TSTP Solution File: SEU354+2 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU354+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 : n022.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 17:44:15 EDT 2023
% Result : Theorem 180.13s 24.57s
% Output : Proof 180.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU354+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 16:10:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.63 Running up to 7 provers in parallel.
% 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 14.77/2.82 Prover 1: Preprocessing ...
% 15.50/2.89 Prover 4: Preprocessing ...
% 15.50/2.94 Prover 6: Preprocessing ...
% 15.50/2.95 Prover 2: Preprocessing ...
% 15.50/2.95 Prover 0: Preprocessing ...
% 15.50/2.95 Prover 3: Preprocessing ...
% 16.56/3.00 Prover 5: Preprocessing ...
% 47.46/7.09 Prover 1: Warning: ignoring some quantifiers
% 49.52/7.33 Prover 1: Constructing countermodel ...
% 50.64/7.52 Prover 3: Warning: ignoring some quantifiers
% 50.64/7.56 Prover 6: Proving ...
% 51.53/7.61 Prover 3: Constructing countermodel ...
% 52.92/7.89 Prover 5: Proving ...
% 71.84/10.31 Prover 2: Proving ...
% 80.90/11.59 Prover 4: Warning: ignoring some quantifiers
% 84.41/11.95 Prover 4: Constructing countermodel ...
% 85.11/12.03 Prover 2: stopped
% 85.11/12.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 90.60/12.83 Prover 7: Preprocessing ...
% 94.54/13.26 Prover 0: Proving ...
% 100.14/13.98 Prover 5: stopped
% 100.14/14.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.00/14.10 Prover 7: Warning: ignoring some quantifiers
% 102.23/14.37 Prover 7: Constructing countermodel ...
% 103.47/14.50 Prover 8: Preprocessing ...
% 111.57/15.51 Prover 8: Warning: ignoring some quantifiers
% 111.86/15.62 Prover 8: Constructing countermodel ...
% 114.77/15.99 Prover 1: stopped
% 114.77/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 120.12/16.67 Prover 9: Preprocessing ...
% 129.71/17.89 Prover 6: stopped
% 129.71/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 135.94/18.72 Prover 10: Preprocessing ...
% 141.67/19.45 Prover 10: Warning: ignoring some quantifiers
% 142.27/19.55 Prover 10: Constructing countermodel ...
% 156.75/21.43 Prover 9: Warning: ignoring some quantifiers
% 158.16/21.65 Prover 9: Constructing countermodel ...
% 179.29/24.56 Prover 10: Found proof (size 17)
% 179.29/24.56 Prover 10: proved (6668ms)
% 179.29/24.56 Prover 9: stopped
% 179.29/24.56 Prover 4: stopped
% 179.29/24.57 Prover 8: stopped
% 179.29/24.57 Prover 7: stopped
% 179.29/24.57 Prover 0: stopped
% 180.13/24.57 Prover 3: stopped
% 180.13/24.57
% 180.13/24.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 180.13/24.57
% 180.13/24.57 % SZS output start Proof for theBenchmark
% 180.57/24.59 Assumptions after simplification:
% 180.57/24.59 ---------------------------------
% 180.57/24.59
