TSTP Solution File: SET668+3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET668+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 14:39:49 EDT 2023
% Result : Theorem 31.94s 32.25s
% Output : Proof 31.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET668+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n010.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 : Sat Aug 26 11:46:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 31.94/32.25 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.gC1K5ga1gk/cvc5---1.0.5_5066.p...
% 31.94/32.25 ------- get file name : TPTP file name is SET668+3
% 31.94/32.25 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5066.smt2...
% 31.94/32.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.94/32.25 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.94/32.25 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.94/32.25 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.94/32.25 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.94/32.25 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.94/32.25 % SZS status Theorem for SET668+3
% 31.94/32.25 % SZS output start Proof for SET668+3
% 31.94/32.25 (
% 31.94/32.25 (let ((_let_1 (not (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type C B)) (=> (tptp.subset (tptp.identity_relation_of C) D) (and (= C (tptp.domain C B D)) (tptp.subset C (tptp.range C B D))))))))))))) (let ((_let_2 (forall ((B $$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) (forall ((D $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (tptp.ilf_type (tptp.domain B C D) (tptp.subset_type B)))))))))) (let ((_let_4 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (and (not (tptp.empty C)) (tptp.ilf_type C tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type C)) (tptp.member B C)))))))) (let ((_let_5 (forall ((B $$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))))))) (let ((_let_6 (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 $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (=> (tptp.member D B) (tptp.member D C))))))))))) (let ((_let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (tptp.ilf_type C (tptp.subset_type B)) (tptp.ilf_type C (tptp.member_type (tptp.power_set B)))))))))) (let ((_let_8 (forall ((B $$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_9 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (forall ((E $$unsorted)) (=> (tptp.ilf_type E (tptp.relation_type B C)) (=> (tptp.subset (tptp.identity_relation_of D) E) (and (tptp.subset D (tptp.domain B C E)) (tptp.subset D (tptp.range B C E)))))))))))))) (let ((_let_10 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (=> (and (tptp.subset B C) (tptp.subset C B)) (= B C)))))))) (let ((_let_11 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.set_type))) (let ((_let_12 (tptp.domain SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (tptp.ilf_type _let_12 tptp.set_type))) (let ((_let_14 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.domain SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_15 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (tptp.member _let_12 _let_15))) (let ((_let_17 (= _let_16 _let_14))) (let ((_let_18 (not _let_11))) (let ((_let_19 (not _let_13))) (let ((_let_20 (or _let_19 _let_18 _let_17))) (let ((_let_21 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.range SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_12))) (let ((_let_23 (and _let_22 _let_21))) (let ((_let_24 (tptp.subset (tptp.identity_relation_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.relation_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.ilf_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.set_type))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_18 _let_27 _let_25 _let_23))) (let ((_let_31 (forall ((B $$unsorted) (BOUND_VARIABLE_1943 $$unsorted) (BOUND_VARIABLE_1941 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1941 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1943 (tptp.relation_type BOUND_VARIABLE_1941 B))) (not (tptp.subset (tptp.identity_relation_of BOUND_VARIABLE_1941) BOUND_VARIABLE_1943)) (and (= BOUND_VARIABLE_1941 (tptp.domain BOUND_VARIABLE_1941 B BOUND_VARIABLE_1943)) (tptp.subset BOUND_VARIABLE_1941 (tptp.range BOUND_VARIABLE_1941 B BOUND_VARIABLE_1943))))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (or))) (let ((_let_35 (not _let_31))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_31))) (REFL :args (_let_32)) :args _let_34)) _let_33 :args (_let_32 true _let_31)))) (let ((_let_37 (REFL :args (_let_30)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_11))) :args _let_34)) :args ((or _let_11 _let_30))) _let_36 :args (_let_11 true _let_30)))) (let ((_let_39 (_let_2))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_39)) _let_40 :args (_let_13 false _let_2)))) (let ((_let_42 (forall ((B $$unsorted) (BOUND_VARIABLE_1570 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1570 tptp.set_type)) (= (tptp.member B (tptp.power_set BOUND_VARIABLE_1570)) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1570)))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (not _let_17))) (let ((_let_45 (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D (tptp.domain SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_46 (tptp.subset _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_47 (= _let_46 _let_45))) (let ((_let_48 (not _let_45))) (let ((_let_49 (or _let_19 _let_18 _let_47))) (let ((_let_50 (forall ((B $$unsorted) (BOUND_VARIABLE_1366 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1366 tptp.set_type)) (= (tptp.subset B BOUND_VARIABLE_1366) (forall ((D $$unsorted)) (or (not (tptp.ilf_type D tptp.set_type)) (not (tptp.member D B)) (tptp.member D BOUND_VARIABLE_1366)))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (not _let_46))) (let ((_let_53 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_12))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_18 _let_19 _let_54 _let_52 _let_22))) (let ((_let_56 (forall ((B $$unsorted) (BOUND_VARIABLE_1105 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1105 tptp.set_type)) (not (tptp.subset B BOUND_VARIABLE_1105)) (not (tptp.subset BOUND_VARIABLE_1105 B)) (= B BOUND_VARIABLE_1105))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (and _let_53 _let_21))) (let ((_let_59 (or _let_18 _let_29 _let_18 _let_27 _let_25 _let_58))) (let ((_let_60 (forall ((B $$unsorted) (BOUND_VARIABLE_1184 $$unsorted) (BOUND_VARIABLE_1182 $$unsorted) (BOUND_VARIABLE_1180 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1180 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1184 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1182 (tptp.relation_type B BOUND_VARIABLE_1180))) (not (tptp.subset (tptp.identity_relation_of BOUND_VARIABLE_1184) BOUND_VARIABLE_1182)) (and (tptp.subset BOUND_VARIABLE_1184 (tptp.domain B BOUND_VARIABLE_1180 BOUND_VARIABLE_1182)) (tptp.subset BOUND_VARIABLE_1184 (tptp.range B BOUND_VARIABLE_1180 BOUND_VARIABLE_1182))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 2)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_34)) :args ((or _let_26 _let_30))) _let_36 :args (_let_26 true _let_30)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_34)) :args ((or _let_28 _let_30))) _let_36 :args (_let_28 true _let_30)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_59))) :args ((or _let_29 _let_18 _let_27 _let_25 _let_58 (not _let_59)))) _let_63 _let_38 _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 3)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_34)) :args ((or _let_24 _let_30))) _let_36 :args (_let_24 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.subset BOUND_VARIABLE_1184 (tptp.range B BOUND_VARIABLE_1180 BOUND_VARIABLE_1182))))) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_58 false _let_28 false _let_11 false _let_26 false _let_24 false _let_59)))) (let ((_let_65 (not _let_58))) (let ((_let_66 (tptp.ilf_type _let_12 (tptp.member_type _let_15)))) (let ((_let_67 (= _let_66 _let_16))) (let ((_let_68 (tptp.ilf_type _let_15 tptp.set_type))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.empty _let_15))) (let ((_let_71 (or _let_19 _let_70 _let_69 _let_67))) (let ((_let_72 (forall ((B $$unsorted) (BOUND_VARIABLE_1601 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (tptp.empty BOUND_VARIABLE_1601) (not (tptp.ilf_type BOUND_VARIABLE_1601 tptp.set_type)) (= (tptp.ilf_type B (tptp.member_type BOUND_VARIABLE_1601)) (tptp.member B BOUND_VARIABLE_1601)))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (not _let_70))) (let ((_let_75 (and _let_74 _let_68))) (let ((_let_76 (or _let_18 _let_75))) (let ((_let_77 (forall ((B $$unsorted)) (let ((_let_1 (tptp.power_set B))) (or (not (tptp.ilf_type B tptp.set_type)) (and (not (tptp.empty _let_1)) (tptp.ilf_type _let_1 tptp.set_type))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_18 _let_75 (not _let_76)))) _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_75 false _let_11 false _let_76)))) (let ((_let_80 (not _let_75))) (let ((_let_81 (tptp.ilf_type _let_12 (tptp.subset_type SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_82 (= _let_81 _let_66))) (let ((_let_83 (or _let_18 _let_19 _let_82))) (let ((_let_84 (forall ((B $$unsorted) (BOUND_VARIABLE_1523 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1523 tptp.set_type)) (= (tptp.ilf_type BOUND_VARIABLE_1523 (tptp.subset_type B)) (tptp.ilf_type BOUND_VARIABLE_1523 (tptp.member_type (tptp.power_set B)))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (or _let_18 _let_29 _let_27 _let_81))) (let ((_let_87 (forall ((B $$unsorted) (BOUND_VARIABLE_1804 $$unsorted) (BOUND_VARIABLE_1802 $$unsorted)) (or (not (tptp.ilf_type B tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1802 tptp.set_type)) (not (tptp.ilf_type BOUND_VARIABLE_1804 (tptp.relation_type B BOUND_VARIABLE_1802))) (tptp.ilf_type (tptp.domain B BOUND_VARIABLE_1802 BOUND_VARIABLE_1804) (tptp.subset_type B)))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_18 _let_19 _let_17 (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or (not _let_16) _let_14 _let_44))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_67)) :args ((or (not _let_66) _let_16 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_82)) :args ((or (not _let_81) _let_66 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_29 _let_18 _let_27 _let_81 (not _let_86)))) _let_63 _let_38 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ilf_type