TSTP Solution File: SEU305+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 16:30:46 EDT 2023
% Result : Theorem 0.20s 0.57s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 12:37:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.M1HFWcvOGd/cvc5---1.0.5_14337.p...
% 0.20/0.57 ------- get file name : TPTP file name is SEU305+1
% 0.20/0.57 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_14337.smt2...
% 0.20/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.57 % SZS status Theorem for SEU305+1
% 0.20/0.57 % SZS output start Proof for SEU305+1
% 0.20/0.57 (
% 0.20/0.57 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (and (tptp.below A B C) (tptp.below A C B)) (= B C))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.join_commut A B C) (tptp.join A B C))))))) (let ((_let_3 (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 $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.below A B C) (= (tptp.join A B C) C)))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.join_commut A B C) (tptp.join_commut A C B))))))) (let ((_let_5 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_6 (tptp.join SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_6))) (let ((_let_8 (tptp.join SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_8))) (let ((_let_10 (tptp.join_commut SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_11 (= _let_6 _let_10))) (let ((_let_12 (tptp.join_commut SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_13 (= _let_8 _let_12))) (let ((_let_14 (= _let_10 _let_12))) (let ((_let_15 (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.below SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_19))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_19))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.join_semilatt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.join_commutative SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (or _let_28 _let_27 _let_25 _let_23 _let_21 _let_18 _let_16 _let_5))) (let ((_let_30 (not _let_5))) (let ((_let_31 (forall ((A $$unsorted) (BOUND_VARIABLE_1303 $$unsorted) (BOUND_VARIABLE_1301 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.join_commutative A)) (not (tptp.join_semilatt_str A)) (not (tptp.element BOUND_VARIABLE_1301 _let_1)) (not (tptp.element BOUND_VARIABLE_1303 _let_1)) (not (tptp.below A BOUND_VARIABLE_1301 BOUND_VARIABLE_1303)) (not (tptp.below A BOUND_VARIABLE_1303 BOUND_VARIABLE_1301)) (= BOUND_VARIABLE_1301 BOUND_VARIABLE_1303)))))) (let ((_let_32 (not _let_29))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (or))) (let ((_let_35 (not _let_31))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_33) :args (_let_35)) (REWRITE :args ((=> _let_35 (not (or _let_28 _let_27 _let_25 _let_23 _let_21 _let_18 _let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_31))) (REFL :args (_let_32)) :args _let_34)) _let_33 :args (_let_32 true _let_31)))) (let ((_let_37 (= _let_15 _let_7))) (let ((_let_38 (or _let_28 _let_25 _let_21 _let_23 _let_37))) (let ((_let_39 (forall ((A $$unsorted) (BOUND_VARIABLE_1103 $$unsorted) (BOUND_VARIABLE_1101 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.join_semilatt_str A)) (not (tptp.element BOUND_VARIABLE_1101 _let_1)) (not (tptp.element BOUND_VARIABLE_1103 _let_1)) (= (tptp.below A BOUND_VARIABLE_1101 BOUND_VARIABLE_1103) (= BOUND_VARIABLE_1103 (tptp.join A BOUND_VARIABLE_1101 BOUND_VARIABLE_1103)))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 ((tptp.below A BOUND_VARIABLE_1101 BOUND_VARIABLE_1103)))) (let ((_let_43 (REFL :args (_let_29)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 4)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_34)) :args ((or _let_20 _let_29))) _let_36 :args (_let_20 true _let_29)))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 3)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_34)) :args ((or _let_22 _let_29))) _let_36 :args (_let_22 true _let_29)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_34)) :args ((or _let_24 _let_29))) _let_36 :args (_let_24 true _let_29)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 0)) _let_36 :args ((not _let_28) true _let_29)))) (let ((_let_48 (= _let_17 _let_9))) (let ((_let_49 (or _let_28 _let_25 _let_23 _let_21 _let_48))) (let ((_let_50 (or _let_28 _let_27 _let_25 _let_21 _let_23 _let_11))) (let ((_let_51 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.join_commutative A)) (not (tptp.join_semilatt_str A)) (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.join_commut A B C) (tptp.join A B C))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_51))) (let ((_let_54 ((tptp.join A B C)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_34)) :args ((or _let_26 _let_29))) _let_36 :args (_let_26 true _let_29)))) (let ((_let_56 (or _let_28 _let_27 _let_25 _let_23 _let_21 _let_13))) (let ((_let_57 (or _let_28 _let_27 _let_25 _let_21 _let_23 _let_14))) (let ((_let_58 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.join_commutative A)) (not (tptp.join_semilatt_str A)) (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.join_commut A B C) (tptp.join_commut