%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU299+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n012.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 16:30:44 EDT 2023

% Result   : Theorem 0.21s 0.55s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU299+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n012.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Wed Aug 23 23:24:12 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.UluafD3D1J/cvc5---1.0.5_3944.p...
% 0.21/0.55  ------- get file name : TPTP file name is SEU299+1
% 0.21/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3944.smt2...
% 0.21/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.55  % SZS status Theorem for SEU299+1
% 0.21/0.55  % SZS output start Proof for SEU299+1
% 0.21/0.55  (
% 0.21/0.55  (let ((_let_1 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (= B C) (exists ((E $$unsorted)) (and (tptp.ordinal E) (= C E) (=> (tptp.in E tptp.omega) (forall ((F $$unsorted)) (=> (tptp.element F (tptp.powerset (tptp.powerset E))) (not (and (not (= F tptp.empty_set)) (forall ((G $$unsorted)) (not (and (tptp.in G F) (forall ((H $$unsorted)) (=> (and (tptp.in H F) (tptp.subset G H)) (= H G))))))))))))) (= B D) (exists ((I $$unsorted)) (and (tptp.ordinal I) (= D I) (=> (tptp.in I tptp.omega) (forall ((J $$unsorted)) (=> (tptp.element J (tptp.powerset (tptp.powerset I))) (not (and (not (= J tptp.empty_set)) (forall ((K $$unsorted)) (not (and (tptp.in K J) (forall ((L $$unsorted)) (=> (and (tptp.in L J) (tptp.subset K L)) (= L K)))))))))))))) (= C D))) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D (tptp.succ A)) (= D C) (exists ((M $$unsorted)) (and (tptp.ordinal M) (= C M) (=> (tptp.in M tptp.omega) (forall ((N $$unsorted)) (=> (tptp.element N (tptp.powerset (tptp.powerset M))) (not (and (not (= N tptp.empty_set)) (forall ((O $$unsorted)) (not (and (tptp.in O N) (forall ((P $$unsorted)) (=> (and (tptp.in P N) (tptp.subset O P)) (= P O))))))))))))))))))))))) (let ((_let_2 (tptp.empty tptp.empty_set))) (let ((_let_3 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_4 (tptp.relation tptp.empty_set))) (let ((_let_5 (not (forall ((A $$unsorted)) (=> (tptp.ordinal A) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.in C (tptp.succ A)) (exists ((D $$unsorted)) (and (tptp.ordinal D) (= C D) (=> (tptp.in D tptp.omega) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.powerset (tptp.powerset D))) (not (and (not (= E tptp.empty_set)) (forall ((F $$unsorted)) (not (and (tptp.in F E) (forall ((G $$unsorted)) (=> (and (tptp.in G E) (tptp.subset F G)) (= G F)))))))))))))))))))))) (let ((_let_6 (forall ((A $$unsorted)) (or (not (tptp.ordinal A)) (not (forall ((B $$unsorted)) (not (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.ordinal C) (or (not (tptp.in C tptp.omega)) (forall ((N $$unsorted)) (or (not (tptp.element N (tptp.powerset (tptp.powerset C)))) (= tptp.empty_set N) (not (forall ((O $$unsorted)) (or (not (tptp.in O N)) (not (forall ((P $$unsorted)) (or (not (tptp.in P N)) (not (tptp.subset O P)) (= O P)))))))))) (tptp.in C (tptp.succ A)))))))))))) (let ((_let_7 (forall ((A $$unsorted)) (or (not (tptp.ordinal A)) (not (forall ((B $$unsorted)) (not (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.in C (tptp.succ A)) (tptp.ordinal C) (or (not (tptp.in C tptp.omega)) (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.powerset (tptp.powerset C)))) (= tptp.empty_set E) (not (forall ((F $$unsorted)) (or (not (tptp.in F E)) (not (forall ((G $$unsorted)) (or (not (tptp.in G E)) (not (tptp.subset F G)) (= F G)))))))))))))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_7 (= B B) (= C C) (= A A) (= E N) (= F O) (= G P))) (MACRO_SR_PRED_INTRO :args ((= (forall ((A $$unsorted)) (or (not (tptp.ordinal A)) (not (forall ((B $$unsorted)) (not (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.in C (tptp.succ A)) (tptp.ordinal C) (or (not (tptp.in C tptp.omega)) (forall ((N $$unsorted)) (or (not (tptp.element N (tptp.powerset (tptp.powerset C)))) (= tptp.empty_set N) (not (forall ((O $$unsorted)) (or (not (tptp.in O N)) (not (forall ((P $$unsorted)) (or (not (tptp.in P N)) (not (tptp.subset O P)) (= O P)))))))))))))))))) _let_6) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args ((not _let_6) true _let_7)) :args (false true _let_6)) :args (_let_5 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B) (tptp.natural B) (tptp.finite B)))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (forall ((A $$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)))))) (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) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.ordinal A))) (=> (and (tptp.empty A) _let_1) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) _let_1 (tptp.natural A))))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.succ A))) (=> (and (tptp.ordinal A) (tptp.natural A)) (and (not (tptp.empty _let_1)) (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1) (tptp.natural _let_1))))) (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$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))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) true true true true true (and (tptp.epsilon_transitive tptp.omega) (tptp.epsilon_connected tptp.omega) (tptp.ordinal tptp.omega) (not (tptp.empty tptp.omega))) (and _let_2 _let_4) (and _let_2 _let_4 _let_3) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B)))))) (forall ((A $$unsorted)) (=> (tptp.element A tptp.omega) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.succ A)))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (and _let_4 _let_3 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_2 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.succ A))) (=> (tptp.ordinal A) (and (not (tptp.empty _let_1)) (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_2 _let_1 true))))))))))
% 0.21/0.55  )
% 0.21/0.55  % SZS output end Proof for SEU299+1
% 0.21/0.56  % cvc5---1.0.5 exiting
% 0.21/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------