%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n001.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 0.20s 0.55s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Aug 25 14:02:28 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.E6i8ljK47U/cvc5---1.0.5_15904.p...
% 0.20/0.55  ------- get file name : TPTP file name is NUM412+1
% 0.20/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15904.smt2...
% 0.20/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.55  % SZS status Theorem for NUM412+1
% 0.20/0.55  % SZS output start Proof for NUM412+1
% 0.20/0.55  (
% 0.20/0.55  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.transfinite_sequence_of B A) (forall ((C $$unsorted)) (=> (tptp.ordinal C) (tptp.transfinite_sequence_of (tptp.tseq_dom_restriction B C) A)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.transfinite_sequence_of C A) (tptp.transfinite_sequence_of C 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.transfinite_sequence_of B A) (and (tptp.relation B) (tptp.function B) (tptp.transfinite_sequence B)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A) (tptp.ordinal B)) (tptp.transfinite_sequence_of (tptp.tseq_dom_restriction A B) (tptp.relation_rng A)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B) (tptp.transfinite_sequence B)) (= (tptp.transfinite_sequence_of B A) (tptp.subset (tptp.relation_rng B) A)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1241 $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.transfinite_sequence_of BOUND_VARIABLE_1241 A)) (tptp.transfinite_sequence_of BOUND_VARIABLE_1241 B))))) (let ((_let_10 (tptp.tseq_dom_restriction SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_11 (tptp.transfinite_sequence_of _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_12 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_13 (tptp.transfinite_sequence_of _let_10 _let_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.subset _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14 _let_11))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.transfinite_sequence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_21 _let_13))) (let ((_let_29 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.transfinite_sequence A)) (not (tptp.ordinal B)) (tptp.transfinite_sequence_of (tptp.tseq_dom_restriction A B) (tptp.relation_rng A)))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (and _let_26 _let_24 _let_22))) (let ((_let_32 (tptp.transfinite_sequence_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.transfinite_sequence_of B A)) (and (tptp.relation B) (tptp.function B) (tptp.transfinite_sequence B)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or _let_33 _let_21 _let_11))) (let ((_let_38 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1261 $$unsorted)) (or (not (tptp.transfinite_sequence_of B A)) (not (tptp.ordinal BOUND_VARIABLE_1261)) (tptp.transfinite_sequence_of (tptp.tseq_dom_restriction B BOUND_VARIABLE_1261) A))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_40) :args (_let_42))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (REFL :args (_let_37)))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_41)) :args ((or _let_32 _let_37))) _let_43 :args (_let_32 true _let_37)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_31 (not _let_34)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.transfinite_sequence_of B A) false))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_31 false _let_32 false _let_34)))) (let ((_let_47 (not _let_31))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 2)) :args ((or _let_22 _let_47))) _let_46 :args (_let_22 false _let_31)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 1)) :args ((or _let_24 _let_47))) _let_46 :args (_let_24 false _let_31)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 0)) :args ((or _let_26 _let_47))) _let_46 :args (_let_26 false _let_31)))) (let ((_let_51 (= _let_32 _let_15))) (let ((_let_52 (or _let_27 _let_25 _let_23 _let_51))) (let ((_let_53 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.transfinite_sequence B)) (= (tptp.transfinite_sequence_of B A) (tptp.subset (tptp.relation_rng B) A)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subset A B) false)) (not (= (tptp.transfinite_sequence_of BOUND_VARIABLE_1241 A) false))))) :args (_let_9))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_11 _let_16 _let_14 _let_19))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 2)) _let_43 :args ((not _let_11) true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_51)) :args ((or _let_33 _let_15 (not _let_51)))) _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_27 _let_25 _let_23 _let_51 (not _let_52)))) _let_50 _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.transfinite_sequence_of B A)))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_51 false _let_26 false _let_24 false _let_22 false _let_52)) :args (_let_15 false _let_32 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_21 _let_27 _let_25 _let_23 _let_13 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 1)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_41)) :args ((or _let_20 _let_37))) _let_43 :args (_let_20 true _let_37)) _let_50 _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tseq_dom_restriction A B)))) :args (_let_29))) _let_30 :args (_let_28 false _let_29)) :args (_let_13 false _let_20 false _let_26 false _let_24 false _let_22 false _let_28)) :args (_let_19 true _let_11 false _let_15 false _let_13)) _let_18 :args (false true _let_17 false _let_9)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$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_8 _let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))) _let_6 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.transfinite_sequence_of B A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_4 _let_3 _let_5) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.relation_empty_yielding A)) (and (tptp.relation _let_1) (tptp.relation_empty_yielding _let_1))))) _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)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (and _let_4 _let_3) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A)) (tptp.with_non_empty_elements (tptp.relation_rng A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (exists ((A $$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 $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A) (tptp.ordinal B)) (= (tptp.tseq_dom_restriction A B) (tptp.relation_dom_restriction A B)))) (forall ((A $$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 $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_2 _let_1 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.56  )
% 0.20/0.56  % SZS output end Proof for NUM412+1
% 0.20/0.56  % cvc5---1.0.5 exiting
% 0.20/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------