%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU090+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n007.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 16:29:14 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU090+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n007.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 15:25:54 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.b0c0OGtZeF/cvc5---1.0.5_7192.p...
% 0.20/0.61  ------- get file name : TPTP file name is SEU090+1
% 0.20/0.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7192.smt2...
% 0.20/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.61  % SZS status Theorem for SEU090+1
% 0.20/0.61  % SZS output start Proof for SEU090+1
% 0.20/0.61  (
% 0.20/0.61  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B) (tptp.finite C) (tptp.finite D)) (tptp.finite (tptp.cartesian_product4 A B C D))))))) (let ((_let_2 (tptp.relation tptp.empty_set))) (let ((_let_3 (tptp.empty tptp.empty_set))) (let ((_let_4 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B) (tptp.finite C)) (tptp.finite (tptp.cartesian_product3 A B C)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.cartesian_product4 A B C D) (tptp.cartesian_product2 (tptp.cartesian_product3 A B C) D))))) (let ((_let_8 (tptp.cartesian_product4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_9 (tptp.finite _let_8))) (let ((_let_10 (tptp.cartesian_product3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_11 (tptp.cartesian_product2 _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_12 (= _let_8 _let_11))) (let ((_let_13 (tptp.finite _let_11))) (let ((_let_14 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_17 _let_15 _let_9))) (let ((_let_23 (not _let_9))) (let ((_let_24 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.finite A)) (not (tptp.finite B)) (not (tptp.finite C)) (not (tptp.finite D)) (tptp.finite (tptp.cartesian_product4 A B C D)))))) (let ((_let_25 (not _let_22))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (not _let_24))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_27)) _let_26 :args (_let_25 true _let_24)))) (let ((_let_30 (_let_7))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (tptp.finite _let_10))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_15 _let_13))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.finite A)) (not (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or _let_21 _let_19 _let_17 _let_32))) (let ((_let_38 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.finite A)) (not (tptp.finite B)) (not (tptp.finite C)) (tptp.finite (tptp.cartesian_product3 A B C)))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (REFL :args (_let_22)))) (let ((_let_41 (ASSUME :args (_let_13)))) (let ((_let_42 (ASSUME :args (_let_12)))) (let ((_let_43 (ASSUME :args (_let_23)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_41 _let_42 _let_43) :args (_let_23 _let_12 _let_13)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_43)) (CONG (SYMM (SYMM _let_42)) :args (APPLY_UF tptp.finite)) (TRUE_INTRO _let_41))) :args (_let_13 _let_12 _let_23)) :args ((not (and _let_23 _let_12 _let_13)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_9))) (REFL :args ((not _let_12))) (REFL :args ((not _let_13))) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_15 _let_33 _let_13 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 3)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_27)) :args ((or _let_14 _let_22))) _let_29 :args (_let_14 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_21 _let_19 _let_17 _let_32 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_27)) :args ((or _let_20 _let_22))) _let_29 :args (_let_20 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_27)) :args ((or _let_18 _let_22))) _let_29 :args (_let_18 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 2)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_27)) :args ((or _let_16 _let_22))) _let_29 :args (_let_16 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cartesian_product3 A B C)))) :args (_let_38))) _let_39 :args (_let_37 false _let_38)) :args (_let_32 false _let_20 false _let_18 false _let_16 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cartesian_product2 A B)))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_13 false _let_14 false _let_32 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cartesian_product4 A B C D)))) :args _let_30)) _let_31 :args (_let_12 false _let_7)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 4)) _let_29 :args (_let_23 true _let_22)) :args (false false _let_13 false _let_12 true _let_9)) :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 $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$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))))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (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)))))) _let_7 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_3 _let_2 _let_4) _let_6 _let_5 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_3 (and _let_2 _let_4 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_3 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (and _let_3 _let_2) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (not (tptp.empty C))) (not (tptp.empty (tptp.cartesian_product3 A B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (not (tptp.empty C)) (not (tptp.empty D))) (not (tptp.empty (tptp.cartesian_product4 A B C D))))) (not (tptp.empty tptp.positive_rationals)) (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 $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B) (tptp.finite C)) (tptp.finite (tptp.cartesian_product3 A B C)))) _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))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.62  )
% 0.20/0.62  % SZS output end Proof for SEU090+1
% 0.20/0.62  % cvc5---1.0.5 exiting
% 0.20/0.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------