%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET919+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n027.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 14:41:00 EDT 2023

% Result   : Theorem 30.08s 30.27s
% Output   : Proof 30.08s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET919+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n027.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 09:10:34 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 30.08/30.27  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.yYDnI6RAKr/cvc5---1.0.5_6151.p...
% 30.08/30.27  ------- get file name : TPTP file name is SET919+1
% 30.08/30.27  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6151.smt2...
% 30.08/30.27  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 30.08/30.27  --- Run --no-e-matching --full-saturate-quant at 5...
% 30.08/30.27  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 30.08/30.27  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 30.08/30.27  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.08/30.27  % SZS status Theorem for SET919+1
% 30.08/30.27  % SZS output start Proof for SET919+1
% 30.08/30.27  (
% 30.08/30.27  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.in A B) (or (and (tptp.in C B) (not (= A C))) (= (tptp.set_intersection2 (tptp.unordered_pair A C) B) (tptp.singleton A)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (and _let_8 _let_7))) (let ((_let_10 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_11 (tptp.set_intersection2 _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (= _let_11 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_13 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_9 _let_12))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.in A B)) (and (tptp.in C B) (not (= A C))) (= (tptp.set_intersection2 (tptp.unordered_pair A C) B) (tptp.singleton A)))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (or))) (let ((_let_20 (not _let_16))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_18) :args (_let_20))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_16))) (REFL :args (_let_17)) :args _let_19)) _let_18 :args (_let_17 true _let_16)))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99))) (let ((_let_24 (or _let_23 _let_22))) (let ((_let_25 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 _let_10))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (forall ((D $$unsorted)) (= (tptp.in D (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (or (= D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (= D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_28 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= A D) (= B D)))))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_10 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_28)))) _let_29 :args (_let_27 false _let_28)))) (let ((_let_31 (_let_27))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_34 (and _let_25 _let_33))) (let ((_let_35 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 _let_11))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (forall ((D $$unsorted)) (let ((_let_1 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (= (tptp.in D (tptp.set_intersection2 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (and (tptp.in D _let_1) (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))) (let ((_let_38 (_let_2))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (_let_37))) (let ((_let_41 (= _let_35 _let_23))) (let ((_let_42 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_10))) (let ((_let_43 (= _let_11 _let_42))) (let ((_let_44 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_42))) (let ((_let_45 (forall ((C $$unsorted)) (= (= C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.in C (tptp.set_intersection2 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_46 (not _let_41))) (let ((_let_47 (= _let_12 _let_45))) (let ((_let_48 (not _let_45))) (let ((_let_49 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= A C))))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_48))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_51)) :args _let_51) (REWRITE :args ((=> _let_48 (not (= (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_35))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_45))) (REFL :args (_let_46)) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_47)) :args ((or _let_12 _let_48 (not _let_47)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_15 2)) _let_21 :args ((not _let_12) true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_11 QUANTIFIERS_INST_ENUM)) :args (_let_49)))) _let_50 :args (_let_47 false _let_49)) :args (_let_48 true _let_12 false _let_47)) :args (_let_46 true _let_45)))) (let ((_let_53 (_let_41))) (let ((_let_54 (_let_5))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10))) (let ((_let_57 (and _let_13 _let_56))) (let ((_let_58 (= _let_44 _let_57))) (let ((_let_59 (forall ((D $$unsorted)) (let ((_let_1 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (= (tptp.in D (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_1)) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.in D _let_1))))))) (let ((_let_60 (_let_59))) (let ((_let_61 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_62 (not _let_23))) (let ((_let_63 (not _let_44))) (let ((_let_64 (not _let_43))) (let ((_let_65 (not _let_35))) (let ((_let_66 (_let_62))) (let ((_let_67 (ASSUME :args (_let_44)))) (let ((_let_68 (APPLY_UF tptp.in))) (let ((_let_69 (ASSUME :args (_let_23)))) (let ((_let_70 (ASSUME :args (_let_43)))) (let ((_let_71 (ASSUME :args (_let_65)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_67 _let_69 _let_70 _let_71) :args (_let_43 _let_44 _let_23 _let_65)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_71)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99)) (SYMM (SYMM _let_70)) :args _let_68) (CONG (SYMM _let_69) (REFL :args (_let_42)) :args _let_68) (TRUE_INTRO _let_67))) :args (_let_44 _let_23 _let_43 _let_65)) :args ((not (and _let_43 _let_44 _let_23 _let_65)) SB_LITERAL))) (CONG (REFL :args (_let_64)) (REFL :args (_let_63)) (REFL :args _let_66) (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_35))) :args _let_19)) :args ((or _let_64 _let_63 _let_35 _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_58)) :args ((or _let_44 (not _let_57) (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_57)) :args ((or _let_14 (not _let_56) _let_57))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 0)) (CONG (REFL :args (_let_15)) (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_19)) :args ((or _let_13 _let_15))) _let_21 :args (_let_13 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args _let_61) :args _let_31))) _let_30 :args (_let_56 false _let_27)) :args (_let_57 false _let_13 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_60) :args _let_61) :args _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_10 _let_42 QUANTIFIERS_INST_CBQI_PROP)) :args _let_38))) _let_39 :args (_let_59 false _let_2)) :args (_let_58 false _let_59)) :args (_let_44 false _let_57 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_54)) _let_55 :args (_let_43 false _let_5)) (REORDERING (CNF_EQUIV_NEG1 :args _let_53) :args ((or _let_35 _let_23 _let_41))) _let_52 :args (_let_35 false _let_44 false _let_43 false _let_23 true _let_41)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or _let_65 _let_34 (not _let_36)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_40) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D _let_11)))) :args _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_11 QUANTIFIERS_INST_CBQI_PROP)) :args _let_38))) _let_39 :args (_let_37 false _let_2)) :args (_let_36 false _let_37)) :args (_let_34 false _let_35 false _let_36)))) (let ((_let_74 (not _let_34))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_53) _let_52 _let_72 :args (_let_62 true _let_41 false _let_35)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_22 (not _let_24)))) _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or (not _let_25) _let_24 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_25 _let_74))) _let_73 :args (_let_25 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 QUANTIFIERS_INST_CBQI_PROP)) :args _let_31))) _let_30 :args (_let_26 false _let_27)) :args (_let_24 false _let_25 false _let_26)) :args (_let_22 true _let_23 false _let_24)))) (let ((_let_77 (not _let_22))) (let ((_let_78 (and _let_62 _let_22))) (let ((_let_79 (_let_62 _let_22))) (let ((_let_80 (ASSUME :args _let_66))) (let ((_let_81 (ASSUME :args (_let_22)))) (let ((_let_82 (SYMM (SYMM _let_81)))) (let ((_let_83 (and _let_33 _let_22))) (let ((_let_84 (_let_33 _let_22))) (let ((_let_85 (ASSUME :args (_let_33)))) (let ((_let_86 (not _let_8))) (let ((_let_87 (_let_9))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_87) (CONG (REFL :args _let_87) (REFL :args (_let_86)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_19)) :args ((or _let_6 _let_9 _let_86))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_83)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_85 _let_81) (SCOPE (TRUE_ELIM (TRANS (CONG _let_82 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args _let_68) (TRUE_INTRO _let_85))) :args _let_84)) :args _let_84)) :args (true _let_83)) :args ((or _let_8 (not _let_33) _let_77))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 1)) :args ((or _let_33 _let_74))) _let_73 :args (_let_33 false _let_34)) _let_76 :args (_let_8 false _let_33 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_80 _let_81) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_82 :args (=)) (FALSE_INTRO _let_80))) :args _let_79)) :args _let_79)) :args (true _let_78)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_23))) (REFL :args (_let_77)) (REFL :args (_let_7)) :args _let_19)) :args ((or _let_7 _let_23 _let_77))) _let_75 _let_76 :args (_let_7 true _let_23 false _let_22)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_15 1)) _let_21 :args ((not _let_9) true _let_15)) :args (false false _let_8 true _let_6 true _let_9)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_5 _let_4 _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 30.08/30.27  )
% 30.08/30.27  % SZS output end Proof for SET919+1
% 30.08/30.27  % cvc5---1.0.5 exiting
% 30.08/30.27  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------