%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 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 10:43:43 EDT 2023

% Result   : Theorem 0.22s 0.57s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n010.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri Aug 25 09:55:05 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.57  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.CKSGqYRs5j/cvc5---1.0.5_13934.p...
% 0.22/0.57  ------- get file name : TPTP file name is NUM414+1
% 0.22/0.57  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13934.smt2...
% 0.22/0.57  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.57  % SZS status Theorem for NUM414+1
% 0.22/0.57  % SZS output start Proof for NUM414+1
% 0.22/0.57  (
% 0.22/0.57  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (and (not (tptp.proper_subset A B)) (not (= A B)) (not (tptp.proper_subset B A))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))))) (let ((_let_3 (tptp.relation tptp.empty_set))) (let ((_let_4 (tptp.empty tptp.empty_set))) (let ((_let_5 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))))) (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 $$unsorted) (B $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal B)) (tptp.ordinal_subset A B) (tptp.ordinal_subset B A))))) (let ((_let_9 (tptp.ordinal_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_10 (tptp.ordinal_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_11 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_10 _let_9))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_19 (= _let_18 _let_9))) (let ((_let_20 (not _let_9))) (let ((_let_21 (or _let_12 _let_14 _let_19))) (let ((_let_22 (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_23 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (_let_22))) (let ((_let_25 ((tptp.subset A B)))) (let ((_let_26 (tptp.proper_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_27 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_28 (tptp.proper_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_29 (or _let_14 _let_12 _let_28 _let_27 _let_26))) (let ((_let_30 (forall ((A $$unsorted) (BOUND_VARIABLE_1138 $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal BOUND_VARIABLE_1138)) (tptp.proper_subset A BOUND_VARIABLE_1138) (= A BOUND_VARIABLE_1138) (tptp.proper_subset BOUND_VARIABLE_1138 A))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_32) :args (_let_34))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_33)) :args ((or _let_11 _let_29))) _let_35 :args (_let_11 true _let_29)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_33)) :args ((or _let_13 _let_29))) _let_35 :args (_let_13 true _let_29)))) (let ((_let_39 (not _let_27))) (let ((_let_40 (and _let_18 _let_39))) (let ((_let_41 (not _let_18))) (let ((_let_42 (= _let_26 _let_40))) (let ((_let_43 (not _let_40))) (let ((_let_44 (_let_6))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 ((tptp.proper_subset A B)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 3)) _let_35 :args (_let_39 true _let_29)))) (let ((_let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_27))))) (let ((_let_49 (_let_40))) (let ((_let_50 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_51 (= _let_50 _let_10))) (let ((_let_52 (not _let_10))) (let ((_let_53 (or _let_14 _let_12 _let_51))) (let ((_let_54 (and _let_50 _let_39))) (let ((_let_55 (not _let_50))) (let ((_let_56 (= _let_28 _let_54))) (let ((_let_57 (not _let_54))) (let ((_let_58 (_let_54))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ordinal_subset A B) true))))) :args (_let_8))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_12 _let_10 _let_9 _let_17))) _let_38 _let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_51)) :args ((or _let_50 _let_52 (not _let_51)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_58) (CONG (REFL :args _let_58) (REFL :args (_let_55)) _let_48 :args _let_33)) :args ((or _let_27 _let_54 _let_55))) _let_47 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_56)) :args ((or _let_28 _let_57 (not _let_56)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 2)) _let_35 :args ((not _let_28) true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_44)) _let_45 :args (_let_56 false _let_6)) :args (_let_57 true _let_28 false _let_56)) :args (_let_55 true _let_27 true _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_14 _let_12 _let_51 (not _let_53)))) _let_38 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24))) _let_23 :args (_let_53 false _let_22)) :args (_let_51 false _let_13 false _let_11 false _let_53)) :args (_let_52 true _let_50 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_19)) :args ((or _let_18 _let_20 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_49) (CONG (REFL :args _let_49) (REFL :args (_let_41)) _let_48 :args _let_33)) :args ((or _let_27 _let_40 _let_41))) _let_47 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_42)) :args ((or _let_26 _let_43 (not _let_42)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 4)) _let_35 :args ((not _let_26) true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_44))) _let_45 :args (_let_42 false _let_6)) :args (_let_43 true _let_26 false _let_42)) :args (_let_41 true _let_27 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_14 _let_12 _let_19 (not _let_21)))) _let_38 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24))) _let_23 :args (_let_21 false _let_22)) :args (_let_19 false _let_13 false _let_11 false _let_21)) :args (_let_20 true _let_18 false _let_19)) :args (_let_17 false _let_13 false _let_11 true _let_10 true _let_9)) _let_16 :args (false true _let_15 false _let_8)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected 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 $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (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_4 _let_3 _let_5) _let_4 (and _let_3 _let_5 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_4 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (and _let_4 _let_3) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (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 (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal 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 (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal 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 $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) _let_2 (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))) (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 $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) _let_1 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.58  )
% 0.22/0.58  % SZS output end Proof for NUM414+1
% 0.22/0.58  % cvc5---1.0.5 exiting
% 0.22/0.58  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------