%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 14:40:17 EDT 2023

% Result   : Theorem 0.20s 0.55s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n013.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   : Sat Aug 26 16:06:32 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.55  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.51X7m5uSaG/cvc5---1.0.5_22620.p...
% 0.20/0.55  ------- get file name : TPTP file name is SET776+4
% 0.20/0.55  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22620.smt2...
% 0.20/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.55  % SZS status Theorem for SET776+4
% 0.20/0.55  % SZS output start Proof for SET776+4
% 0.20/0.55  (
% 0.20/0.55  (let ((_let_1 (not (forall ((E $$unsorted) (P $$unsorted) (R $$unsorted)) (=> (and (tptp.pre_order P E) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.member A E) (tptp.member B E)) (= (tptp.apply R A B) (and (tptp.apply P A B) (tptp.apply P B A)))))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 E) (tptp.member X2 E) (tptp.member Y1 E) (tptp.member Y2 E)) (=> (and (tptp.apply R X1 Y1) (tptp.apply R X2 Y2) (tptp.apply P X1 X2)) (tptp.apply P Y1 Y2))))))))) (let ((_let_2 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z))))) (let ((_let_4 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_6 (not _let_5))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_10 _let_8 _let_6 _let_4))) (let ((_let_16 (and (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X))) _let_3))) (let ((_let_17 (tptp.pre_order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (= _let_17 _let_16))) (let ((_let_19 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.member Z E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (not _let_27))) (let ((_let_29 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.member A SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 A B) (and (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 A B) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 B A))))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (not _let_17))) (let ((_let_32 (or _let_31 _let_30 _let_12 _let_28 _let_14 _let_10 _let_26 _let_24 _let_22 _let_4))) (let ((_let_33 (forall ((E $$unsorted) (P $$unsorted) (R $$unsorted) (BOUND_VARIABLE_1047 $$unsorted) (BOUND_VARIABLE_1045 $$unsorted) (BOUND_VARIABLE_1043 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.pre_order P E)) (not (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.member A E)) (not (tptp.member B E)) (= (tptp.apply R A B) (and (tptp.apply P A B) (tptp.apply P B A)))))) (not (tptp.member BOUND_VARIABLE_1041 E)) (not (tptp.member BOUND_VARIABLE_1043 E)) (not (tptp.member BOUND_VARIABLE_1045 E)) (not (tptp.member BOUND_VARIABLE_1047 E)) (not (tptp.apply R BOUND_VARIABLE_1041 BOUND_VARIABLE_1045)) (not (tptp.apply R BOUND_VARIABLE_1043 BOUND_VARIABLE_1047)) (not (tptp.apply P BOUND_VARIABLE_1041 BOUND_VARIABLE_1043)) (tptp.apply P BOUND_VARIABLE_1045 BOUND_VARIABLE_1047))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (or))) (let ((_let_37 (not _let_33))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_35) :args (_let_37))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_33))) (REFL :args (_let_34)) :args _let_36)) _let_35 :args (_let_34 true _let_33)))) (let ((_let_39 (REFL :args (_let_32)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 1)) :args ((or _let_3 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_18)) :args ((or _let_31 _let_16 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 0)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_17))) :args _let_36)) :args ((or _let_17 _let_32))) _let_38 :args (_let_17 true _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.pre_order R E)))) :args (_let_19))) _let_20 :args (_let_18 false _let_19)) :args (_let_16 false _let_17 false _let_18)) :args (_let_3 false _let_16)))) (let ((_let_41 (not _let_15))) (let ((_let_42 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_12 _let_28 _let_10 _let_22 _let_43 _let_5))) (let ((_let_45 (_let_3))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (and _let_42 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_48 (= _let_23 _let_47))) (let ((_let_49 (or _let_28 _let_10 _let_48))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 1)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_36)) :args ((or _let_29 _let_32))) _let_38 :args (_let_29 true _let_32)))) (let ((_let_51 (_let_29))) (let ((_let_52 ((tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 A B)))) (let ((_let_53 (ASSUME :args _let_51))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 5)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_36)) :args ((or _let_9 _let_32))) _let_38 :args (_let_9 true _let_32)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 3)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_36)) :args ((or _let_27 _let_32))) _let_38 :args (_let_27 true _let_32)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 2)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_36)) :args ((or _let_11 _let_32))) _let_38 :args (_let_11 true _let_32)))) (let ((_let_57 (and (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_7))) (let ((_let_58 (= _let_25 _let_57))) (let ((_let_59 (or _let_12 _let_14 _let_58))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 4)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_36)) :args ((or _let_13 _let_32))) _let_38 :args (_let_13 true _let_32)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z) true)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_12 _let_14 _let_10 _let_4 _let_8 _let_6 _let_41))) _let_56 _let_60 _let_54 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_32 9)) _let_38 :args ((not _let_4) true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_57 1)) :args ((or _let_7 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_58)) :args ((or _let_26 _let_57 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 6)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_36)) :args ((or _let_25 _let_32))) _let_38 :args (_let_25 true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_12 _let_14 _let_58 (not _let_59)))) _let_56 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_59 false _let_29)) :args (_let_58 false _let_11 false _let_13 false _let_59)) :args (_let_57 false _let_25 false _let_58)) :args (_let_7 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_12 _let_28 _let_10 _let_22 _let_43 _let_5 (not _let_44)))) _let_56 _let_55 _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 8)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_36)) :args ((or _let_21 _let_32))) _let_38 :args (_let_21 true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 0)) :args ((or _let_42 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_48)) :args ((or _let_24 _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 7)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_36)) :args ((or _let_23 _let_32))) _let_38 :args (_let_23 true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_28 _let_10 _let_48 (not _let_49)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_52)) :args _let_51)) _let_50 :args (_let_49 false _let_29)) :args (_let_48 false _let_27 false _let_9 false _let_49)) :args (_let_47 false _let_23 false _let_48)) :args (_let_42 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false)) (not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false)) (not (= (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_45)) _let_40 :args (_let_44 false _let_3)) :args (_let_5 false _let_11 false _let_27 false _let_9 false _let_21 false _let_42 false _let_44)) :args (_let_41 false _let_11 false _let_13 false _let_9 true _let_4 false _let_7 false _let_5)) _let_40 :args (false true _let_15 false _let_3)) :args ((forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (not (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.member X B)))))) (forall ((A $$unsorted) (E $$unsorted)) (= (tptp.partition A E) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X E))) (forall ((X $$unsorted)) (=> (tptp.member X E) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (exists ((Z $$unsorted)) (and (tptp.member Z X) (tptp.member Z Y))) (= X Y))))))) (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (tptp.apply R X Y) (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A) (tptp.member Z A)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.equivalence_class A E R)) (and (tptp.member X E) (tptp.apply R A X)))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.56  )
% 0.20/0.56  % SZS output end Proof for SET776+4
% 0.20/0.56  % cvc5---1.0.5 exiting
% 0.20/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------