TSTP Solution File: SEU345+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU345+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 16:31:03 EDT 2023
% Result : Theorem 67.77s 68.04s
% Output : Proof 67.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU345+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : do_cvc5 %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 23 21:47:26 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.13/0.39 %----Proving TF0_NAR, FOF, or CNF
% 67.77/68.04 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.nX3w5ZGY2A/cvc5---1.0.5_4926.p...
% 67.77/68.04 ------- get file name : TPTP file name is SEU345+1
% 67.77/68.04 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4926.smt2...
% 67.77/68.04 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 67.77/68.04 --- Run --no-e-matching --full-saturate-quant at 5...
% 67.77/68.04 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 67.77/68.04 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 67.77/68.04 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 67.77/68.04 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 67.77/68.04 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 67.77/68.04 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 67.77/68.04 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 67.77/68.04 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 67.77/68.04 --- Run --relevant-triggers --full-saturate-quant at 5...
% 67.77/68.04 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 67.77/68.04 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 67.77/68.04 % SZS status Theorem for SEU345+1
% 67.77/68.04 % SZS output start Proof for SEU345+1
% 67.77/68.04 (
% 67.77/68.04 (let ((_let_1 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_3 (not (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (tptp.lower_bounded_semilattstr _let_1) (= (tptp.bottom_of_semilattstr _let_1) tptp.empty_set))))))) (let ((_let_4 (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)))) (let ((_let_5 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.boole_lattice A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (=> (tptp.element C (tptp.the_carrier _let_1)) (and (= (tptp.join _let_1 B C) (tptp.set_union2 B C)) (= (tptp.meet _let_1 B C) (tptp.set_intersection2 B C)))))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.meet_commut A B C) (tptp.meet A B C))))))) (let ((_let_8 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B B) B)))))) (let ((_let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1) (tptp.join_commutative _let_1) (tptp.join_associative _let_1) (tptp.meet_commutative _let_1) (tptp.meet_associative _let_1) (tptp.meet_absorbing _let_1) (tptp.join_absorbing _let_1) (tptp.lattice _let_1)))))) (let ((_let_11 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (tptp.element (tptp.bottom_of_semilattstr A) (tptp.the_carrier A)))))) (let ((_let_14 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.strict_latt_str B) (tptp.latt_str B)) (= (= B (tptp.boole_lattice A)) (and (= (tptp.the_carrier B) (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (and (= (tptp.apply_binary (tptp.the_L_join B) C D) (tptp.subset_union2 A C D)) (= (tptp.apply_binary (tptp.the_L_meet B) C D) (tptp.subset_intersection2 A C D))))))))))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (=> (tptp.lower_bounded_semilattstr A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (= B (tptp.bottom_of_semilattstr A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (and (= (tptp.meet A B C) B) (= (tptp.meet A C B) B)))))))))))) (let ((_let_17 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (= (tptp.lower_bounded_semilattstr A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (and (= (tptp.meet A B C) B) (= (tptp.meet A C B) B))))))))))) (let ((_let_18 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.meet_commut A B C) (tptp.meet_commut A C B))))))) (let ((_let_19 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_20 (skop_11 skv_19))) (let ((_let_21 (= _let_20 (tptp.subset_union2 skv_19 _let_20 _let_20)))) (let ((_let_22 (= tptp.empty_set _let_20))) (let ((_let_23 (tptp.boole_lattice skv_19))) (let ((_let_24 (tptp.bottom_of_semilattstr _let_23))) (let ((_let_25 (tptp.meet _let_23 _let_24 _let_20))) (let ((_let_26 (= _let_20 _let_25))) (let ((_let_27 (= tptp.empty_set _let_24))) (let ((_let_28 (= _let_24 _let_25))) (let ((_let_29 (tptp.powerset skv_19))) (let ((_let_30 (tptp.element _let_24 _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.element _let_20 _let_29))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31 _let_21))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= B (tptp.subset_union2 A B B))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (tptp.powerset A))) (let ((_let_38 (forall ((BOUND_VARIABLE_2565 $$unsorted)) (tptp.element (skop_11 