TSTP Solution File: SEU368+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU368+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 16:31:13 EDT 2023
% Result : Theorem 0.74s 0.95s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU368+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:35:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.74/0.95 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.eSTrynQUfI/cvc5---1.0.5_13158.p...
% 0.74/0.95 ------- get file name : TPTP file name is SEU368+1
% 0.74/0.95 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13158.smt2...
% 0.74/0.95 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.74/0.95 % SZS status Theorem for SEU368+1
% 0.74/0.95 % SZS output start Proof for SEU368+1
% 0.74/0.95 (
% 0.74/0.95 (let ((_let_1 (not (forall ((A $$unsorted)) (let ((_let_1 (tptp.incl_POSet A))) (and (= (tptp.the_carrier _let_1) A) (= (tptp.the_InternalRel _let_1) (tptp.inclusion_order A)))))))) (let ((_let_2 (forall ((A $$unsorted)) (= (tptp.incl_POSet A) (tptp.rel_str_of A (tptp.inclusion_order A)))))) (let ((_let_3 (forall ((A $$unsorted)) (let ((_let_1 (tptp.incl_POSet A))) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1)))))) (let ((_let_4 (forall ((A $$unsorted)) (let ((_let_1 (tptp.inclusion_order A))) (and (tptp.reflexive _let_1) (tptp.antisymmetric _let_1) (tptp.transitive _let_1) (tptp.v1_partfun1 _let_1 A A) (tptp.relation_of2_as_subset _let_1 A A)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.strict_rel_str A) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A)))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.rel_str_of A B) (tptp.rel_str_of C D)) (and (= A C) (= B D)))))))) (let ((_let_8 (tptp.inclusion_order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_9 (tptp.rel_str_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_8))) (let ((_let_10 (tptp.incl_POSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.the_InternalRel _let_10))) (let ((_let_13 (tptp.the_carrier _let_10))) (let ((_let_14 (tptp.rel_str_of _let_13 _let_12))) (let ((_let_15 (= _let_10 _let_14))) (let ((_let_16 (= _let_14 _let_9))) (let ((_let_17 (_let_2))) (let ((_let_18 (ASSUME :args _let_17))) (let ((_let_19 ((tptp.incl_POSet A)))) (let ((_let_20 (tptp.strict_rel_str _let_10))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.rel_str _let_10))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_15))) (let ((_let_25 (forall ((A $$unsorted)) (or (not (tptp.rel_str A)) (not (tptp.strict_rel_str A)) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (_let_25))) (let ((_let_28 (forall ((BOUND_VARIABLE_1282 $$unsorted)) (tptp.strict_rel_str (tptp.incl_POSet BOUND_VARIABLE_1282))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (AND_ELIM _let_29 :args (0)))) (let ((_let_31 (_let_28))) (let ((_let_32 ((tptp.incl_POSet BOUND_VARIABLE_1282)))) (let ((_let_33 (ASSUME :args _let_31))) (let ((_let_34 (forall ((BOUND_VARIABLE_1288 $$unsorted)) (tptp.rel_str (tptp.incl_POSet BOUND_VARIABLE_1288))))) (let ((_let_35 (AND_ELIM _let_29 :args (1)))) (let ((_let_36 (_let_34))) (let ((_let_37 ((tptp.incl_POSet BOUND_VARIABLE_1288)))) (let ((_let_38 (ASSUME :args _let_36))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_13))) (let ((_let_40 (and _let_39 (= _let_12 _let_8)))) (let ((_let_41 (not _let_16))) (let ((_let_42 (tptp.relation_of2 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41 _let_40))) (let ((_let_45 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1184 $$unsorted) (BOUND_VARIABLE_1182 $$unsorted)) (or (not (tptp.relation_of2 B A A)) (not (= (tptp.rel_str_of A B) (tptp.rel_str_of BOUND_VARIABLE_1182 BOUND_VARIABLE_1184))) (and (= A BOUND_VARIABLE_1182) (= B BOUND_VARIABLE_1184)))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (_let_45))) (let ((_let_48 (tptp.rel_str_of BOUND_VARIABLE_1182 BOUND_VARIABLE_1184))) (let ((_let_49 (not _let_40))) (let ((_let_50 (forall ((BOUND_VARIABLE_1329 $$unsorted)) (= BOUND_VARIABLE_1329 (tptp.the_carrier (tptp.incl_POSet BOUND_VARIABLE_1329)))))) (let ((_let_51 (not _let_39))) (let ((_let_52 (forall ((BOUND_VARIABLE_1336 $$unsorted)) (= (tptp.the_InternalRel (tptp.incl_POSet BOUND_VARIABLE_1336)) (tptp.inclusion_order BOUND_VARIABLE_1336))))) (let ((_let_53 (not _let_50))) (let ((_let_54 (tptp.inclusion_order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_55 (tptp.incl_POSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_56 (tptp.the_InternalRel _let_55))) (let ((_let_57 (= _let_56 _let_54))) (let ((_let_58 (tptp.the_carrier _let_55))) (let ((_let_59 (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_58) _let_57))) (let ((_let_60 (tptp.rel_str_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_54))) (let ((_let_61 (tptp.rel_str_of _let_58 _let_56))) (let ((_let_62 (= _let_61 _let_60))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.relation_of2 _let_54 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63 _let_59))) (let ((_let_67 (= _let_55 _let_60))) (let ((_let_68 (= _let_55 _let_61))) (let ((_let_69 (tptp.strict_rel_str _let_55))) (let ((_let_70 (not _let_69))) (let ((_let_71 (tptp.rel_str _let_55))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_70 _let_68))) (let ((_let_74 (and _let_68 _let_67))) (let ((_let_75 (ASSUME :args (_let_67)))) (let ((_let_76 (ASSUME :args (_let_68)))) (let ((_let_77 (tptp.relation_of2_as_subset _let_54 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_78 (= _let_77 _let_64))) (let ((_let_79 (_let_5))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 ((tptp.relation_of2_as_subset C A B)))) (let ((_let_82 (forall ((BOUND_VARIABLE_1274 $$unsorted)) (tptp.relation_of2_as_subset (tptp.inclusion_order BOUND_VARIABLE_1274) BOUND_VARIABLE_1274 BOUND_VARIABLE_1274)))) (let ((_let_83 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args (4)))) (let ((_let_84 (_let_82))) (let ((_let_85 ((tptp.inclusion_order BOUND_VARIABLE_1274)))) (let ((_let_86 (ASSUME :args _let_84))) (let ((_let_87 (or))) (let ((_let_88 (not _let_52))) (let ((_let_89 (_let_88))) (let ((_let_90 (_let_53))) (let ((_let_91 (tptp.relation_of2_as_subset _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_92 (= _let_91 _let_42))) (let ((_let_93 (ASSUME :args (_let_41)))) (let ((_let_94 (ASSUME :args (_let_11)))) (let ((_let_95 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_93 _let_95 _let_94) :args (_let_15 _let_11 _let_41)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (TRANS (SYMM _let_95) (SYMM (SYMM _let_94))))) (FALSE_INTRO _let_93))) :args (_let_41 _let_15 _let_11)) :args ((not (and _let_15 _let_11 _let_41)) SB_LITERAL))) (CONG (REFL :args ((not _let_15))) (REFL :args ((not _let_11))) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_16))) :args _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_41 _let_40 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_92)) :args ((or (not _let_91) _let_42 (not _let_92)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args (_let_91 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_81)) :args _let_79)) _let_80 :args (_let_92 false _let_5)) :args (_let_42 false _let_91 false _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 0)) :args ((or _let_39 _let_49))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_90)) :args _let_90)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_50))) (REFL :args (_let_51)) :args _let_87)) (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_89)) :args _let_89)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_52))) (REFL :args ((not _let_57))) :args _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 1)) :args ((or _let_57 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_63 _let_59 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or (not _let_77) _let_64 (not _let_78)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args (_let_77 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_54 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_81)) :args _let_79)) _let_80 :args (_let_78 false _let_5)) :args (_let_64 false _let_77 false _let_78)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_74)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_75 _let_76) (SCOPE (TRANS (SYMM _let_76) (SYMM (SYMM _let_75))) :args (_let_67 _let_68))) :args (_let_68 _let_67))) :args (true _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_70 _let_68 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_71 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_69 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (_let_55 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.the_InternalRel A)))) :args _let_27)) _let_26 :args (_let_73 false _let_25)) :args (_let_68 false _let_71 false _let_69 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_19)) :args _let_17)) _let_18 :args (_let_67 false _let_2)) :args (_let_62 false _let_68 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_54 _let_56 _let_58 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.relation_of2 B A A) false)) _let_48))) :args _let_47))) _let_46 :args (_let_66 false _let_45)) :args (_let_59 false _let_64 false _let_62 false _let_66)) :args (_let_57 false _let_59)) :args (_let_52 false _let_57)) :args (_let_53 false _let_52)) :args (_let_51 true _let_50)) :args (_let_49 true _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_8 _let_12 _let_13 QUANTIFIERS_INST_E_MATCHING ((tptp.rel_str_of A B) _let_48))) :args _let_47))) _let_46 :args (_let_44 false _let_45)) :args (_let_41 false _let_42 true _let_40 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_21 _let_15 (not _let_24)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_22 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_32)) :args _let_31)) _let_30 :args (_let_20 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (_let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.the_carrier A)))) :args _let_27)) _let_26 :args (_let_24 false _let_25)) :args (_let_15 false _let_22 false _let_20 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_19)) :args _let_17)) _let_18 :args (_let_11 false _let_2)) :args (false true _let_16 false _let_15 false _let_11)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) true (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)) (not (tptp.empty (tptp.the_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 $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$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 $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.incl_POSet A))) (=> (not (tptp.empty A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (and (not (tptp.empty A)) (tptp.relation_of2 B A A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (and (tptp.reflexive B) (tptp.antisymmetric B) (tptp.transitive B) (tptp.v1_partfun1 B A A) (tptp.relation_of2 B A A)) (and (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_7 _let_6 (exists ((A $$unsorted)) (tptp.rel_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1))))) (forall ((A $$unsorted)) (tptp.relation (tptp.inclusion_relation A))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (tptp.strict_rel_str A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.the_InternalRel A))) (=> (and (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (and (tptp.relation _let_2) (tptp.reflexive _let_2) (tptp.antisymmetric _let_2) (tptp.transitive _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1)))))) (forall ((A $$unsorted)) (= (tptp.inclusion_order A) (tptp.inclusion_relation A))) _let_4 _let_3 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true (forall ((A $$unsorted)) (let ((_let_1 (tptp.incl_POSet A))) (and (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1)))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.74/0.96 )
% 0.74/0.96 % SZS output end Proof for SEU368+1
% 0.74/0.96 % cvc5---1.0.5 exiting
% 0.74/0.96 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------