%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU178+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% 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 16:29:50 EDT 2023

% Result   : Theorem 25.96s 26.24s
% Output   : Proof 25.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU178+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 23 20:51:56 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 25.96/26.24  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.2BJhOkQQAd/cvc5---1.0.5_9793.p...
% 25.96/26.24  ------- get file name : TPTP file name is SEU178+1
% 25.96/26.24  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9793.smt2...
% 25.96/26.24  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.96/26.24  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.96/26.24  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.96/26.24  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.96/26.24  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.96/26.24  % SZS status Theorem for SEU178+1
% 25.96/26.24  % SZS output start Proof for SEU178+1
% 25.96/26.24  (
% 25.96/26.24  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair D C) A)))))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair C D) A)))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))) (let ((_let_6 (forall ((A $$unsorted)) (= (tptp.relation A) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))))) (let ((_let_7 (forall ((C $$unsorted)) (= (not (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair D C) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (tptp.in C (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_8 (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_10))) (let ((_let_12 (= _let_11 _let_9))) (let ((_let_13 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_7))) (let ((_let_16 (forall ((A $$unsorted) (BOUND_VARIABLE_928 $$unsorted)) (or (not (tptp.relation A)) (= (= (tptp.relation_rng A) BOUND_VARIABLE_928) (forall ((C $$unsorted)) (= (not (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair D C) A)))) (tptp.in C BOUND_VARIABLE_928)))))))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (tptp.cartesian_product2 _let_18 _let_10))) (let ((_let_20 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_19))) (let ((_let_21 (or _let_14 _let_20))) (let ((_let_22 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (or))) (let ((_let_26 (not _let_22))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_24) :args (_let_26))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_22))) (REFL :args (_let_23)) :args _let_25)) _let_24 :args (_let_23 true _let_22)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG (REFL :args (_let_21)) (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_25)) :args ((or _let_13 _let_21))) _let_27 :args (_let_13 true _let_21)))) (let ((_let_29 (not _let_12))) (let ((_let_30 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_31 (tptp.in _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_32 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_33 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_30))) (let ((_let_34 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_19))) (let ((_let_35 (not _let_32))) (let ((_let_36 (or _let_35 _let_34))) (let ((_let_37 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.in C (tptp.cartesian_product2 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (= _let_20 _let_37))) (let ((_let_40 (not _let_37))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_40))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_43)) :args _let_43)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_37))) (REFL :args (_let_38)) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_39)) :args ((or _let_20 _let_40 (not _let_39)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 1)) _let_27 :args ((not _let_20) true _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_41))) _let_42 :args (_let_39 false _let_41)) :args (_let_40 true _let_20 false _let_39)) :args (_let_38 true _let_37)))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG (REFL :args (_let_36)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_32))) :args _let_25)) :args ((or _let_32 _let_36))) _let_44 :args (_let_32 true _let_36)))) (let ((_let_46 (forall ((C $$unsorted) (D $$unsorted)) (not (= (tptp.ordered_pair C D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_35 _let_47))) (let ((_let_49 (forall ((B $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))) (let ((_let_50 (= _let_13 _let_49))) (let ((_let_51 (forall ((A $$unsorted)) (= (tptp.relation A) (forall ((B $$unsorted)) (or (not (tptp.in B A)) (not (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_49))) (let ((_let_54 (_let_33))) (let ((_let_55 (_let_47))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_55)) :args _let_55) (REWRITE :args ((=> _let_47 (not (not (= _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) (REFL :args _let_54) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_35 _let_47 (not _let_48)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_53) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_53))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_50)) :args ((or _let_14 _let_49 (not _let_50)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation A)))) :args (_let_51))) _let_52 :args (_let_50 false _let_51)) :args (_let_49 false _let_13 false _let_50)) :args (_let_48 false _let_49)) :args (_let_47 false _let_32 false _let_48)) :args (_let_33 true _let_46)))) (let ((_let_57 (not _let_31))) (let ((_let_58 (REFL :args ((not _let_33))))) (let ((_let_59 (ASSUME :args (_let_57)))) (let ((_let_60 (APPLY_UF tptp.in))) (let ((_let_61 (ASSUME :args _let_54))) (let ((_let_62 (SYMM _let_61))) (let ((_let_63 (ASSUME :args (_let_32)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_59 _let_61 _let_63) :args (_let_32 _let_33 _let_57)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_63)) (CONG (SYMM _let_62) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args _let_60) (FALSE_INTRO _let_59))) :args (_let_57 _let_33 _let_32)) :args ((not (and _let_32 _let_33 _let_57)) SB_LITERAL))) (CONG (REFL :args (_let_35)) _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_31))) :args _let_25)) _let_56 _let_45 :args (_let_31 false _let_33 false _let_32)))) (let ((_let_65 (_let_8))) (let ((_let_66 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_18))) (let ((_let_67 (and _let_66 _let_11))) (let ((_let_68 (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_69 (not _let_68))) (let ((_let_70 (= _let_66 _let_69))) (let ((_let_71 (forall ((C $$unsorted)) (= (not (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair C D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (tptp.in C (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_72 (or _let_14 _let_71))) (let ((_let_73 (forall ((A $$unsorted) (BOUND_VARIABLE_899 $$unsorted)) (or (not (tptp.relation A)) (= (= (tptp.relation_dom A) BOUND_VARIABLE_899) (forall ((C $$unsorted)) (= (not (forall ((D $$unsorted)) (not (tptp.in (tptp.ordered_pair C D) A)))) (tptp.in C BOUND_VARIABLE_899)))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (_let_71))) (let ((_let_76 (_let_68))) (let ((_let_77 (not _let_70))) (let ((_let_78 (tptp.in _let_30 _let_19))) (let ((_let_79 (= _let_78 _let_67))) (let ((_let_80 (not _let_67))) (let ((_let_81 (_let_2))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (not _let_78))) (let ((_let_84 (not _let_34))) (let ((_let_85 (and _let_84 _let_33))) (let ((_let_86 (_let_84 _let_33))) (let ((_let_87 (ASSUME :args (_let_84)))) (let ((_let_88 (_let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_88) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_PROP)) :args _let_88))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_12)) (CONG (REFL :args (_let_29)) (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_25)) :args ((or _let_11 _let_8 _let_29))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_79)) :args ((or _let_78 _let_80 (not _let_79)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_85)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_87 _let_61) (SCOPE (FALSE_ELIM (TRANS (CONG _let_62 (REFL :args (_let_19)) :args _let_60) (FALSE_INTRO _let_87))) :args _let_86)) :args _let_86)) :args (true _let_85)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_34))) _let_58 (REFL :args (_let_83)) :args _let_25)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_36 1)) _let_44 :args (_let_84 true _let_36)) _let_56 :args (_let_83 true _let_34 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_18 _let_10 QUANTIFIERS_INST_E_MATCHING ((tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D))))) :args _let_81)) _let_82 :args (_let_79 false _let_2)) :args (_let_80 true _let_78 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_70)) (CONG (REFL :args (_let_77)) (REFL :args (_let_66)) (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_25)) :args ((or _let_66 _let_68 _let_77))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_76)) _let_64 :args (_let_69 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_75) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_PROP)) :args _let_75))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_14 _let_71 (not _let_72)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_18 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_73)))) _let_74 :args (_let_72 false _let_73)) :args (_let_71 false _let_13 false _let_72)) :args (_let_70 false _let_71)) :args (_let_66 true _let_68 false _let_70)) :args ((not _let_11) true _let_67 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_65) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_65)) :args ((or _let_57 _let_9))) _let_64 :args (_let_9 false _let_31)) :args (_let_29 true _let_11 true _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_7 (not _let_15)))) _let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_10 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_16)))) _let_17 :args (_let_15 false _let_16)) :args (_let_7 false _let_13 false _let_15)) :args (false true _let_12 false _let_7)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_6 _let_5 _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) true true true true true true true true true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$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)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$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)) (=> (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)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.96/26.24  )
% 25.96/26.24  % SZS output end Proof for SEU178+1
% 25.96/26.24  % cvc5---1.0.5 exiting
% 26.10/26.25  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------