26.85/4.37 Prover 13: Preprocessing ... % 28.72/4.64 Prover 10: Warning: ignoring some quantifiers % 29.19/4.68 Prover 7: Warning: ignoring some quantifiers % 29.19/4.73 Prover 10: Constructing countermodel ... % 29.90/4.77 Prover 7: Constructing countermodel ... % 29.90/4.91 Prover 13: Warning: ignoring some quantifiers % 30.73/4.93 Prover 8: Warning: ignoring some quantifiers % 30.73/4.94 Prover 13: Constructing countermodel ... % 31.35/4.98 Prover 8: Constructing countermodel ... % 33.65/5.30 Prover 11: Warning: ignoring some quantifiers % 34.35/5.37 Prover 11: Constructing countermodel ... % 39.92/6.23 Prover 7: Found proof (size 39) % 39.92/6.23 Prover 7: proved (2129ms) % 40.74/6.23 Prover 8: stopped % 40.74/6.23 Prover 13: stopped % 40.74/6.23 Prover 11: stopped % 40.74/6.23 Prover 10: stopped % 40.74/6.23 Prover 1: stopped % 40.74/6.24 Prover 4: stopped % 40.74/6.24 % 40.74/6.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 40.74/6.24 % 40.74/6.24 % SZS output start Proof for theBenchmark % 40.74/6.25 Assumptions after simplification: % 40.74/6.25 --------------------------------- % 40.74/6.25 % 40.74/6.25 (commutativity_k2_xboole_0) % 41.14/6.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 41.14/6.27 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 41.14/6.28 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 41.14/6.28 | (set_union2(v1, v0) = v2 & $i(v2))) % 41.14/6.28 % 41.14/6.28 (d1_relat_1) % 41.14/6.28 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 41.14/6.28 in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 & $i(v3) % 41.14/6.28 & $i(v2))) & ? [v0: $i] : ( ~ $i(v0) | relation(v0) | ? [v1: $i] : % 41.14/6.28 ($i(v1) & in(v1, v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) % 41.14/6.28 = v1) | ~ $i(v3) | ~ $i(v2)))) % 41.14/6.28 % 41.14/6.28 (d2_xboole_0) % 41.14/6.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, % 41.14/6.28 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, % 41.14/6.28 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 41.14/6.28 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 41.14/6.28 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i] % 41.14/6.28 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ % 41.14/6.28 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] : % 41.14/6.28 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) = % 41.14/6.28 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~ % 41.14/6.28 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) % 41.14/6.28 | in(v4, v0)))) % 41.14/6.28 % 41.14/6.28 (d4_relat_1) % 41.14/6.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 41.14/6.29 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 41.14/6.29 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2, % 41.14/6.29 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = % 41.14/6.29 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) % 41.14/6.29 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & % 41.14/6.29 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 41.14/6.29 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: % 41.14/6.29 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | ! % 41.14/6.29 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) | % 41.14/6.29 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) & % 41.14/6.29 in(v5, v1))))) % 41.14/6.29 % 41.14/6.29 (d5_relat_1) % 41.14/6.