BOUND_VARIABLE_2565) (tptp.powerset BOUND_VARIABLE_2565))))) (let ((_let_39 (0))) (let ((_let_40 (forall ((BOUND_VARIABLE_2572 $$unsorted)) (tptp.empty (skop_11 BOUND_VARIABLE_2572))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (not (tptp.empty B)))))) (and _let_38 _let_40)))))))) (let ((_let_42 (_let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (skv_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.powerset BOUND_VARIABLE_2565)))) :args _let_42)) (AND_ELIM _let_41 :args _let_39) :args (_let_32 false _let_38)))) (let ((_let_44 (tptp.the_carrier _let_23))) (let ((_let_45 (= _let_29 _let_44))) (let ((_let_46 (tptp.element _let_24 _let_44))) (let ((_let_47 (and _let_45 (forall ((C $$unsorted) (BOUND_VARIABLE_1816 $$unsorted)) (let ((_let_1 (tptp.boole_lattice skv_19))) (let ((_let_2 (tptp.powerset skv_19))) (or (not (tptp.element C _let_2)) (not (tptp.element BOUND_VARIABLE_1816 _let_2)) (and (= (tptp.subset_union2 skv_19 C BOUND_VARIABLE_1816) (tptp.apply_binary (tptp.the_L_join _let_1) C BOUND_VARIABLE_1816)) (= (tptp.subset_intersection2 skv_19 C BOUND_VARIABLE_1816) (tptp.apply_binary (tptp.the_L_meet _let_1) C BOUND_VARIABLE_1816)))))))))) (let ((_let_48 (tptp.latt_str _let_23))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.strict_latt_str _let_23))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_47))) (let ((_let_53 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.strict_latt_str B)) (not (tptp.latt_str B)) (= (= B (tptp.boole_lattice A)) (and (= (tptp.the_carrier B) (tptp.powerset A)) (forall ((C $$unsorted) (BOUND_VARIABLE_1816 $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element C _let_1)) (not (tptp.element BOUND_VARIABLE_1816 _let_1)) (and (= (tptp.apply_binary (tptp.the_L_join B) C BOUND_VARIABLE_1816) (tptp.subset_union2 A C BOUND_VARIABLE_1816)) (= (tptp.apply_binary (tptp.the_L_meet B) C BOUND_VARIABLE_1816) (tptp.subset_intersection2 A C BOUND_VARIABLE_1816)))))))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 (forall ((BOUND_VARIABLE_1953 $$unsorted)) (tptp.latt_str (tptp.boole_lattice BOUND_VARIABLE_1953))))) (let ((_let_57 (1))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (AND_ELIM _let_58 :args _let_57))) (let ((_let_60 (_let_56))) (let ((_let_61 ((tptp.boole_lattice BOUND_VARIABLE_1953)))) (let ((_let_62 (ASSUME :args _let_60))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (skv_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_61)) :args _let_60)) _let_59 :args (_let_48 false _let_56)))) (let ((_let_64 (forall ((BOUND_VARIABLE_1947 $$unsorted)) (tptp.strict_latt_str (tptp.boole_lattice BOUND_VARIABLE_1947))))) (let ((_let_65 (AND_ELIM _let_58 :args _let_39))) (let ((_let_66 (_let_64))) (let ((_let_67 ((tptp.boole_lattice BOUND_VARIABLE_1947)))) (let ((_let_68 (ASSUME :args _let_66))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 0)) :args ((or _let_45 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_49 _let_47 (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (skv_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_50 false _let_64)) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (skv_19 _let_23 QUANTIFIERS_INST_CBQI_PROP)) :args _let_55))) _let_54 :args (_let_52 false _let_53)) :args (_let_47 false _let_50 false _let_48 false _let_52)) :args (_let_45 false _let_47)))) (let ((_let_70 (tptp.meet_semilatt_str _let_23))) (let ((_let_71 (not _let_70))) (let ((_let_72 (tptp.empty_carrier _let_23))) (let ((_let_73 (or _let_72 _let_71 _let_46))) (let ((_let_74 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.meet_semilatt_str A)) (tptp.element (tptp.bottom_of_semilattstr A) (tptp.the_carrier A)))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (and _let_70 (tptp.join_semilatt_str _let_23)))) (let ((_let_77 (or _let_49 _let_76))) (let ((_let_78 (forall ((A $$unsorted)) (or (not (tptp.latt_str A)) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_76 0)) :args ((or _let_70 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_49 _let_76 (not _let_77)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_23 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_80)) _let_79 :args (_let_77 false _let_78)) :args (_let_76 false _let_48 false _let_77)) :args (_let_70 false _let_76)))) (let ((_let_82 (forall ((BOUND_VARIABLE_2071 $$unsorted)) (not (tptp.empty_carrier (tptp.boole_lattice BOUND_VARIABLE_2071)))))) (let ((_let_83 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) :args _let_39))) (let ((_let_84 (_let_82))) (let ((_let_85 ((tptp.boole_lattice BOUND_VARIABLE_2071)))) (let ((_let_86 (ASSUME :args _let_84))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (skv_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args ((not _let_72) false _let_82)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_71 _let_46 (not _let_73)))) _let_87 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.bottom_of_semilattstr