% 180.57/24.59 (d2_tex_2)
% 180.72/24.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0) = v2) | ~
% 180.72/24.62 $i(v1) | ~ $i(v0) | ~ element(v1, v0) | proper_element(v1, v0)) & ! [v0:
% 180.72/24.62 $i] : ! [v1: $i] : ( ~ (union(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~
% 180.72/24.62 proper_element(v1, v0) | ~ element(v1, v0))
% 180.72/24.62
% 180.72/24.62 (t5_tex_2)
% 180.72/24.62 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (powerset(v0) = v2 & $i(v2) & $i(v1)
% 180.72/24.62 & $i(v0) & element(v1, v2) & ((v1 = v0 & proper_element(v0, v2)) | ( ~ (v1 =
% 180.72/24.62 v0) & ~ proper_element(v1, v2))))
% 180.72/24.62
% 180.72/24.62 (t99_zfmisc_1)
% 180.72/24.62 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | union(v1) =
% 180.72/24.62 v0)
% 180.72/24.62
% 180.72/24.62 Further assumptions not needed in the proof:
% 180.72/24.62 --------------------------------------------
% 180.72/24.63 abstractness_v1_orders_2, abstractness_v3_lattices, antisymmetry_r2_hidden,
% 180.72/24.63 antisymmetry_r2_xboole_0, cc10_membered, cc11_membered, cc12_membered,
% 180.72/24.63 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered,
% 180.72/24.63 cc18_membered, cc19_membered, cc1_arytm_3, cc1_finset_1, cc1_finsub_1,
% 180.72/24.63 cc1_funct_1, cc1_funct_2, cc1_lattices, cc1_membered, cc1_ordinal1,
% 180.72/24.63 cc1_partfun1, cc1_relat_1, cc1_relset_1, cc20_membered, cc2_arytm_3,
% 180.72/24.63 cc2_finset_1, cc2_finsub_1, cc2_funct_1, cc2_funct_2, cc2_lattices,
% 180.72/24.63 cc2_membered, cc2_ordinal1, cc3_arytm_3, cc3_funct_2, cc3_membered,
% 180.72/24.63 cc3_ordinal1, cc4_funct_2, cc4_membered, cc5_funct_2, cc6_funct_2,
% 180.72/24.63 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_lattices,
% 180.72/24.63 commutativity_k3_xboole_0, commutativity_k4_lattices, commutativity_k4_subset_1,
% 180.72/24.63 commutativity_k5_subset_1, connectedness_r1_ordinal1, d10_relat_1, d10_xboole_0,
% 180.72/24.63 d11_grcat_1, d11_relat_1, d12_funct_1, d12_relat_1, d12_relat_2, d13_funct_1,
% 180.72/24.63 d13_lattices, d13_pre_topc, d13_relat_1, d14_relat_1, d14_relat_2, d16_lattice3,
% 180.72/24.63 d16_lattices, d16_relat_2, d17_lattice3, d1_binop_1, d1_connsp_2, d1_enumset1,
% 180.72/24.63 d1_finset_1, d1_funct_1, d1_funct_2, d1_lattice3, d1_lattices, d1_mcart_1,
% 180.72/24.63 d1_ordinal1, d1_pre_topc, d1_relat_1, d1_relat_2, d1_relset_1, d1_setfam_1,
% 180.72/24.63 d1_struct_0, d1_tarski, d1_tops_1, d1_tops_2, d1_wellord1, d1_wellord2,
% 180.72/24.63 d1_xboole_0, d1_zfmisc_1, d21_lattice3, d22_lattice3, d2_compts_1, d2_lattice3,
% 180.72/24.63 d2_lattices, d2_mcart_1, d2_ordinal1, d2_pre_topc, d2_relat_1, d2_subset_1,
% 180.72/24.63 d2_tarski, d2_tops_2, d2_wellord1, d2_xboole_0, d2_zfmisc_1, d3_compts_1,
% 180.72/24.63 d3_lattice3, d3_lattices, d3_ordinal1, d3_pre_topc, d3_relat_1, d3_tarski,