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 41.14/6.29 (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ $i(v3) | ~ % 41.14/6.29 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2, % 41.14/6.29 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = % 41.14/6.29 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) % 41.14/6.29 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) & $i(v3) & % 41.14/6.29 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 41.14/6.29 (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: % 41.14/6.29 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | ! % 41.14/6.29 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v3) = v7) | ~ $i(v6) | % 41.14/6.29 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & $i(v5) & % 41.14/6.29 in(v5, v1))))) % 41.14/6.29 % 41.14/6.29 (d6_relat_1) % 41.14/6.29 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ~ % 41.14/6.29 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_rng(v0) = v3 & % 41.14/6.29 relation_dom(v0) = v2 & set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & % 41.14/6.29 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 41.14/6.29 $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_field(v0) = % 41.14/6.29 v2 & relation_dom(v0) = v3 & set_union2(v3, v1) = v2 & $i(v3) & $i(v2))) & % 41.14/6.29 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 41.14/6.29 relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_field(v0) = v2 & % 41.14/6.29 relation_rng(v0) = v3 & set_union2(v1, v3) = v2 & $i(v3) & $i(v2))) % 41.14/6.29 % 41.14/6.29 (t30_relat_1) % 41.14/6.29 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 41.14/6.29 (relation_field(v2) = v4 & ordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & % 41.14/6.29 $i(v2) & $i(v1) & $i(v0) & relation(v2) & in(v3, v2) & ( ~ in(v1, v4) | ~ % 41.14/6.29 in(v0, v4))) % 41.14/6.29 % 41.14/6.29 (t33_zfmisc_1) % 41.14/6.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 % 41.14/6.29 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4) | ~ % 41.14/6.29 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 41.14/6.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (ordered_pair(v2, v3) = % 41.14/6.29 v4) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 41.14/6.29 ~ $i(v0)) % 41.14/6.29 % 41.14/6.29 (t39_xboole_1) % 41.14/6.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = v2) | % 41.14/6.29 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_union2(v0, v2) = v3 & % 41.14/6.29 set_union2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 41.14/6.29 $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 41.14/6.29 (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2 & $i(v3) & $i(v2))) % 41.14/6.29 % 41.14/6.29 Further assumptions not needed in the proof: % 41.14/6.29 -------------------------------------------- % 41.14/6.29 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 41.14/6.30 commutativity_k3_xboole_0, d10_xboole_0, d1_setfam_1, d1_tarski, d1_xboole_0, % 41.14/6.30 d1_zfmisc_1, d2_subset_1, d2_tarski, d2_zfmisc_1, d3_tarski, d3_xboole_0, % 41.14/6.30 d4_subset_1, d4_tarski, d4_xboole_0, d5_subset_1, d5_tarski, d7_xboole_0, % 41.14/6.30 d8_setfam_1, d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, % 41.14/6.30 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, % 41.14/6.30 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, % 41.14/6.30 dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, dt_k5_setfam_1, dt_k6_setfam_1, % 41.14/6.30 dt_k6_subset_1, dt_k7_setfam_1, dt_m1_subset_1, existence_m1_subset_1, % 41.14/6.30 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1, % 41.14/6.30 