TSTP Solution File: SEU292+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 16:30:40 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Wed Aug 23 20:01:32 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.58 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vHMtbeirSu/cvc5---1.0.5_6121.p...
% 0.21/0.58 ------- get file name : TPTP file name is SEU292+1
% 0.21/0.58 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_6121.smt2...
% 0.21/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.58 % SZS status Theorem for SEU292+1
% 0.21/0.58 % SZS output start Proof for SEU292+1
% 0.21/0.58 (
% 0.21/0.58 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom B)) (= (tptp.apply (tptp.relation_composition B C) A) (tptp.apply C (tptp.apply B A)))))))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (forall ((E $$unsorted)) (=> (and (tptp.relation E) (tptp.function E)) (=> (tptp.in C A) (or (= B tptp.empty_set) (= (tptp.apply (tptp.relation_composition D E) C) (tptp.apply E (tptp.apply D C)))))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_dom_as_subset A B C) (tptp.relation_dom C)))))) (let ((_let_5 (tptp.relation tptp.empty_set))) (let ((_let_6 (tptp.empty tptp.empty_set))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (= A tptp.empty_set))) (let ((_let_3 (= B tptp.empty_set))) (=> (tptp.relation_of2_as_subset C A B) (and (=> (=> _let_3 _let_2) (= _let_1 (= A (tptp.relation_dom_as_subset A B C)))) (=> _let_3 (or _let_2 (= _let_1 (= C tptp.empty_set)))))))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))))) (let ((_let_10 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_11 (tptp.relation_dom_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_11))) (let ((_let_13 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_14 (= _let_11 _let_13))) (let ((_let_15 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_13))) (let ((_let_16 (= (tptp.apply (tptp.relation_composition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_17 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_20 (not _let_19))) (let ((_let_21 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_22 (not _let_10))) (let ((_let_23 (tptp.relation_of2_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.quasi_total SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_24 _let_22 _let_21 _let_20 _let_18 _let_16))) (let ((_let_30 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (BOUND_VARIABLE_1324 $$unsorted)) (or (not (tptp.function D)) (not (tptp.quasi_total D A B)) (not (tptp.relation_of2_as_subset D A B)) (not (tptp.in C A)) (= tptp.empty_set B) (not (tptp.relation BOUND_VARIABLE_1324)) (not (tptp.function BOUND_VARIABLE_1324)) (= (tptp.apply (tptp.relation_composition D BOUND_VARIABLE_1324) C) (tptp.apply BOUND_VARIABLE_1324 (tptp.apply D C))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_32) :args (_let_34))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (= _let_25 _let_12))) (let ((_let_38 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_39 (and _let_21 (not _let_38)))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (not _let_21))) (let ((_let_42 (and _let_40 (or _let_41 _let_38 (= _let_25 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))))) (let ((_let_43 (or _let_24 _let_42))) (let ((_let_44 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (= tptp.empty_set A))) (let ((_let_3 (= tptp.empty_set B))) (or (not (tptp.relation_of2_as_subset C A B)) (and (or (and _let_3 (not _let_2)) (= _let_1 (= A (tptp.relation_dom_as_subset A B C)))) (or (not _let_3) _let_2 (= _let_1 (= tptp.empty_set C))))))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_33)) :args ((or _let_23 _let_29))) _let_35 :args (_let_23 true _let_29)))) (let ((_let_47 (not _let_39))) (let ((_let_48 (tptp.relation_of2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_14))) (let ((_let_51 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation_of2 C A B)) (= (tptp.relation_dom_as_subset A B C) (tptp.relation_dom C)))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (= _let_23 _let_48))) (let ((_let_54 (_let_3))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (not _let_15))) (let ((_let_57 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_28 _let_56 _let_20 _let_18 _let_16))) (let ((_let_60 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1361 $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.in A (tptp.relation_dom B))) (not (tptp.relation BOUND_VARIABLE_1361)) (not (tptp.function BOUND_VARIABLE_1361)) (= (tptp.apply (tptp.relation_composition B BOUND_VARIABLE_1361) A) (tptp.apply BOUND_VARIABLE_1361 (tptp.apply B A))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 (tptp.powerset (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_57))) (let ((_let_65 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B)))) (tptp.relation C))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (or _let_24 _let_62))) (let ((_let_68 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation_of2_as_subset C A B)) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (and _let_10 _let_12 _let_14))) (let ((_let_71 (_let_10 _let_12 _let_14))) (let ((_let_72 (ASSUME :args (_let_10)))) (let ((_let_73 (ASSUME :args (_let_12)))) (let ((_let_74 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_70)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_73 _let_74) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) (TRANS (SYMM _let_74) (SYMM _let_73)) :args (APPLY_UF tptp.in)) (TRUE_INTRO _let_72))) :args _let_71)) :args _let_71)) :args (true _let_70)) :args ((or _let_22 _let_15 (not _let_12) (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_28 _let_20 _let_18 _let_16 _let_58 _let_56 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_33)) :args ((or _let_27 _let_29))) _let_35 :args (_let_27 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 5)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_33)) :args ((or _let_19 _let_29))) _let_35 :args (_let_19 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 6)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_33)) :args ((or _let_17 _let_29))) _let_35 :args (_let_17 true _let_29)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 7)) _let_35 :args ((not _let_16) true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_57 _let_63 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_24 _let_62 (not _let_67)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation_of2_as_subset C A B) false))))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_62 false _let_23 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) false))))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_57 false _let_62 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING ((tptp.apply (tptp.relation_composition B BOUND_VARIABLE_1361) A)))) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_56 false _let_27 false _let_19 false _let_17 true _let_16 false _let_57 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_14 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_53)) :args ((or _let_24 _let_48 (not _let_53)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_of2_as_subset C A B)))) :args _let_54)) _let_55 :args (_let_53 false _let_3)) :args (_let_48 false _let_23 false _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation_of2 C A B) false))))) :args (_let_51))) _let_52 :args (_let_50 false _let_51)) :args (_let_14 false _let_48 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_26 _let_12 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_33)) :args ((or _let_25 _let_29))) _let_35 :args (_let_25 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 0)) :args ((or _let_21 _let_47))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 4)) _let_35 :args (_let_41 true _let_29)) :args (_let_47 true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 0)) :args ((or _let_40 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_24 _let_42 (not _let_43)))) _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation_of2_as_subset C A B) false))))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_42 false _let_23 false _let_43)) :args (_let_40 false _let_42)) :args (_let_37 true _let_39 false _let_40)) :args (_let_12 false _let_25 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 3)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_10))) :args _let_33)) :args ((or _let_10 _let_29))) _let_35 :args (_let_10 true _let_29)) :args (false true _let_15 false _let_14 false _let_12 false _let_10)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) _let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) _let_8 true true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_dom_as_subset A B C) (tptp.powerset A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))) true true _let_7 (forall ((A $$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) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition B A))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (and _let_6 _let_5 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.relation A) (tptp.function A) (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_6 (and _let_6 _let_5) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C) (tptp.quasi_total C A B)))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A))) (exists ((A $$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 $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C)))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_2 _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.59 )
% 0.21/0.59 % SZS output end Proof for SEU292+1
% 0.21/0.59 % cvc5---1.0.5 exiting
% 0.21/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------