%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n007.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 10:43:37 EDT 2023

% Result   : Theorem 27.24s 27.62s
% Output   : Proof 27.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri Aug 25 07:38:10 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 27.24/27.62  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.kLW1UFXSP7/cvc5---1.0.5_23838.p...
% 27.24/27.62  ------- get file name : TPTP file name is NUM385+1
% 27.24/27.62  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23838.smt2...
% 27.24/27.62  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.24/27.62  --- Run --no-e-matching --full-saturate-quant at 5...
% 27.24/27.62  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.24/27.62  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.24/27.62  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.24/27.62  % SZS status Theorem for NUM385+1
% 27.24/27.62  % SZS output start Proof for NUM385+1
% 27.24/27.62  (
% 27.24/27.62  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (= (tptp.succ A) (tptp.succ B)) (= A B)))))) (let ((_let_2 (forall ((A $$unsorted)) (tptp.in A (tptp.succ A))))) (let ((_let_3 (tptp.relation tptp.empty_set))) (let ((_let_4 (tptp.empty tptp.empty_set))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.succ A) (tptp.set_union2 A (tptp.singleton A)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))))) (let ((_let_9 (forall ((C $$unsorted)) (= (= C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) (tptp.in C (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))) (let ((_let_10 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_11 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_10))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_13 (= _let_12 _let_11))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= A C))))))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_16 (_let_14))) (let ((_let_17 (not _let_13))) (let ((_let_18 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_19 (or _let_18 _let_11))) (let ((_let_20 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_10))) (let ((_let_21 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_20))) (let ((_let_22 (= _let_21 _let_19))) (let ((_let_23 (forall ((D $$unsorted)) (let ((_let_1 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (= (tptp.in D (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_1)) (or (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) (tptp.in D _let_1))))))) (let ((_let_24 (_let_5))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (_let_23))) (let ((_let_27 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_28 (tptp.succ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_29 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_28))) (let ((_let_30 (tptp.succ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_31 (= _let_30 _let_20))) (let ((_let_32 (= _let_28 _let_30))) (let ((_let_33 (_let_2))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 ((tptp.succ A)))) (let ((_let_36 (_let_7))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 ((tptp.succ A)))) (let ((_let_39 (not _let_32))) (let ((_let_40 (or _let_39 _let_12))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted)) (or (not (= (tptp.succ A) (tptp.succ B))) (= A B))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_43) :args (_let_45))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) _let_43 :args (_let_42 true _let_41)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_32))) :args _let_44)) :args ((or _let_32 _let_40))) _let_46 :args (_let_32 true _let_40)))) (let ((_let_48 (and _let_32 _let_31 _let_29))) (let ((_let_49 (ASSUME :args (_let_29)))) (let ((_let_50 (APPLY_UF tptp.in))) (let ((_let_51 (ASSUME :args (_let_32)))) (let ((_let_52 (SYMM (SYMM _let_51)))) (let ((_let_53 (ASSUME :args (_let_31)))) (let ((_let_54 (not _let_18))) (let ((_let_55 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54))) (let ((_let_58 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (not (tptp.in B A)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_61 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_60))) (let ((_let_62 (or _let_55 _let_61))) (let ((_let_63 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_60))) (let ((_let_64 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_63))) (let ((_let_65 (= _let_64 _let_62))) (let ((_let_66 (forall ((D $$unsorted)) (let ((_let_1 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (= (tptp.in D (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_1)) (or (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) (tptp.in D _let_1))))))) (let ((_let_67 (_let_66))) (let ((_let_68 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_30))) (let ((_let_69 (= _let_28 _let_63))) (let ((_let_70 (and _let_32 _let_69 _let_68))) (let ((_let_71 (ASSUME :args (_let_68)))) (let ((_let_72 (ASSUME :args (_let_69)))) (let ((_let_73 (= _let_12 _let_61))) (let ((_let_74 (not _let_61))) (let ((_let_75 (forall ((C $$unsorted)) (= (= C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) (tptp.in C (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_76 (_let_75))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 1)) _let_46 :args ((not _let_12) true _let_40)))) (let ((_let_78 (_let_9))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_78) :args _let_27) :args _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_13)) :args ((or _let_12 (not _let_11) _let_17))) _let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_11 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_56 _let_54 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_55 _let_61 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_73)) :args ((or _let_12 _let_74 (not _let_73)))) _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in C _let_60)))) :args _let_76))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_60 QUANTIFIERS_INST_CBQI_PROP)) :args _let_16))) _let_15 :args (_let_75 false _let_14)) :args (_let_73 false _let_75)) :args (_let_74 true _let_12 false _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_65)) :args ((or _let_62 (not _let_64) (not _let_65)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_70)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_71 _let_51 _let_72) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)) (TRANS (SYMM _let_72) _let_52) :args _let_50) (TRUE_INTRO _let_71))) :args (_let_68 _let_32 _let_69))) :args (_let_32 _let_69 _let_68))) :args (true _let_70)) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_36)) _let_37 :args (_let_69 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33)) _let_34 :args (_let_68 false _let_2)) :args (_let_64 false _let_32 false _let_69 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D _let_63)))) :args _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_60 _let_63 QUANTIFIERS_INST_CBQI_PROP)) :args _let_24))) _let_25 :args (_let_66 false _let_5)) :args (_let_65 false _let_66)) :args (_let_62 false _let_64 false _let_65)) :args (_let_55 true _let_61 false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in A B) false))))) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_54 false _let_55 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_22)) :args ((or _let_19 (not _let_21) (not _let_22)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_48)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_49 _let_51 _let_53) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (TRANS (SYMM _let_53) (SYMM _let_52)) :args _let_50) (TRUE_INTRO _let_49))) :args (_let_29 _let_32 _let_31))) :args (_let_32 _let_31 _let_29))) :args (true _let_48)) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_38)) :args _let_36)) _let_37 :args (_let_31 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33)) _let_34 :args (_let_29 false _let_2)) :args (_let_21 false _let_32 false _let_31 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args _let_27) :args _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_10 _let_20 QUANTIFIERS_INST_CBQI_PROP)) :args _let_24))) _let_25 :args (_let_23 false _let_5)) :args (_let_22 false _let_23)) :args (_let_19 false _let_21 false _let_22)) :args (_let_11 true _let_18 false _let_19)) :args (_let_17 true _let_12 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_10 QUANTIFIERS_INST_CBQI_PROP)) :args _let_16))) _let_15 :args (_let_9 false _let_14)) :args (false true _let_13 false _let_9)) :args (_let_8 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) _let_7 _let_6 _let_5 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_4 _let_3 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted)) (not (tptp.empty (tptp.succ A)))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_union2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (and _let_4 _let_3) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) _let_2 _let_1 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.24/27.62  )
% 27.24/27.62  % SZS output end Proof for NUM385+1
% 27.24/27.62  % cvc5---1.0.5 exiting
% 27.24/27.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------