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, fc4_subset_1, idempotence_k2_xboole_0, % 41.14/6.30 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k7_setfam_1, % 41.14/6.30 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 41.14/6.30 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, % 41.14/6.30 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_relat_1, rc1_subset_1, % 41.14/6.30 rc1_xboole_0, rc2_subset_1, rc2_xboole_0, redefinition_k5_setfam_1, % 41.14/6.30 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski, % 41.14/6.30 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, % 41.14/6.30 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, % 41.14/6.30 t1_xboole_1, t1_zfmisc_1, t20_relat_1, t21_relat_1, t25_relat_1, t26_xboole_1, % 41.14/6.30 t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, t33_xboole_1, % 41.14/6.30 t36_xboole_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_zfmisc_1, t3_boole, % 41.14/6.30 t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t45_xboole_1, % 41.14/6.30 t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, % 41.14/6.30 t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, t5_subset, t60_xboole_1, % 41.14/6.30 t63_xboole_1, t65_zfmisc_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, % 41.14/6.30 t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, % 41.14/6.30 t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 41.14/6.30 % 41.14/6.30 Those formulas are unsatisfiable: % 41.14/6.30 --------------------------------- % 41.14/6.30 % 41.14/6.30 Begin of proof % 41.14/6.30 | % 41.14/6.30 | ALPHA: (commutativity_k2_xboole_0) implies: % 41.14/6.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 41.14/6.30 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 41.14/6.30 | % 41.14/6.30 | ALPHA: (d1_relat_1) implies: % 41.14/6.30 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | % 41.14/6.30 | ~ in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 % 41.14/6.30 | & $i(v3) & $i(v2))) % 41.14/6.30 | % 41.14/6.30 | ALPHA: (d2_xboole_0) implies: % 41.14/6.30 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 41.14/6.30 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 41.14/6.30 | $i(v0) | ~ in(v3, v0) | in(v3, v2)) % 41.14/6.30 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 41.14/6.30 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 41.14/6.30 | $i(v0) | ~ in(v3, v1) | in(v3, v2)) % 41.14/6.30 | % 41.14/6.30 | ALPHA: (d4_relat_1) implies: % 41.14/6.30 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 41.14/6.30 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 41.14/6.30 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 41.14/6.30 | in(v4, v0) | in(v2, v1)) % 41.14/6.30 | % 41.14/6.30 | ALPHA: (d5_relat_1) implies: % 41.14/6.30 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 41.14/6.30 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ % 41.14/6.30 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 41.14/6.30 | in(v4, v0) | in(v2, v1)) % 41.14/6.30 | % 41.14/6.30 | ALPHA: (d6_relat_1) implies: % 41.14/6.30 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | % 41.14/6.30 | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : (relation_rng(v0) = v3 % 41.14/6.30 | & relation_dom(v0) = v2 & set_union2(v2, v3) = v1 & $i(v3) & $i(v2) % 41.14/6.30 | & $i(v1))) % 41.14/6.30 | % 41.14/6.30 | ALPHA: (t33_zfmisc_1) implies: % 41.14/6.30 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 41.14/6.30 | (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = % 41.14/6.30 