%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n012.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 14:39:53 EDT 2023

% Result   : Theorem 25.77s 26.09s
% Output   : Proof 25.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 12:55:10 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 25.77/26.09  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.MPUWS98ajI/cvc5---1.0.5_23735.p...
% 25.77/26.09  ------- get file name : TPTP file name is SET679+3
% 25.77/26.09  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23735.smt2...
% 25.77/26.09  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.77/26.09  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.77/26.09  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.77/26.09  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.77/26.09  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.77/26.09  % SZS status Theorem for SET679+3
% 25.77/26.09  % SZS output start Proof for SET679+3
% 25.77/26.09  (
% 25.77/26.09  (let ((_let_1 (not (forall ((B $$unsorted)) (=> (and (not (tptp.empty B)) (tptp.ilf_type B tptp.set_type)) (tptp.not_equal (tptp.identity_relation_of B) tptp.empty_set)))))) (let ((_let_2 (forall ((B $$unsorted)) (tptp.ilf_type B tptp.set_type)))) (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.ordered_pair B C) tptp.set_type))))))) (let ((_let_4 (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))))))))) (let ((_let_5 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.not_equal B C) (not (= B C))))))))) (let ((_let_6 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (not (tptp.member B tptp.empty_set)))))) (let ((_let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.member C B) (tptp.member (tptp.ordered_pair C C) (tptp.identity_relation_of B))))))))) (let ((_let_8 (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (= tptp.empty_set _let_8))) (let ((_let_10 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_11 (tptp.member _let_10 tptp.empty_set))) (let ((_let_12 (tptp.member _let_10 _let_8))) (let ((_let_13 (not _let_9))) (let ((_let_14 (tptp.not_equal _let_8 tptp.empty_set))) (let ((_let_15 (= _let_14 _let_13))) (let ((_let_16 (tptp.ilf_type tptp.empty_set tptp.set_type))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.ilf_type _let_8 tptp.set_type))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_15))) (let ((_let_21 (forall ((B $$unsorted) (BOUND_VARIABLE_1003 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1003 tptp.set_type)) (= (tptp.not_equal B BOUND_VARIABLE_1003) (not (= B BOUND_VARIABLE_1003))))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (_let_2))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_28 (or _let_27 _let_26 _let_14))) (let ((_let_29 (forall ((B $$unsorted)) (or (tptp.empty B) (not (tptp.ilf_type B tptp.set_type)) (tptp.not_equal (tptp.identity_relation_of B) tptp.empty_set))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) _let_31 :args (_let_30 true _let_29)))) (let ((_let_35 (not _let_15))) (let ((_let_36 (not _let_11))) (let ((_let_37 (tptp.ilf_type _let_10 tptp.set_type))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36))) (let ((_let_40 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.member B tptp.empty_set)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.set_type))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_43 _let_37))) (let ((_let_45 (forall ((B $$unsorted) (BOUND_VARIABLE_1036 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1036 tptp.set_type)) (tptp.ilf_type (tptp.ordered_pair B BOUND_VARIABLE_1036) tptp.set_type))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_43 _let_48))) (let ((_let_50 (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (not (tptp.member C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (= _let_27 _let_50))) (let ((_let_53 (not _let_50))) (let ((_let_54 (or _let_26 _let_52))) (let ((_let_55 (forall ((B $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (= (tptp.empty B) (forall ((C $$unsorted)) (or (not (tptp.ilf_type C tptp.set_type)) (not (tptp.member C B))))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_32)) :args ((or _let_25 _let_28))) _let_34 :args (_let_25 true _let_28)))) (let ((_let_58 (_let_53))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_50))) (REFL :args (_let_51)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_52)) :args ((or _let_27 _let_53 (not _let_52)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 0)) _let_34 :args ((not _let_27) true _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_26 _let_52 (not _let_54)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ilf_type B tptp.set_type) false))))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_52 false _let_25 false _let_54)) :args (_let_53 true _let_27 false _let_52)) :args (_let_51 true _let_50)))) (let ((_let_60 (REFL :args (_let_49)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 0)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_32)) :args ((or _let_42 _let_49))) _let_59 :args (_let_42 true _let_49)))) (let ((_let_62 (= _let_47 _let_12))) (let ((_let_63 (or _let_26 _let_43 _let_62))) (let ((_let_64 (forall ((B $$unsorted) (BOUND_VARIABLE_892 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_892 tptp.set_type)) (= (tptp.member BOUND_VARIABLE_892 B) (tptp.member (tptp.ordered_pair BOUND_VARIABLE_892 BOUND_VARIABLE_892) (tptp.identity_relation_of B))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (ASSUME :args (_let_12)))) (let ((_let_67 (ASSUME :args (_let_9)))) (let ((_let_68 (ASSUME :args (_let_36)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_66 _let_67 _let_68) :args (_let_9 _let_36 _let_12)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_68)) (CONG (REFL :args (_let_10)) (SYMM (SYMM _let_67)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_66))) :args (_let_12 _let_9 _let_36)) :args ((not (and _let_9 _let_36 _let_12)) SB_LITERAL))) (CONG (REFL :args (_let_13)) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_11))) (REFL :args ((not _let_12))) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or _let_48 _let_12 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_32)) :args ((or _let_47 _let_49))) _let_59 :args (_let_47 true _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_26 _let_43 _let_62 (not _let_63)))) _let_57 _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_64))) _let_65 :args (_let_63 false _let_64)) :args (_let_62 false _let_25 false _let_42 false _let_63)) :args (_let_12 false _let_47 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_36 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_44))) :args ((or _let_43 _let_37 (not _let_44)))) _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair B BOUND_VARIABLE_1036)))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_37 false _let_42 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_36 false _let_37 false _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_15)) (CONG (REFL :args (_let_35)) (REFL :args (_let_14)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_9))) :args _let_32)) :args ((or _let_14 _let_9 _let_35))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 2)) _let_34 :args ((not _let_14) true _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_17 _let_15 (not _let_20)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_23)) _let_24 :args (_let_18 false _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (tptp.empty_set QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_23)) _let_24 :args (_let_16 false _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 :args (_let_8 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.not_equal B BOUND_VARIABLE_1003)))) :args (_let_21)))) _let_22 :args (_let_20 false _let_21)) :args (_let_15 false _let_18 false _let_16 false _let_20)) :args (_let_9 true _let_14 false _let_15)) :args (false false _let_12 true _let_11 false _let_9)) :args (_let_7 _let_6 (tptp.empty tptp.empty_set) (tptp.type tptp.empty_set tptp.set_type) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member (tptp.ordered_pair C D) (tptp.identity_relation_of B)) (and (tptp.member C B) (= C D))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.ilf_type (tptp.identity_relation_of B) tptp.binary_relation_type))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (= B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (= (tptp.member D B) (tptp.member D C))))))))) _let_5 _let_4 _let_3 (forall ((B $$unsorted)) (let ((_let_1 (tptp.ilf_type B tptp.set_type))) (=> _let_1 (= (tptp.ilf_type B tptp.binary_relation_type) (and (tptp.relation_like B) _let_1))))) (exists ((B $$unsorted)) (tptp.ilf_type B tptp.binary_relation_type)) (forall ((B $$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) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.cross_product B C) tptp.set_type))))) (forall ((B $$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 $$unsorted)) (tptp.ilf_type C (tptp.subset_type B))))) (forall ((B $$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))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.77/26.09  )
% 25.77/26.09  % SZS output end Proof for SET679+3
% 25.77/26.09  % cvc5---1.0.5 exiting
% 25.77/26.10  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------