%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n003.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 10:43:39 EDT 2023

% Result   : Theorem 0.21s 0.56s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM394+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n003.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   : Fri Aug 25 16:43:53 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.56  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.HrClYouLHM/cvc5---1.0.5_1700.p...
% 0.21/0.56  ------- get file name : TPTP file name is NUM394+1
% 0.21/0.56  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1700.smt2...
% 0.21/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.56  % SZS status Theorem for NUM394+1
% 0.21/0.56  % SZS output start Proof for NUM394+1
% 0.21/0.56  (
% 0.21/0.56  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (or (tptp.ordinal_subset A B) (tptp.in B A))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (and (not (tptp.in A B)) (not (= A B)) (not (tptp.in B A)))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))))) (let ((_let_4 (tptp.relation tptp.empty_set))) (let ((_let_5 (tptp.empty tptp.empty_set))) (let ((_let_6 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (or (tptp.ordinal_subset A B) (tptp.ordinal_subset B A)))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))) (let ((_let_9 (forall ((B $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) (tptp.subset B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_10 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_11 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10))) (let ((_let_14 (tptp.epsilon_transitive SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_15 (= _let_14 _let_9))) (let ((_let_16 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (or (not (tptp.in B A)) (tptp.subset B A))))))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (and _let_14 (tptp.epsilon_connected SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_19 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18))) (let ((_let_22 (forall ((A $$unsorted)) (or (not (tptp.ordinal A)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_25 (tptp.ordinal_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_26 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_20 _let_25 _let_24))) (let ((_let_29 (forall ((A $$unsorted) (BOUND_VARIABLE_1066 $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal BOUND_VARIABLE_1066)) (tptp.ordinal_subset A BOUND_VARIABLE_1066) (tptp.in BOUND_VARIABLE_1066 A))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) _let_31 :args (_let_30 true _let_29)))) (let ((_let_35 (REFL :args (_let_28)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_32)) :args ((or _let_19 _let_28))) _let_34 :args (_let_19 true _let_28)))) (let ((_let_37 (not _let_13))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_39 (or _let_20 _let_27 _let_24 _let_38 _let_11))) (let ((_let_40 (forall ((A $$unsorted) (BOUND_VARIABLE_1044 $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal BOUND_VARIABLE_1044)) (tptp.in A BOUND_VARIABLE_1044) (= A BOUND_VARIABLE_1044) (tptp.in BOUND_VARIABLE_1044 A))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (tptp.ordinal_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_43 (not _let_38))) (let ((_let_44 (not _let_25))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 2)) _let_34 :args (_let_44 true _let_28)))) (let ((_let_46 (or _let_27 _let_20 _let_25 _let_42))) (let ((_let_47 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal B)) (tptp.ordinal_subset A B) (tptp.ordinal_subset B A))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_32)) :args ((or _let_26 _let_28))) _let_34 :args (_let_26 true _let_28)))) (let ((_let_50 (ASSUME :args (_let_42)))) (let ((_let_51 (ASSUME :args (_let_38)))) (let ((_let_52 (ASSUME :args (_let_44)))) (let ((_let_53 (= _let_25 _let_10))) (let ((_let_54 (not _let_10))) (let ((_let_55 (or _let_27 _let_20 _let_53))) (let ((_let_56 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (_let_9))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_58) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) false))))) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_10 _let_12 _let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_53)) :args ((or _let_25 _let_54 (not _let_53)))) _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_27 _let_20 _let_53 (not _let_55)))) _let_49 _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordinal_subset A B)))) :args (_let_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_53 false _let_26 false _let_19 false _let_55)) :args (_let_54 true _let_25 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_27 _let_20 _let_24 _let_11 _let_38 (not _let_39)))) _let_49 _let_36 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 3)) _let_34 :args ((not _let_24) true _let_28)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_50 _let_51 _let_52) :args (_let_44 _let_42 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_52)) (CONG _let_51 (SYMM _let_51) :args (APPLY_UF tptp.ordinal_subset)) (TRUE_INTRO _let_50))) :args (_let_42 _let_38 _let_44)) :args ((not (and _let_44 _let_42 _let_38)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_25))) (REFL :args ((not _let_42))) (REFL :args (_let_43)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_27 _let_20 _let_25 _let_42 (not _let_46)))) _let_49 _let_36 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ordinal_subset A B) true))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_42 false _let_26 false _let_19 true _let_25 false _let_46)) _let_45 :args (_let_43 false _let_42 true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in A BOUND_VARIABLE_1044) true))))) :args (_let_40)))) _let_41 :args (_let_39 false _let_40)) :args (_let_11 false _let_26 false _let_19 true _let_24 true _let_38 false _let_39)) :args (_let_37 true _let_10 false _let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_15)) :args ((or (not _let_14) _let_9 (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_18 0)) :args ((or _let_14 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_18 (not _let_21)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ordinal A) false))))) :args (_let_22))) _let_23 :args (_let_21 false _let_22)) :args (_let_18 false _let_19 false _let_21)) :args (_let_14 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.epsilon_transitive A)))) :args (_let_16))) _let_17 :args (_let_15 false _let_16)) :args (_let_9 false _let_14 false _let_15)) :args (false true _let_13 false _let_9)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) _let_8 (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 $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) _let_7 _let_6 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_5 _let_4 (tptp.relation_empty_yielding tptp.empty_set)) _let_5 (and _let_5 _let_4) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$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_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (tptp.ordinal_subset A A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.57  )
% 0.21/0.57  % SZS output end Proof for NUM394+1
% 0.21/0.57  % cvc5---1.0.5 exiting
% 0.21/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------