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 41.14/6.30 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 41.14/6.30 | (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = % 41.14/6.30 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 41.14/6.30 | % 41.14/6.30 | ALPHA: (t39_xboole_1) implies: % 41.14/6.30 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = % 41.14/6.30 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (set_difference(v1, % 41.14/6.30 | v0) = v3 & set_union2(v0, v3) = v2 & $i(v3) & $i(v2))) % 41.14/6.31 | % 41.14/6.31 | DELTA: instantiating (t30_relat_1) with fresh symbols all_152_0, all_152_1, % 41.14/6.31 | all_152_2, all_152_3, all_152_4 gives: % 41.14/6.31 | (11) relation_field(all_152_2) = all_152_0 & ordered_pair(all_152_4, % 41.14/6.31 | all_152_3) = all_152_1 & $i(all_152_0) & $i(all_152_1) & % 41.14/6.31 | $i(all_152_2) & $i(all_152_3) & $i(all_152_4) & relation(all_152_2) & % 41.14/6.31 | in(all_152_1, all_152_2) & ( ~ in(all_152_3, all_152_0) | ~ % 41.14/6.31 | in(all_152_4, all_152_0)) % 41.14/6.31 | % 41.14/6.31 | ALPHA: (11) implies: % 41.14/6.31 | (12) in(all_152_1, all_152_2) % 41.14/6.31 | (13) relation(all_152_2) % 41.14/6.31 | (14) $i(all_152_4) % 41.14/6.31 | (15) $i(all_152_3) % 41.14/6.31 | (16) $i(all_152_2) % 41.14/6.31 | (17) $i(all_152_1) % 41.14/6.31 | (18) ordered_pair(all_152_4, all_152_3) = all_152_1 % 41.14/6.31 | (19) relation_field(all_152_2) = all_152_0 % 41.14/6.31 | (20) ~ in(all_152_3, all_152_0) | ~ in(all_152_4, all_152_0) % 41.14/6.31 | % 41.14/6.31 | GROUND_INST: instantiating (2) with all_152_2, all_152_1, simplifying with % 41.14/6.31 | (12), (13), (16), (17) gives: % 41.14/6.31 | (21) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_152_1 & $i(v1) % 41.14/6.31 | & $i(v0)) % 41.14/6.31 | % 41.14/6.31 | GROUND_INST: instantiating (7) with all_152_2, all_152_0, simplifying with % 41.14/6.31 | (13), (16), (19) gives: % 41.14/6.31 | (22) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_152_2) = v1 & % 41.14/6.31 | relation_dom(all_152_2) = v0 & set_union2(v0, v1) = all_152_0 & % 41.14/6.31 | $i(v1) & $i(v0) & $i(all_152_0)) % 41.14/6.31 | % 41.14/6.31 | DELTA: instantiating (21) with fresh symbols all_188_0, all_188_1 gives: % 41.14/6.31 | (23) ordered_pair(all_188_1, all_188_0) = all_152_1 & $i(all_188_0) & % 41.14/6.31 | $i(all_188_1) % 41.14/6.31 | % 41.14/6.31 | ALPHA: (23) implies: % 41.14/6.31 | (24) $i(all_188_1) % 41.14/6.31 | (25) $i(all_188_0) % 41.14/6.31 | (26) ordered_pair(all_188_1, all_188_0) = all_152_1 % 41.14/6.31 | % 41.14/6.31 | DELTA: instantiating (22) with fresh symbols all_190_0, all_190_1 gives: % 41.14/6.31 | (27) relation_rng(all_152_2) = all_190_0 & relation_dom(all_152_2) = % 41.14/6.31 | all_190_1 & set_union2(all_190_1, all_190_0) = all_152_0 & % 41.14/6.31 | $i(all_190_0) & $i(all_190_1) & $i(all_152_0) % 41.14/6.31 | % 41.14/6.31 | ALPHA: (27) implies: % 41.14/6.31 | (28) $i(all_190_1) % 41.14/6.31 | (29) $i(all_190_0) % 41.14/6.31 | (30) set_union2(all_190_1, all_190_0) = all_152_0 % 41.14/6.31 | (31) relation_dom(all_152_2) = all_190_1 % 41.14/6.31 | (32) relation_rng(all_152_2) = all_190_0 % 41.14/6.31 | % 41.14/6.31 | GROUND_INST: instantiating (1) with all_190_0, all_190_1, all_152_0, % 41.14/6.31 | simplifying with (28), (29), (30) gives: % 41.14/6.31 | (33) set_union2(all_190_0, all_190_1) = all_152_0 & $i(all_152_0) % 41.14/6.31 | % 41.14/6.31 | ALPHA: (33) implies: % 41.14/6.31 | (34) set_union2(all_190_0, all_190_1) = all_152_0 % 41.14/6.31 | % 41.14/6.31 | GROUND_INST: instantiating (10) with all_190_1, all_190_0, all_152_0, % 41.14/6.31 | simplifying with (28), (29), (30) gives: % 41.14/6.31 | (35) ? [v0: $i] : (set_difference(all_190_0, all_190_1) = v0 & % 41.14/6.31 | set_union2(all_190_1, v0) = all_152_0 & $i(v0) & $i(all_152_0)) % 41.14/6.31 | % 41.14/6.31 | GROUND_INST: instantiating (9) with all_152_4, all_152_3, all_188_1, % 41.14/6.31 | all_188_0, all_152_1, simplifying with (14), (15), (18), (24), % 41.14/6.31 | (25), (26) gives: % 41.14/6.31 | (36) all_188_0 = all_152_3 % 41.14/6.31 | % 41.14/6.31 | GROUND_INST: instantiating (8) with all_152_4, all_152_3, all_188_1, % 41.14/6.31 | all_188_0, all_152_1, simplifying with (14), (15), (18), (24), % 41.14/6.31 | (25), (26) gives: % 41.14/6.32 | (37) all_188_1 = all_152_4 % 41.14/6.32 | % 41.14/6.32 | GROUND_INST: instantiating (5) with all_152_2, all_190_1, all_188_1, % 41.14/6.32 | all_188_0, all_152_1, simplifying with (12), (13), (16), (24), % 41.14/6.32 | (25), (26), (28), (31) gives: % 41.14/6.32 | (38) in(all_188_1, all_190_1) % 41.14/6.32 | % 41.14/6.32 | GROUND_INST: instantiating (6) with all_152_2, all_190_0, all_188_0, % 41.14/6.32 | all_188_1, all_152_1, simplifying with (12), (13), (16), (24), % 41.14/6.32 | (25), (26), (29), (32) gives: % 41.14/6.32 | (39) in(all_188_0, all_190_0) % 41.14/6.32 | % 41.14/6.32 | DELTA: instantiating (35) with fresh symbol all_222_0 gives: % 41.14/6.32 | (40) set_difference(all_190_0, all_190_1) = all_222_0 & % 41.14/6.32 | set_union2(all_190_1, all_222_0) = all_152_0 & $i(all_222_0) & % 41.14/6.32 | $i(all_152_0) % 41.14/6.32 | % 41.14/6.32 | ALPHA: (40) implies: % 41.14/6.32 | (41) $i(all_222_0) % 41.14/6.32 | (42) set_union2(all_190_1, all_222_0) = all_152_0 % 41.14/6.32 | % 41.14/6.32 | REDUCE: (36), (39) imply: % 41.14/6.32 | (43) in(all_152_3, all_190_0) % 41.14/6.32 | % 41.14/6.32 | REDUCE: (37), (38) imply: % 41.14/6.32 | (44) in(all_152_4, all_190_1) % 41.14/6.32 | % 41.14/6.32 | GROUND_INST: instantiating (1) with all_222_0, all_190_1, all_152_0, % 41.14/6.32 | simplifying with (28), (41), (42) gives: % 41.14/6.32 | (45) set_union2(all_222_0, all_190_1) = all_152_0 & $i(all_152_0) % 41.14/6.32 | % 41.14/6.32 | ALPHA: (45) implies: % 41.14/6.32 | (46) $i(all_152_0) % 41.14/6.32 | % 41.14/6.32 | GROUND_INST: instantiating (3) with all_190_0, all_190_1, all_152_0, % 41.14/6.32 | all_152_3, simplifying with (15), (28), (29), (34), (43), (46) % 41.14/6.32 | gives: % 41.14/6.32 | (47) in(all_152_3, all_152_0) % 41.14/6.32 | % 41.14/6.32 | GROUND_INST: instantiating (4) with all_190_0, all_190_1, all_152_0, % 41.14/6.32 | all_152_4, simplifying with (14), (28), (29), (34), (44), (46) % 41.14/6.32 | gives: % 41.14/6.32 | (48) in(all_152_4, all_152_0) % 41.14/6.32 | % 41.14/6.32 | BETA: splitting (20) gives: % 41.14/6.32 | % 41.14/6.32 | Case 1: % 41.14/6.32 | | % 41.14/6.32 | | (49) ~ in(all_152_3, all_152_0) % 41.14/6.32 | | % 41.14/6.32 | | PRED_UNIFY: (47), (49) imply: % 41.14/6.32 | | (50) $false % 41.14/6.32 | | % 41.14/6.32 | | CLOSE: (50) is inconsistent. % 41.14/6.32 | | % 41.14/6.32 | Case 2: % 41.14/6.32 | | % 41.14/6.32 | | (51) ~ in(all_152_4, all_152_0) % 41.14/6.32 | | % 41.14/6.32 | | PRED_UNIFY: (48), (51) imply: % 41.14/6.32 | | (52) $false % 41.14/6.32 | | % 41.14/6.32 | | CLOSE: (52) is inconsistent. % 41.14/6.32 | | % 41.14/6.32 | End of split % 41.14/6.32 | % 41.14/6.32 End of proof % 41.14/6.32 % SZS output end Proof for theBenchmark % 41.14/6.32 % 41.14/6.32 5685ms %------------------------------------------------------------------------------