%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU118+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 16:29:19 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU118+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14  % 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   : Wed Aug 23 13:03:07 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.60  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8yV8JN20K6/cvc5---1.0.5_15176.p...
% 0.20/0.60  ------- get file name : TPTP file name is SEU118+1
% 0.20/0.60  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15176.smt2...
% 0.20/0.60  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.60  % SZS status Theorem for SEU118+1
% 0.20/0.60  % SZS output start Proof for SEU118+1
% 0.20/0.60  (
% 0.20/0.60  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (=> (tptp.finite A) (tptp.element B (tptp.finite_subsets A)))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))) (let ((_let_4 (forall ((A $$unsorted)) (tptp.preboolean (tptp.finite_subsets A))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.preboolean B) (= (= B (tptp.finite_subsets A)) (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.subset C A) (tptp.finite C))))))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))))) (let ((_let_7 (tptp.finite_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_7))) (let ((_let_9 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_10 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_11 (and _let_10 _let_9))) (let ((_let_12 (= _let_8 _let_11))) (let ((_let_13 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_7))) (let ((_let_14 (not _let_8))) (let ((_let_15 (or _let_14 _let_13))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.element A B))))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_13))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (not (tptp.finite A)) (tptp.element B (tptp.finite_subsets A)))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (or))) (let ((_let_27 (not _let_23))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_27))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) _let_25 :args (_let_24 true _let_23)))) (let ((_let_29 (= _let_20 _let_10))) (let ((_let_30 (_let_1))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (REFL :args (_let_22)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 0)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_26)) :args ((or _let_20 _let_22))) _let_28 :args (_let_20 true _let_22)))) (let ((_let_34 (or _let_19 _let_21 _let_9))) (let ((_let_35 (forall ((A $$unsorted) (BOUND_VARIABLE_915 $$unsorted)) (or (not (tptp.finite A)) (not (tptp.element BOUND_VARIABLE_915 (tptp.powerset A))) (tptp.finite BOUND_VARIABLE_915))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (forall ((C $$unsorted)) (= (and (tptp.subset C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.finite C)) (tptp.in C (tptp.finite_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_38 (tptp.preboolean _let_7))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.preboolean B)) (= (= B (tptp.finite_subsets A)) (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.subset C A) (tptp.finite C))))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_4))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 (_let_37))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_12)) :args ((or _let_8 (not _let_11) (not _let_12)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) :args _let_45))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.finite_subsets A)))) :args _let_43)) _let_44 :args (_let_38 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.preboolean B) false)) (tptp.finite_subsets A)))) :args (_let_41)))) _let_42 :args (_let_40 false _let_41)) :args (_let_37 false _let_38 false _let_40)) :args (_let_12 false _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_11)) :args ((or (not _let_9) (not _let_10) _let_11))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_21 _let_19 _let_9 (not _let_34)))) _let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_26)) :args ((or _let_18 _let_22))) _let_28 :args (_let_18 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_915 (tptp.powerset A)) false))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_9 false _let_20 false _let_18 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_29)) :args ((or _let_21 _let_10 (not _let_29)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.element A (tptp.powerset B))))) :args _let_30)) _let_31 :args (_let_29 false _let_1)) :args (_let_10 false _let_20 false _let_29)) :args (_let_11 false _let_9 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_13 _let_14 (not _let_15)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 2)) _let_28 :args ((not _let_13) true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.element A B) true))))) :args (_let_16))) _let_17 :args (_let_15 false _let_16)) :args (_let_14 true _let_13 false _let_15)) :args (false false _let_12 false _let_11 true _let_8)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.preboolean A) (and (tptp.cup_closed A) (tptp.diff_closed A)))) _let_6 (forall ((A $$unsorted)) (=> (and (tptp.cup_closed A) (tptp.diff_closed A)) (tptp.preboolean A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.finite_subsets A)) (tptp.finite B))) _let_5 _let_4 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.powerset A))) (and (not (tptp.empty _let_1)) (tptp.cup_closed _let_1) (tptp.diff_closed _let_1) (tptp.preboolean _let_1)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted)) (let ((_let_1 (tptp.finite_subsets A))) (and (not (tptp.empty _let_1)) (tptp.cup_closed _let_1) (tptp.diff_closed _let_1) (tptp.preboolean _let_1)))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.cup_closed A) (tptp.cap_closed A) (tptp.diff_closed A) (tptp.preboolean A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (forall ((A $$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)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (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 $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.subset A B) (tptp.finite B)) (tptp.finite A))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in 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))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.60  )
% 0.20/0.60  % SZS output end Proof for SEU118+1
% 0.20/0.60  % cvc5---1.0.5 exiting
% 0.20/0.60  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------