A C B))))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (ASSUME :args (_let_7)))) (let ((_let_61 (ASSUME :args (_let_11)))) (let ((_let_62 (ASSUME :args (_let_14)))) (let ((_let_63 (ASSUME :args (_let_13)))) (let ((_let_64 (ASSUME :args (_let_9)))) (let ((_let_65 (ASSUME :args (_let_30)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_60 _let_61 _let_62 _let_63 _let_64 _let_65) :args (_let_30 _let_7 _let_9 _let_11 _let_13 _let_14)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_65)) (TRUE_INTRO (TRANS (SYMM (SYMM _let_64)) (SYMM (SYMM _let_63)) (SYMM _let_62) (SYMM _let_61) (SYMM _let_60))))) :args (_let_7 _let_11 _let_14 _let_13 _let_9 _let_30)) :args ((not (and _let_30 _let_7 _let_9 _let_11 _let_13 _let_14)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_5))) (REFL :args ((not _let_7))) (REFL :args ((not _let_9))) (REFL :args ((not _let_11))) (REFL :args ((not _let_13))) (REFL :args ((not _let_14))) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_28 _let_27 _let_25 _let_23 _let_21 _let_14 (not _let_57)))) _let_47 _let_55 _let_46 _let_45 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.join_commut A B C)))) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_14 true _let_28 false _let_26 false _let_24 false _let_22 false _let_20 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_28 _let_27 _let_25 _let_23 _let_21 _let_13 (not _let_56)))) _let_47 _let_55 _let_46 _let_45 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53))) _let_52 :args (_let_56 false _let_51)) :args (_let_13 true _let_28 false _let_26 false _let_24 false _let_22 false _let_20 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_28 _let_27 _let_25 _let_23 _let_21 _let_11 (not _let_50)))) _let_47 _let_55 _let_46 _let_45 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53))) _let_52 :args (_let_50 false _let_51)) :args (_let_11 true _let_28 false _let_26 false _let_24 false _let_22 false _let_20 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_48)) :args ((or _let_18 _let_9 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 5)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_34)) :args ((or _let_17 _let_29))) _let_36 :args (_let_17 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_28 _let_25 _let_23 _let_21 _let_48 (not _let_49)))) _let_47 _let_46 _let_45 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_41)) _let_40 :args (_let_49 false _let_39)) :args (_let_48 true _let_28 false _let_24 false _let_22 false _let_20 false _let_49)) :args (_let_9 false _let_17 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_16 _let_7 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 6)) (CONG _let_43 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_34)) :args ((or _let_15 _let_29))) _let_36 :args (_let_15 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_28 _let_25 _let_23 _let_21 _let_37 (not _let_38)))) _let_47 _let_46 _let_45 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_41)) _let_40 :args (_let_38 false _let_39)) :args (_let_37 true _let_28 false _let_24 false _let_22 false _let_20 false _let_38)) :args (_let_7 false _let_15 false _let_37)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 7)) _let_36 :args (_let_30 true _let_29)) :args (false false _let_14 false _let_13 false _let_11 false _let_9 false _let_7 true _let_5)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.preboolean A) (and (tptp.cup_closed A) (tptp.diff_closed A)))) (forall ((A $$unsorted)) (=> (and (tptp.cup_closed A) (tptp.diff_closed A)) (tptp.preboolean A))) _let_4 (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 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.join A B C) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_join A) B C))))))))) _let_3 true (forall ((A $$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 (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)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_commutative A) (tptp.join_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.join_commut A B C) _let_1)))) true (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) true (forall ((A $$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 $$unsorted)) (tptp.one_sorted_str A)) (exists ((A $$unsorted)) (tptp.join_semilatt_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))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.powerset A))) (and (not (tptp.empty _let_1)) (tptp.cup_closed _let_1) (tptp.diff_closed _let_1) (tptp.preboolean _let_1)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier 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 $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D _let_1 C) (tptp.relation_of2 D _let_1 C) (tptp.element E A) (tptp.element F B)) (= (tptp.apply_binary_as_element A B C D E F) (tptp.apply_binary D E F))))) _let_2 (forall ((A $$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 $$unsorted) (B $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.57 )
% 0.20/0.57 % SZS output end Proof for SEU305+1
% 0.20/0.57 % cvc5---1.0.5 exiting
% 0.20/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------