% 180.72/24.63 d3_wellord1, d3_xboole_0, d4_funct_1, d4_lattice3, d4_ordinal1, d4_relat_1,
% 180.72/24.63 d4_relat_2, d4_subset_1, d4_tarski, d4_wellord1, d4_wellord2, d4_xboole_0,
% 180.72/24.63 d5_funct_1, d5_orders_2, d5_ordinal2, d5_pre_topc, d5_relat_1, d5_subset_1,
% 180.72/24.63 d5_tarski, d5_wellord1, d6_orders_2, d6_ordinal1, d6_pre_topc, d6_relat_1,
% 180.72/24.63 d6_relat_2, d6_wellord1, d7_relat_1, d7_wellord1, d7_xboole_0, d8_filter_1,
% 180.72/24.63 d8_funct_1, d8_lattice3, d8_lattices, d8_pre_topc, d8_relat_1, d8_relat_2,
% 180.72/24.63 d8_setfam_1, d8_xboole_0, d9_funct_1, d9_lattice3, d9_orders_2, d9_relat_2,
% 180.72/24.63 dt_g1_orders_2, dt_g3_lattices, dt_k10_filter_1, dt_k10_relat_1,
% 180.72/24.63 dt_k15_lattice3, dt_k16_lattice3, dt_k1_binop_1, dt_k1_domain_1, dt_k1_enumset1,
% 180.72/24.63 dt_k1_funct_1, dt_k1_lattice3, dt_k1_lattices, dt_k1_mcart_1, dt_k1_ordinal1,
% 180.72/24.63 dt_k1_pcomps_1, dt_k1_pre_topc, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski,
% 180.72/24.63 dt_k1_tops_1, dt_k1_wellord1, dt_k1_wellord2, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 180.72/24.63 dt_k2_binop_1, dt_k2_funct_1, dt_k2_lattice3, dt_k2_lattices, dt_k2_mcart_1,
% 180.72/24.63 dt_k2_pre_topc, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_wellord1,
% 180.72/24.63 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_lattice3, dt_k3_lattices, dt_k3_relat_1,
% 180.72/24.63 dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_lattice3, dt_k4_lattices,
% 180.72/24.63 dt_k4_relat_1, dt_k4_relset_1, dt_k4_subset_1, dt_k4_tarski, dt_k4_xboole_0,
% 180.72/24.63 dt_k5_lattice3, dt_k5_lattices, dt_k5_ordinal2, dt_k5_relat_1, dt_k5_relset_1,
% 180.72/24.63 dt_k5_setfam_1, dt_k5_subset_1, dt_k6_partfun1, dt_k6_pre_topc, dt_k6_relat_1,
% 180.72/24.63 dt_k6_setfam_1, dt_k6_subset_1, dt_k7_grcat_1, dt_k7_relat_1, dt_k7_setfam_1,
% 180.72/24.63 dt_k8_filter_1, dt_k8_funct_2, dt_k8_relat_1, dt_k9_filter_1, dt_k9_relat_1,
% 180.72/24.63 dt_l1_lattices, dt_l1_orders_2, dt_l1_pre_topc, dt_l1_struct_0, dt_l2_lattices,
% 180.72/24.63 dt_l3_lattices, dt_m1_connsp_2, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1,
% 180.72/24.63 dt_u1_lattices, dt_u1_orders_2, dt_u1_pre_topc, dt_u1_struct_0, dt_u2_lattices,
% 180.76/24.63 existence_l1_lattices, existence_l1_orders_2, existence_l1_pre_topc,
% 180.76/24.63 existence_l1_struct_0, existence_l2_lattices, existence_l3_lattices,
% 180.76/24.63 existence_m1_connsp_2, existence_m1_relset_1, existence_m1_subset_1,
% 180.76/24.63 existence_m2_relset_1, fc10_finset_1, fc10_relat_1, fc11_finset_1, fc11_relat_1,
% 180.76/24.63 fc12_finset_1, fc12_relat_1, fc13_finset_1, fc13_relat_1, fc1_finset_1,
% 180.76/24.63 fc1_finsub_1, fc1_funct_1, fc1_lattice3, fc1_orders_2, fc1_ordinal1,
% 180.76/24.63 fc1_ordinal2, fc1_pre_topc, fc1_relat_1, fc1_struct_0, fc1_subset_1,