A)))) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_46 true _let_72 false _let_70 false _let_73)))) (let ((_let_89 (and _let_46 _let_45))) (let ((_let_90 (_let_46 _let_45))) (let ((_let_91 (ASSUME :args (_let_46)))) (let ((_let_92 (APPLY_UF tptp.element))) (let ((_let_93 (ASSUME :args (_let_45)))) (let ((_let_94 (SYMM _let_93))) (let ((_let_95 (tptp.empty _let_20))) (let ((_let_96 (not _let_95))) (let ((_let_97 (or _let_96 _let_22))) (let ((_let_98 (forall ((A $$unsorted)) (or (not (tptp.empty A)) (= tptp.empty_set A))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (_let_40))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_96 _let_22 (not _let_97)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_100) :args (skv_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((skop_11 BOUND_VARIABLE_2572)))) :args _let_100)) (AND_ELIM _let_41 :args _let_57) :args (_let_95 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (_let_20 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_98))) _let_99 :args (_let_97 false _let_98)) :args (_let_22 false _let_95 false _let_97)))) (let ((_let_102 (tptp.meet _let_23 _let_20 _let_24))) (let ((_let_103 (and (= _let_20 _let_102) _let_26))) (let ((_let_104 (not _let_46))) (let ((_let_105 (or _let_104 _let_103))) (let ((_let_106 (forall ((C $$unsorted)) (let ((_let_1 (skop_11 skv_19))) (let ((_let_2 (tptp.boole_lattice skv_19))) (or (not (tptp.element C (tptp.the_carrier _let_2))) (and (= _let_1 (tptp.meet _let_2 _let_1 C)) (= _let_1 (tptp.meet _let_2 C _let_1))))))))) (let ((_let_107 (tptp.meet _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 _let_20))) (let ((_let_108 (= _let_20 _let_107))) (let ((_let_109 (tptp.meet _let_23 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_110 (= _let_20 _let_109))) (let ((_let_111 (and _let_110 _let_108))) (let ((_let_112 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 _let_44))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_113 _let_111))) (let ((_let_115 (tptp.meet_commutative _let_23))) (let ((_let_116 (tptp.element _let_20 _let_44))) (let ((_let_117 (tptp.meet_commut _let_23 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_118 (= _let_109 _let_117))) (let ((_let_119 (not _let_116))) (let ((_let_120 (not _let_115))) (let ((_let_121 (or _let_72 _let_120 _let_71 _let_119 _let_113 _let_118))) (let ((_let_122 (tptp.meet_commut _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 _let_20))) (let ((_let_123 (= _let_107 _let_122))) (let ((_let_124 (or _let_72 _let_120 _let_71 _let_113 _let_119 _let_123))) (let ((_let_125 (= _let_117 _let_122))) (let ((_let_126 (or _let_72 _let_120 _let_71 _let_119 _let_113 _let_125))) (let ((_let_127 (tptp.set_intersection2 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_128 (= _let_109 _let_127))) (let ((_let_129 (and (= (tptp.set_union2 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27) (tptp.join _let_23 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27)) _let_128))) (let ((_let_130 (or _let_119 _let_113 _let_129))) (let ((_let_131 (= (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 _let_20) _let_127))) (let ((_let_132 (= tptp.empty_set (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 tptp.empty_set)))) (let ((_let_133 (or))) (let ((_let_134 (forall ((BOUND_VARIABLE_2126 $$unsorted)) 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false _let_196)) :args (_let_182 true _let_201)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_187)) :args ((or _let_186 _let_185 _let_183 (not _let_187)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (skv_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args ((not _let_186) false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_191 0)) :args ((or _let_184 (not _let_191)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_194)) :args ((or _let_193 _let_191 (not _let_194)))) _let_195 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_178 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_80)) _let_79 :args (_let_194 false _let_78)) :args (_let_191 false _let_192 false _let_194)) :args (_let_184 false _let_191)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_189 :args (_let_178 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.lower_bounded_semilattstr A)))) :args _let_190)) _let_189 :args (_let_187 false _let_188)) :args (_let_183 true _let_186 false _let_184 false _let_187)) :args (_let_179 true _let_181 false _let_183)) :args (_let_180 false _let_179)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_103 1)) :args ((or _let_26 (not _let_103)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_104 _let_103 (not _let_105)))) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_177) :args (_let_24 QUANTIFIERS_INST_CBQI_PROP)) :args _let_177)) _let_176 :args (_let_105 false _let_106)) :args (_let_103 false _let_46 false _let_105)) :args (_let_26 