%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% 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 16:29:15 EDT 2023

% Result   : Theorem 0.69s 0.89s
% Output   : Proof 0.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n022.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 19:07:56 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.69/0.89  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.oS3NqVQ8hL/cvc5---1.0.5_14571.p...
% 0.69/0.89  ------- get file name : TPTP file name is SEU094+1
% 0.69/0.89  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14571.smt2...
% 0.69/0.89  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.69/0.89  % SZS status Theorem for SEU094+1
% 0.69/0.89  % SZS output start Proof for SEU094+1
% 0.69/0.89  (
% 0.69/0.89  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_3 (not (forall ((A $$unsorted)) (= (and (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.finite B)))) (tptp.finite (tptp.union A))))))) (let ((_let_4 (forall ((A $$unsorted)) (= (tptp.finite A) (tptp.finite (tptp.powerset A)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.subset A B) (tptp.finite B)) (tptp.finite A))))) (let ((_let_6 (forall ((A $$unsorted)) (tptp.subset A (tptp.powerset (tptp.union A)))))) (let ((_let_7 (forall ((A $$unsorted)) (=> (and (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.finite B)))) (tptp.finite (tptp.union A)))))) (let ((_let_8 (tptp.relation tptp.empty_set))) (let ((_let_9 (tptp.empty tptp.empty_set))) (let ((_let_10 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))))) (let ((_let_12 (forall ((A $$unsorted) (BOUND_VARIABLE_1148 $$unsorted)) (or (not (tptp.finite A)) (not (tptp.element BOUND_VARIABLE_1148 (tptp.powerset A))) (tptp.finite BOUND_VARIABLE_1148))))) (let ((_let_13 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_14 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_15 (tptp.powerset _let_14))) (let ((_let_16 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 (tptp.powerset _let_15)))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.finite _let_15))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_13))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_15))) (let ((_let_24 (= _let_23 _let_16))) (let ((_let_25 (_let_2))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (_let_6))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 (tptp.finite _let_14))) (let ((_let_30 (= _let_29 _let_18))) (let ((_let_31 (_let_4))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 (forall ((B $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)) (tptp.finite B))))) (let ((_let_34 (and _let_13 _let_33))) (let ((_let_35 (= _let_29 _let_34))) (let ((_let_36 (forall ((B $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)) (tptp.finite B))))) (let ((_let_37 (not _let_36))) (let ((_let_38 (not _let_13))) (let ((_let_39 (or _let_38 _let_37 _let_29))) (let ((_let_40 (forall ((A $$unsorted)) (= (tptp.finite (tptp.union A)) (and (tptp.finite A) (forall ((B $$unsorted)) (or (not (tptp.in B A)) (tptp.finite B)))))))) (let ((_let_41 (not _let_35))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (or))) (let ((_let_44 (not _let_40))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_42) :args (_let_44))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_40))) (REFL :args (_let_41)) :args _let_43)) _let_42 :args (_let_41 true _let_40)))) (let ((_let_46 (_let_35))) (let ((_let_47 (not _let_34))) (let ((_let_48 (forall ((A $$unsorted)) (or (not (tptp.finite A)) (not (forall ((B $$unsorted)) (or (not (tptp.in B A)) (tptp.finite B)))) (tptp.finite (tptp.union A)))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_33 (= B B)))) (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_29 _let_38 _let_37 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union A)))) :args (_let_48))) _let_49 :args (_let_39 false _let_48)) (REORDERING (CNF_AND_POS :args (_let_34 1)) :args ((or _let_33 _let_47))) (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_13 _let_47))) (REORDERING (CNF_EQUIV_NEG1 :args _let_46) :args ((or _let_29 _let_34 _let_35))) _let_45 :args (_let_29 true _let_36 false _let_39 false _let_33 false _let_13 false _let_34 true _let_35)))) (let ((_let_51 (not _let_29))) (let ((_let_52 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40))) (let ((_let_53 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52))) (let ((_let_56 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 _let_14))) (let ((_let_57 (or _let_54 _let_56))) (let ((_let_58 (not _let_56))) (let ((_let_59 (or _let_58 _let_51 _let_52))) (let ((_let_60 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.subset A (tptp.union B)))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.finite B)) (tptp.finite A))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (not _let_33))) (let ((_let_65 (_let_64))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1148 (tptp.powerset A)) false))))) :args (_let_12))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_13 _let_19 _let_17 _let_22))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_34)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_46) _let_45 _let_50 :args (_let_47 true _let_35 false _let_29)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_33))) (REFL :args ((not _let_55))) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_51 _let_52 _let_58 (not _let_59)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset A B) false))))) :args (_let_62))) _let_63 :args (_let_59 false _let_62)) _let_50 (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_54 _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in A B) false))))) :args (_let_60))) _let_61 :args (_let_57 false _let_60)) (CNF_OR_NEG :args (_let_55 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 0)) (CONG (REFL :args (_let_55)) (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_43)) :args ((or _let_53 _let_55))) :args (_let_55 false _let_59 false _let_29 false _let_56 false _let_57 true _let_52 false _let_53)) :args (_let_33 false _let_55)) :args (_let_38 true _let_34 false _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or _let_51 _let_18 (not _let_30)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.powerset A)))) :args _let_31)) _let_32 :args (_let_30 false _let_4)) :args (_let_18 false _let_29 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_24)) :args ((or (not _let_23) _let_16 (not _let_24)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union A)))) :args _let_27)) _let_28 :args (_let_23 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args _let_25))) _let_26 :args (_let_24 false _let_2)) :args (_let_16 false _let_23 false _let_24)) :args (_let_22 true _let_13 false _let_18 false _let_16)) _let_21 :args (false true _let_20 false _let_12)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B)))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.ordinal A))) (=> (and (tptp.empty A) _let_1) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) _let_1 (tptp.natural A))))) _let_11 (forall ((A $$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)))))) (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.ordinal A))) (=> (tptp.element A tptp.positive_rationals) (=> _let_1 (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) _let_1 (tptp.natural A)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_9 _let_8 _let_10) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_9 (and _let_8 _let_10 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_9 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.union A))) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1))))) (and _let_9 _let_8) (not (tptp.empty tptp.positive_rationals)) _let_7 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.function_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.being_limit_ordinal A))) (exists ((A $$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.element A tptp.positive_rationals) (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B) (tptp.natural B) (tptp.finite B)))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A) (tptp.ordinal_yielding A))) (exists ((A $$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.element A tptp.positive_rationals) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal 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))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_6 _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_2 (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)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.69/0.90  )
% 0.69/0.90  % SZS output end Proof for SEU094+1
% 0.69/0.90  % cvc5---1.0.5 exiting
% 0.69/0.90  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------