BOUND_VARIABLE_1804 (tptp.relation_type B BOUND_VARIABLE_1802)) false))))) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_81 false _let_28 false _let_11 false _let_26 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_18 _let_19 _let_82 (not _let_83)))) _let_38 _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_12 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type BOUND_VARIABLE_1523 (tptp.subset_type B))))) :args (_let_84))) _let_85 :args (_let_83 false _let_84)) :args (_let_82 false _let_11 false _let_13 false _let_83)) :args (_let_66 false _let_81 false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_19 _let_70 _let_69 _let_67 (not _let_71)))) _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_74 _let_80))) _let_79 :args (_let_74 false _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 1)) :args ((or _let_68 _let_80))) _let_79 :args (_let_68 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_12 _let_15 QUANTIFIERS_INST_E_MATCHING ((tptp.ilf_type B (tptp.member_type BOUND_VARIABLE_1601))))) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_67 false _let_13 true _let_70 false _let_68 false _let_71)) :args (_let_16 false _let_66 false _let_67)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_45 (= D D)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_47)) :args ((or _let_46 _let_48 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_18 _let_22 _let_54 _let_19 _let_52 (not _let_55)))) _let_38 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_23)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 4)) _let_36 :args ((not _let_23) true _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 1)) :args ((or _let_21 _let_65))) _let_64 :args (_let_21 false _let_58)) :args ((not _let_22) true _let_23 false _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 0)) :args ((or _let_53 _let_65))) _let_64 :args (_let_53 false _let_58)) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset B BOUND_VARIABLE_1105) false))))) :args (_let_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_52 false _let_11 true _let_22 false _let_53 false _let_13 false _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_18 _let_19 _let_47 (not _let_49)))) _let_38 _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset B BOUND_VARIABLE_1366)))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_47 false _let_11 false _let_13 false _let_49)) :args (_let_48 true _let_46 false _let_47)) :args ((not _let_14) true _let_45)) :args (_let_44 false _let_16 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_42))) _let_43 :args (_let_20 false _let_42)) _let_41 _let_38 :args (false true _let_17 false _let_20 false _let_13 false _let_11)) :args (_let_10 _let_9 (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 $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (and (forall ((D $$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))))))) _let_8 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.binary_relation_type) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.ilf_type D tptp.set_type) (forall ((E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (=> (tptp.ilf_type E tptp.set_type) (=> (tptp.member _let_1 B) (tptp.member _let_1 C)))))))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (= (= B C) (and (tptp.subset B C) (tptp.subset C B))))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (tptp.ilf_type (tptp.domain_of B) tptp.set_type))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (tptp.ilf_type (tptp.cross_product B C) tptp.set_type))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (tptp.ilf_type (tptp.range_of B) 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 (tptp.ordered_pair B C) tptp.set_type))))) (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)) _let_7 (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (exists ((C $$unsorted)) (tptp.ilf_type C (tptp.subset_type B))))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (tptp.subset B B))) (forall ((B $$unsorted)) (=> (tptp.ilf_type B tptp.binary_relation_type) (tptp.subset B B))) _let_6 _let_5 _let_4 (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 $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (= (tptp.relation_like B) (forall ((C $$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 $$unsorted)) (=> (tptp.ilf_type B tptp.set_type) (forall ((C $$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) (= (tptp.empty B) (forall ((C $$unsorted)) (=> (tptp.ilf_type C tptp.set_type) (not (tptp.member C B))))))) (forall ((B $$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 $$unsorted)) (=> (tptp.ilf_type D (tptp.relation_type B C)) (= (tptp.domain B C D) (tptp.domain_of D)))))))) _let_3 (forall ((B $$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.relation_type B C)) (= (tptp.range B C D) (tptp.range_of D)))))))) (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.relation_type B C)) (tptp.ilf_type (tptp.range B C D) (tptp.subset_type C)))))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.94/32.25 )
% 31.94/32.25 % SZS output end Proof for SET668+3
% 31.94/32.25 % cvc5---1.0.5 exiting
% 31.94/32.25 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------