false _let_103)) _let_101 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_31 _let_33 _let_21 (not _let_34)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_89)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_91 _let_93) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_24)) (SYMM _let_94) :args _let_92) (TRUE_INTRO _let_91))) :args _let_90)) :args _let_90)) :args (true _let_89)) _let_88 _let_69 :args (_let_30 false _let_46 false _let_45)) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (skv_19 _let_20 _let_24 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B _let_37) false)) (not (= (tptp.element C _let_37) false))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_21 false _let_30 false _let_32 false _let_34)) :args (false false _let_28 true _let_27 false _let_26 false _let_22 false _let_21)) :args ((forall ((A $$unsorted)) (=> (tptp.latt_str A) (=> (tptp.strict_latt_str A) (= A (tptp.latt_str_of (tptp.the_carrier A) (tptp.the_L_join A) (tptp.the_L_meet A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.lattice A)) (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)) (and _let_1 (tptp.lattice A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) _let_19 _let_18 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.subset_union2 A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_intersection2 A B C) (tptp.subset_intersection2 A C B))))) _let_17 _let_16 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.apply_binary A B C) (tptp.apply A (tptp.ordered_pair B C)))))) _let_15 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.join A B C) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_join A) B C))))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.meet A B C) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_meet A) B C))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) true true _let_14 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.join A B C) _let_1)))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D _let_1 C) (tptp.relation_of2 D _let_1 C) (tptp.element E A) (tptp.element F B)) (tptp.element (tptp.apply_binary_as_element A B C D E F) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.meet A B C) _let_1)))) true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.meet_commut A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_union2 A B C) _let_1)))) true _let_13 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_intersection2 A B C) _let_1)))) (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))) _let_12 true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (tptp.meet_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) true (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (tptp.join_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) (exists ((A $$unsorted)) (tptp.meet_semilatt_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (exists ((A $$unsorted)) (tptp.join_semilatt_str A)) (exists ((A $$unsorted)) (tptp.latt_str A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) _let_11 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) _let_10 (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_associative A) (tptp.join_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (not (tptp.empty A)) (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_commutative A) (tptp.meet_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_associative A) (tptp.meet_semilatt_str A)) (and (tptp.relation _let_3) (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A A))) (=> (and (tptp.function B) (tptp.quasi_total B _let_1 A) (tptp.relation_of2 B _let_1 A) (tptp.function C) (tptp.quasi_total C _let_1 A) (tptp.relation_of2 C _let_1 A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.latt_str_of A B C) (tptp.latt_str_of D E F)) (and (= A D) (= B E) (= C F))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) _let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_intersection2 A B B) B)))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) _let_8 (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (tptp.strict_latt_str A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A) (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A) (tptp.lattice A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D _let_1 C) (tptp.relation_of2 D _let_1 C) (tptp.element E A) (tptp.element F B)) (= (tptp.apply_binary_as_element A B C D E F) (tptp.apply_binary D E F))))) _let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.set_union2 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_intersection2 A B C) (tptp.set_intersection2 B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_4 _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 67.77/68.04 )
% 67.77/68.04 % SZS output end Proof for SEU345+1
% 67.77/68.04 % cvc5---1.0.5 exiting
% 67.77/68.05 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------