%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n021.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 14:39:52 EDT 2023

% Result   : Theorem 0.22s 0.55s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET676+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat Aug 26 12:14:11 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.55  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.tPM1Jy1bJF/cvc5---1.0.5_17175.p...
% 0.22/0.55  ------- get file name : TPTP file name is SET676+3
% 0.22/0.55  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17175.smt2...
% 0.22/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.55  % SZS status Theorem for SET676+3
% 0.22/0.55  % SZS output start Proof for SET676+3
% 0.22/0.55  (
% 0.22/0.55  (let ((_let_1 (not (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.ilf_type (tptp.cross_product B B) (tptp.identity_relation_of_type B))))))) (let ((_let_2 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.identity_relation_of_type B)) (tptp.ilf_type C (tptp.relation_type B B))))))))) (let ((_let_3 (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.cross_product B C) (tptp.relation_type B C)))))))) (let ((_let_5 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.set_type))) (let ((_let_6 (tptp.cross_product SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_7 (tptp.ilf_type _let_6 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_8 (tptp.ilf_type _let_6 (tptp.identity_relation_of_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_9 (= _let_8 _let_7))) (let ((_let_10 (tptp.ilf_type _let_6 tptp.set_type))) (let ((_let_11 (not _let_10))) (let ((_let_12 (not _let_5))) (let ((_let_13 (or _let_12 _let_11 _let_9))) (let ((_let_14 (or _let_12 _let_8))) (let ((_let_15 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.ilf_type (tptp.cross_product B B) (tptp.identity_relation_of_type B)))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (or))) (let ((_let_19 (not _let_15))) (let ((_let_20 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_17) :args (_let_19))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) (REFL :args (_let_16)) :args _let_18)) _let_17 :args (_let_16 true _let_15)))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG (REFL :args (_let_14)) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_5))) :args _let_18)) :args ((or _let_5 _let_14))) _let_20 :args (_let_5 true _let_14)))) (let ((_let_22 (forall ((B $$unsorted) (BOUND_VARIABLE_1043 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1043 tptp.set_type)) (= (tptp.ilf_type BOUND_VARIABLE_1043 (tptp.identity_relation_of_type B)) (tptp.ilf_type BOUND_VARIABLE_1043 (tptp.relation_type B B))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (or _let_12 _let_12 _let_10))) (let ((_let_25 (forall ((B $$unsorted) (BOUND_VARIABLE_1022 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1022 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_1022) tptp.set_type))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (not _let_9))) (let ((_let_28 (or _let_12 _let_12 _let_7))) (let ((_let_29 (forall ((B $$unsorted) (BOUND_VARIABLE_898 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_898 tptp.set_type)) (tptp.ilf_type (tptp.cross_product B BOUND_VARIABLE_898) (tptp.relation_type B BOUND_VARIABLE_898)))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_12 _let_11 _let_9 (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_9)) :args ((or _let_8 (not _let_7) _let_27))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 1)) _let_20 :args ((not _let_8) true _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_28))) :args ((or _let_12 _let_7 (not _let_28)))) _let_21 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product B BOUND_VARIABLE_898)))) :args (_let_29))) _let_30 :args (_let_28 false _let_29)) :args (_let_7 false _let_5 false _let_28)) :args (_let_27 true _let_8 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_24))) :args ((or _let_12 _let_10 (not _let_24)))) _let_21 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cross_product B BOUND_VARIABLE_1022)))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (_let_10 false _let_5 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_6 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type BOUND_VARIABLE_1043 (tptp.identity_relation_of_type B))))) :args (_let_22))) _let_23 :args (_let_13 false _let_22)) _let_21 :args (false true _let_9 false _let_10 false _let_13 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 $$unsorted)) (and (tptp.ilf_type F tptp.set_type) (tptp.member E B) (tptp.member F C) (= D (tptp.ordered_pair E F))))))))))))) _let_3 _let_2 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.identity_relation_of_type B))))) (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (and (forall ((D $$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 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))))) (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)))))))))))))))))))))))))))))))))
% 0.22/0.56  )
% 0.22/0.56  % SZS output end Proof for SET676+3
% 0.22/0.56  % cvc5---1.0.5 exiting
% 0.22/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------