%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 14:39:43 EDT 2023

% Result   : Theorem 0.19s 0.55s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 10:38:54 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8cWjFbhATn/cvc5---1.0.5_1091.p...
% 0.19/0.55  ------- get file name : TPTP file name is SET643+3
% 0.19/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1091.smt2...
% 0.19/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.55  % SZS status Theorem for SET643+3
% 0.19/0.55  % SZS output start Proof for SET643+3
% 0.19/0.55  (
% 0.19/0.55  (let ((_let_1 (not (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.cross_product B C) (tptp.relation_type B C))))))))) (let ((_let_2 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))))) (let ((_let_3 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.cross_product B C) tptp.set_type))))))) (let ((_let_4 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.subset B (tptp.cross_product C D)) (tptp.ilf_type B (tptp.relation_type C D))))))))))) (let ((_let_5 (forall ((B $$unsorted) (BOUND_VARIABLE_1233 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1233 tptp.set_type)) (= (tptp.subset B BOUND_VARIABLE_1233) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1233)))))))) (let ((_let_6 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_7 (tptp.subset _let_6 _let_6))) (let ((_let_8 (tptp.ilf_type _let_6 tptp.set_type))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_9 _let_7))) (let ((_let_11 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_12 (not _let_10))) (let ((_let_13 (tptp.ilf_type _let_6 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_14 (not _let_7))) (let ((_let_15 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.set_type))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_9 _let_18 _let_16 _let_14 _let_13))) (let ((_let_20 (forall ((B $$unsorted) (BOUND_VARIABLE_935 $$unsorted) (BOUND_VARIABLE_933 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_933 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_935 tptp.set_type)) (not (tptp.subset B (tptp.cross_product BOUND_VARIABLE_933 BOUND_VARIABLE_935))) (tptp.ilf_type B (tptp.relation_type BOUND_VARIABLE_933 BOUND_VARIABLE_935)))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (or _let_18 _let_16 _let_8))) (let ((_let_23 (forall ((B $$unsorted) (BOUND_VARIABLE_1063 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1063 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_1063) tptp.set_type))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (or _let_18 _let_16 _let_13))) (let ((_let_26 (forall ((B $$unsorted) (BOUND_VARIABLE_1439 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1439 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_1439) (tptp.relation_type B BOUND_VARIABLE_1439)))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (REFL :args (_let_25)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_29)) :args ((or _let_15 _let_25))) _let_31 :args (_let_15 true _let_25)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_29)) :args ((or _let_17 _let_25))) _let_31 :args (_let_17 true _let_25)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_18 _let_16 _let_8 (not _let_22)))) _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product B BOUND_VARIABLE_1063)))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_8 false _let_17 false _let_15 false _let_22)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_11 :args (_let_6 _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset B BOUND_VARIABLE_1233)))) :args (_let_5)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_10))) :args ((or _let_9 _let_7 _let_12))) _let_35 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_16 _let_13 _let_9 _let_14 (not _let_19)))) _let_34 _let_33 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 2)) _let_31 :args ((not _let_13) true _let_25)) _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ilf_type B (tptp.relation_type BOUND_VARIABLE_933 BOUND_VARIABLE_935)) true))))) :args (_let_20))) _let_21 :args (_let_19 false _let_20)) :args (_let_14 false _let_17 false _let_15 true _let_13 false _let_8 false _let_19)) :args (_let_12 false _let_8 true _let_7)) _let_11 :args (false true _let_10 false _let_5)) :args (_let_4 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member D (tptp.cross_product B C)) (exists ((E $$unsorted)) (and (tptp.ilf_type E tptp.set_type) (exists ((F $$unsorted)) (and (tptp.ilf_type F tptp.set_type) (tptp.member E B) (tptp.member F C) (= D (tptp.ordered_pair E F))))))))))))) _let_3 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (and (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.ilf_type D (tptp.relation_type B C)))) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type B C)) (tptp.ilf_type E (tptp.subset_type (tptp.cross_product B C)))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (exists ((D $$unsorted)) (tptp.ilf_type D (tptp.relation_type C B))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.ordered_pair B C) tptp.set_type))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.subset_type B)) (tptp.ilf_type C (tptp.member_type (tptp.power_set B)))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.subset_type B))))) _let_2 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset B B))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.member B (tptp.power_set C)) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.power_set B))) (=> (tptp.ilf_type B tptp.set_type) (and (not (tptp.empty _let_1)) (tptp.ilf_type _let_1 tptp.set_type))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))) (forall ((B $$unsorted)) (=> (and (not (tptp.empty B)) (tptp.ilf_type B tptp.set_type)) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.member_type B))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (= (tptp.empty B) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (not (tptp.member C B))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (= (tptp.relation_like B) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (=> (tptp.member C B) (exists ((D $$unsorted)) (and (tptp.ilf_type D tptp.set_type) (exists ((E $$unsorted)) (and (tptp.ilf_type E tptp.set_type) (= C (tptp.ordered_pair D E)))))))))))) (forall ((B $$unsorted)) (=> (and (tptp.empty B) (tptp.ilf_type B tptp.set_type)) (tptp.relation_like B))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.subset_type (tptp.cross_product B C))) (tptp.relation_like D))))))) (forall ((B $$unsorted)) (tptp.ilf_type B tptp.set_type)) _let_1 true))))))))))))))))))))))))))))))))))))))
% 0.19/0.55  )
% 0.19/0.55  % SZS output end Proof for SET643+3
% 0.19/0.55  % cvc5---1.0.5 exiting
% 0.19/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------