%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM410+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 10:43:42 EDT 2023

% Result   : Theorem 0.16s 0.52s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.13  % Command    : do_cvc5 %s %d
% 0.11/0.32  % Computer : n007.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri Aug 25 09:19:40 EDT 2023
% 0.11/0.32  % CPUTime    : 
% 0.16/0.45  %----Proving TF0_NAR, FOF, or CNF
% 0.16/0.52  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.uGxEIMyJfn/cvc5---1.0.5_15888.p...
% 0.16/0.52  ------- get file name : TPTP file name is NUM410+1
% 0.16/0.52  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15888.smt2...
% 0.16/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.16/0.52  % SZS status Theorem for NUM410+1
% 0.16/0.52  % SZS output start Proof for NUM410+1
% 0.16/0.52  (
% 0.16/0.52  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.ordinal (tptp.relation_dom A)) (tptp.transfinite_sequence_of A (tptp.relation_rng A)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)))) (let ((_let_3 (tptp.relation tptp.empty_set))) (let ((_let_4 (tptp.empty tptp.empty_set))) (let ((_let_5 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B) (tptp.transfinite_sequence B)) (= (tptp.transfinite_sequence_of B A) (tptp.subset (tptp.relation_rng B) A)))))) (let ((_let_7 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.transfinite_sequence A) (tptp.ordinal (tptp.relation_dom A))))))) (let ((_let_8 (forall ((A $$unsorted)) (tptp.subset A A)))) (let ((_let_9 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_10 (tptp.subset _let_9 _let_9))) (let ((_let_11 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_12 (tptp.transfinite_sequence_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_9))) (let ((_let_13 (= _let_12 _let_10))) (let ((_let_14 (not _let_10))) (let ((_let_15 (tptp.transfinite_sequence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_16 _let_13))) (let ((_let_22 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.transfinite_sequence B)) (= (tptp.transfinite_sequence_of B A) (tptp.subset (tptp.relation_rng B) A)))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (tptp.ordinal (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_25 (= _let_24 _let_15))) (let ((_let_26 (or _let_20 _let_18 _let_25))) (let ((_let_27 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (= (tptp.transfinite_sequence A) (tptp.ordinal (tptp.relation_dom A))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (not _let_24))) (let ((_let_30 (or _let_20 _let_18 _let_29 _let_12))) (let ((_let_31 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.ordinal (tptp.relation_dom A))) (tptp.transfinite_sequence_of A (tptp.relation_rng A)))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (or))) (let ((_let_35 (not _let_31))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_31))) (REFL :args (_let_32)) :args _let_34)) _let_33 :args (_let_32 true _let_31)))) (let ((_let_37 (REFL :args (_let_30)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_34)) :args ((or _let_17 _let_30))) _let_36 :args (_let_17 true _let_30)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_34)) :args ((or _let_19 _let_30))) _let_36 :args (_let_19 true _let_30)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_11 :args (_let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset A A) true))))) :args (_let_8))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_13)) :args ((or _let_12 _let_14 (not _let_13)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 3)) _let_36 :args ((not _let_12) true _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_18 _let_16 _let_13 (not _let_21)))) _let_39 _let_38 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_25)) :args ((or _let_29 _let_15 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 2)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_24))) :args _let_34)) :args ((or _let_24 _let_30))) _let_36 :args (_let_24 true _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_20 _let_18 _let_25 (not _let_26)))) _let_39 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_27)))) _let_28 :args (_let_26 false _let_27)) :args (_let_25 false _let_19 false _let_17 false _let_26)) :args (_let_15 false _let_24 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.transfinite_sequence_of B A)))) :args (_let_22))) _let_23 :args (_let_21 false _let_22)) :args (_let_13 false _let_19 false _let_17 false _let_15 false _let_21)) :args (_let_14 true _let_12 false _let_13)) _let_11 :args (false true _let_10 false _let_8)) :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 $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.transfinite_sequence_of B A) (and (tptp.relation B) (tptp.function B) (tptp.transfinite_sequence B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.transfinite_sequence_of B A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_4 _let_3 _let_5) _let_4 (and _let_3 _let_5 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_4 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (and _let_4 _let_3) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (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 $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$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))) _let_2 (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_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))))))))))))))))))))))))))))))))))))))))))
% 0.16/0.61  )
% 0.16/0.61  % SZS output end Proof for NUM410+1
% 0.16/0.61  % cvc5---1.0.5 exiting
% 0.16/0.61  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------