% 180.76/24.63 fc1_xboole_0, fc1_zfmisc_1, fc27_membered, fc28_membered, fc29_membered,
% 180.76/24.63 fc2_arytm_3, fc2_funct_1, fc2_lattice2, fc2_lattice3, fc2_orders_2,
% 180.76/24.63 fc2_ordinal1, fc2_partfun1, fc2_pre_topc, fc2_relat_1, fc2_subset_1, fc2_tops_1,
% 180.76/24.63 fc2_xboole_0, fc30_membered, fc31_membered, fc32_membered, fc33_membered,
% 180.76/24.63 fc34_membered, fc35_membered, fc36_membered, fc37_membered, fc38_membered,
% 180.76/24.63 fc39_membered, fc3_funct_1, fc3_lattice2, fc3_lattices, fc3_orders_2,
% 180.76/24.63 fc3_ordinal1, fc3_relat_1, fc3_subset_1, fc3_tops_1, fc3_xboole_0,
% 180.76/24.63 fc40_membered, fc41_membered, fc4_funct_1, fc4_lattice2, fc4_lattice3,
% 180.76/24.63 fc4_ordinal1, fc4_relat_1, fc4_subset_1, fc4_tops_1, fc5_funct_1, fc5_lattice2,
% 180.76/24.63 fc5_pre_topc, fc5_relat_1, fc6_membered, fc6_relat_1, fc6_tops_1, fc7_relat_1,
% 180.76/24.63 fc8_relat_1, fc9_finset_1, fc9_relat_1, fraenkel_a_1_0_filter_1,
% 180.76/24.63 fraenkel_a_2_2_lattice3, fraenkel_a_2_3_lattice3, free_g1_orders_2,
% 180.76/24.63 free_g3_lattices, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 180.76/24.63 idempotence_k4_subset_1, idempotence_k5_subset_1, involutiveness_k3_subset_1,
% 180.76/24.63 involutiveness_k4_relat_1, involutiveness_k7_setfam_1,
% 180.76/24.63 irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1,
% 180.76/24.63 l28_zfmisc_1, l29_wellord1, l2_wellord1, l2_zfmisc_1, l30_wellord2,
% 180.76/24.63 l32_xboole_1, l3_subset_1, l3_wellord1, l3_zfmisc_1, l40_tops_1, l4_wellord1,
% 180.76/24.63 l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, l82_funct_1, rc1_arytm_3,
% 180.76/24.63 rc1_finset_1, rc1_funct_1, rc1_funct_2, rc1_membered, rc1_orders_2,
% 180.76/24.63 rc1_ordinal1, rc1_ordinal2, rc1_partfun1, rc1_relat_1, rc1_subset_1, rc1_tops_1,
% 180.76/24.63 rc1_xboole_0, rc2_finset_1, rc2_funct_1, rc2_funct_2, rc2_orders_2,
% 180.76/24.63 rc2_ordinal1, rc2_partfun1, rc2_relat_1, rc2_subset_1, rc2_tex_2, rc2_tops_1,
% 180.76/24.63 rc2_xboole_0, rc3_finset_1, rc3_funct_1, rc3_lattices, rc3_ordinal1,
% 180.76/24.63 rc3_partfun1, rc3_relat_1, rc3_struct_0, rc4_finset_1, rc4_funct_1,
% 180.76/24.63 rc5_struct_0, rc6_lattices, rc6_pre_topc, rc7_pre_topc, rc9_lattices,
% 180.76/24.63 redefinition_k10_filter_1, redefinition_k1_domain_1, redefinition_k1_pcomps_1,
% 180.76/24.63 redefinition_k2_binop_1, redefinition_k2_lattice3, redefinition_k3_lattices,
% 180.76/24.63 redefinition_k4_lattices, redefinition_k4_relset_1, redefinition_k4_subset_1,
% 180.76/24.63 redefinition_k5_relset_1, redefinition_k5_setfam_1, redefinition_k5_subset_1,
% 180.76/24.63 redefinition_k6_partfun1, redefinition_k6_setfam_1, redefinition_k6_subset_1,
% 180.76/24.63 redefinition_k8_funct_2, redefinition_m2_relset_1, redefinition_r1_ordinal1,
% 180.76/24.63 redefinition_r2_wellord2, redefinition_r3_lattices, redefinition_r3_orders_2,
% 180.76/24.63 reflexivity_r1_ordinal1, reflexivity_r1_tarski, reflexivity_r2_wellord2,
% 180.76/24.63 reflexivity_r3_lattices, reflexivity_r3_orders_2,
% 180.76/24.63 s1_funct_1__e10_24__wellord2__1, s1_funct_1__e16_22__wellord2__1,
% 180.76/24.63 s1_funct_1__e4_7_1__tops_2__1, s1_funct_1__e4_7_2__tops_2__1,
% 180.76/24.63 s1_ordinal1__e8_6__wellord2, s1_ordinal2__e18_27__finset_1,
% 180.76/24.63 s1_relat_1__e6_21__wellord2, s1_tarski__e10_24__wellord2__1,
% 180.76/24.63 s1_tarski__e10_24__wellord2__2, s1_tarski__e16_22__wellord2__1,
% 180.76/24.63 s1_tarski__e16_22__wellord2__2, s1_tarski__e18_27__finset_1__1,
% 180.76/24.63 s1_tarski__e1_40__pre_topc__1, s1_tarski__e2_37_1_1__pre_topc__1,
% 180.76/24.63 s1_tarski__e4_27_3_1__finset_1__1, s1_tarski__e4_7_1__tops_2__1,
% 180.76/24.63 s1_tarski__e4_7_1__tops_2__2, s1_tarski__e4_7_2__tops_2__1,
% 180.76/24.63 s1_tarski__e4_7_2__tops_2__2, s1_tarski__e6_21__wellord2__1,
% 180.76/24.63 s1_tarski__e6_22__wellord2__1, s1_tarski__e6_27__finset_1__1,
% 180.76/24.63 s1_tarski__e8_6__wellord2__1, s1_xboole_0__e10_24__wellord2__1,
% 180.76/24.63 s1_xboole_0__e16_22__wellord2__1, s1_xboole_0__e18_27__finset_1__1,
% 180.76/24.63 s1_xboole_0__e1_40__pre_topc__1, s1_xboole_0__e2_37_1_1__pre_topc__1,
% 180.76/24.63 s1_xboole_0__e4_27_3_1__finset_1, s1_xboole_0__e4_7_1__tops_2__1,
% 180.76/24.63 s1_xboole_0__e4_7_2__tops_2__1, s1_xboole_0__e6_21__wellord2__1,
% 180.76/24.63 s1_xboole_0__e6_22__wellord2, s1_xboole_0__e6_27__finset_1,
% 180.76/24.63 s1_xboole_0__e8_6__wellord2__1, s2_funct_1__e10_24__wellord2,
% 180.76/24.63 s2_funct_1__e16_22__wellord2__1, s2_funct_1__e4_7_1__tops_2,
% 180.76/24.63 s2_funct_1__e4_7_2__tops_2, s2_ordinal1__e18_27__finset_1__1,
% 180.76/24.63 s3_funct_1__e16_22__wellord2, s3_subset_1__e1_40__pre_topc,
% 180.76/24.63 s3_subset_1__e2_37_1_1__pre_topc, symmetry_r1_xboole_0, symmetry_r2_wellord2,
% 180.76/24.63 t106_zfmisc_1, t10_ordinal1, t10_tops_2, t10_zfmisc_1, t115_relat_1,
% 180.76/24.63 t116_relat_1, t117_relat_1, t118_relat_1, t118_zfmisc_1, t119_relat_1,
% 180.76/24.63 t119_zfmisc_1, t11_tops_2, t12_pre_topc, t12_relset_1, t12_tops_2, t12_xboole_1,
% 180.76/24.63 t136_zfmisc_1, t13_compts_1, t13_finset_1, t13_tops_2, t140_relat_1,
% 180.76/24.63 t143_relat_1, t144_relat_1, t145_funct_1, t145_relat_1, t146_funct_1,
% 180.76/24.63 t146_relat_1, t147_funct_1, t14_relset_1, t15_finset_1, t15_pre_topc,
% 180.76/24.63 t160_relat_1, t166_relat_1, t167_relat_1, t16_relset_1, t16_tops_2,
% 180.76/24.63 t16_wellord1, t174_relat_1, t178_relat_1, t17_finset_1, t17_pre_topc,
% 180.76/24.63 t17_tops_2, t17_wellord1, t17_xboole_1, t18_finset_1, t18_wellord1,
% 180.76/24.63 t19_wellord1, t19_xboole_1, t1_boole, t1_lattice3, t1_subset, t1_xboole_1,
% 180.76/24.63 t1_zfmisc_1, t20_relat_1, t20_wellord1, t21_funct_1, t21_funct_2, t21_ordinal1,
% 180.76/24.63 t21_relat_1, t21_wellord1, t22_funct_1, t22_pre_topc, t22_relset_1,
% 180.76/24.63 t22_wellord1, t23_funct_1, t23_lattices, t23_ordinal1, t23_relset_1,
% 180.76/24.63 t23_wellord1, t24_ordinal1, t24_wellord1, t25_orders_2, t25_relat_1,
% 180.76/24.63 t25_wellord1, t25_wellord2, t26_finset_1, t26_lattices, t26_orders_2,
% 180.76/24.63 t26_wellord2, t26_xboole_1, t28_lattice3, t28_wellord2, t28_xboole_1,
% 180.76/24.63 t29_lattice3, t29_tops_1, t2_boole, t2_lattice3, t2_subset, t2_tarski,
% 180.76/24.63 t2_wellord2, t2_xboole_1, t30_lattice3, t30_relat_1, t30_tops_1, t31_lattice3,
% 180.76/24.63 t31_ordinal1, t31_wellord1, t32_filter_1, t32_ordinal1, t32_wellord1,
% 180.76/24.63 t33_ordinal1, t33_xboole_1, t33_zfmisc_1, t34_funct_1, t34_lattice3,
% 180.76/24.63 t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1,
% 180.76/24.63 t38_zfmisc_1, t39_wellord1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_lattice3,
% 180.76/24.63 t3_ordinal1, t3_subset, t3_wellord2, t3_xboole_0, t3_xboole_1, t40_xboole_1,
% 180.76/24.63 t41_ordinal1, t42_ordinal1, t43_subset_1, t44_pre_topc, t44_relat_1, t44_tops_1,
% 180.76/24.63 t45_pre_topc, t45_relat_1, t45_xboole_1, t46_funct_2, t46_pre_topc, t46_relat_1,
% 180.76/24.63 t46_setfam_1, t46_zfmisc_1, t47_relat_1, t47_setfam_1, t48_pre_topc,
% 180.76/24.63 t48_setfam_1, t48_xboole_1, t49_wellord1, t4_boole, t4_subset, t4_wellord2,
% 180.76/24.63 t4_xboole_0, t50_lattice3, t50_subset_1, t51_tops_1, t52_pre_topc, t53_wellord1,
% 180.76/24.63 t54_funct_1, t54_subset_1, t54_wellord1, t55_funct_1, t55_tops_1, t56_relat_1,
% 180.76/24.63 t57_funct_1, t5_connsp_2, t5_subset, t5_tops_2, t5_wellord1, t5_wellord2,
% 180.76/24.63 t60_relat_1, t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1, t65_relat_1,
% 180.76/24.63 t65_zfmisc_1, t68_funct_1, t69_enumset1, t6_boole, t6_funct_2, t6_wellord2,
% 180.76/24.63 t6_zfmisc_1, t70_funct_1, t71_relat_1, t72_funct_1, t74_relat_1, t7_boole,
% 180.76/24.63 t7_lattice3, t7_mcart_1, t7_tarski, t7_wellord2, t7_xboole_1, t83_xboole_1,
% 180.76/24.64 t86_relat_1, t88_relat_1, t8_boole, t8_funct_1, t8_wellord1, t8_xboole_1,
% 180.76/24.64 t8_zfmisc_1, t90_relat_1, t91_tmap_1, t92_zfmisc_1, t94_relat_1, t99_relat_1,
% 180.76/24.64 t9_funct_2, t9_tarski, t9_zfmisc_1
% 180.76/24.64
% 180.76/24.64 Those formulas are unsatisfiable:
% 180.76/24.64 ---------------------------------
% 180.76/24.64
% 180.76/24.64 Begin of proof
% 180.76/24.64 |
% 180.76/24.64 | ALPHA: (d2_tex_2) implies:
% 180.76/24.64 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (union(v0) = v1) | ~ $i(v1) | ~
% 180.76/24.64 | $i(v0) | ~ proper_element(v1, v0) | ~ element(v1, v0))
% 180.76/24.64 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0) =
% 180.76/24.64 | v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v1, v0) |
% 180.76/24.64 | proper_element(v1, v0))
% 180.76/24.64 |
% 180.76/24.64 | DELTA: instantiating (t5_tex_2) with fresh symbols all_627_0, all_627_1,
% 180.76/24.64 | all_627_2 gives:
% 180.76/24.64 | (3) powerset(all_627_2) = all_627_0 & $i(all_627_0) & $i(all_627_1) &
% 180.76/24.64 | $i(all_627_2) & element(all_627_1, all_627_0) & ((all_627_1 = all_627_2
% 180.76/24.64 | & proper_element(all_627_2, all_627_0)) | ( ~ (all_627_1 =
% 180.76/24.64 | all_627_2) & ~ proper_element(all_627_1, all_627_0)))
% 180.76/24.64 |
% 180.76/24.64 | ALPHA: (3) implies:
% 180.76/24.64 | (4) element(all_627_1, all_627_0)
% 180.76/24.64 | (5) $i(all_627_2)
% 180.76/24.64 | (6) $i(all_627_1)
% 180.76/24.64 | (7) $i(all_627_0)
% 180.76/24.64 | (8) powerset(all_627_2) = all_627_0
% 180.76/24.64 | (9) (all_627_1 = all_627_2 & proper_element(all_627_2, all_627_0)) | ( ~
% 180.76/24.64 | (all_627_1 = all_627_2) & ~ proper_element(all_627_1, all_627_0))
% 180.76/24.64 |
% 180.76/24.64 | GROUND_INST: instantiating (t99_zfmisc_1) with all_627_2, all_627_0,
% 180.76/24.64 | simplifying with (5), (8) gives:
% 180.76/24.64 | (10) union(all_627_0) = all_627_2
% 180.76/24.65 |
% 180.76/24.65 | BETA: splitting (9) gives:
% 180.76/24.65 |
% 180.76/24.65 | Case 1:
% 180.76/24.65 | |
% 180.76/24.65 | | (11) all_627_1 = all_627_2 & proper_element(all_627_2, all_627_0)
% 180.76/24.65 | |
% 180.76/24.65 | | ALPHA: (11) implies:
% 180.76/24.65 | | (12) all_627_1 = all_627_2
% 180.76/24.65 | | (13) proper_element(all_627_2, all_627_0)
% 180.76/24.65 | |
% 180.76/24.65 | | REDUCE: (4), (12) imply:
% 180.76/24.65 | | (14) element(all_627_2, all_627_0)
% 180.76/24.65 | |
% 180.76/24.65 | | GROUND_INST: instantiating (1) with all_627_0, all_627_2, simplifying with
% 180.76/24.65 | | (5), (7), (10), (13), (14) gives:
% 180.76/24.65 | | (15) $false
% 180.76/24.65 | |
% 180.76/24.65 | | CLOSE: (15) is inconsistent.
% 180.76/24.65 | |
% 180.76/24.65 | Case 2:
% 180.76/24.65 | |
% 180.76/24.65 | | (16) ~ (all_627_1 = all_627_2) & ~ proper_element(all_627_1, all_627_0)
% 180.76/24.65 | |
% 180.76/24.65 | | ALPHA: (16) implies:
% 180.76/24.65 | | (17) ~ (all_627_1 = all_627_2)
% 180.76/24.65 | | (18) ~ proper_element(all_627_1, all_627_0)
% 180.76/24.65 | |
% 180.76/24.65 | | GROUND_INST: instantiating (2) with all_627_0, all_627_1, all_627_2,
% 180.76/24.65 | | simplifying with (4), (6), (7), (10), (18) gives:
% 180.76/24.65 | | (19) all_627_1 = all_627_2
% 180.76/24.65 | |
% 180.76/24.65 | | REDUCE: (17), (19) imply:
% 180.76/24.65 | | (20) $false
% 180.76/24.65 | |
% 180.76/24.65 | | CLOSE: (20) is inconsistent.
% 180.76/24.65 | |
% 180.76/24.65 | End of split
% 180.76/24.65 |
% 180.76/24.65 End of proof
% 180.76/24.65 % SZS output end Proof for theBenchmark
% 180.76/24.65
% 180.76/24.65 24040ms
%------------------------------------------------------------------------------