%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU008+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n027.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 16:29:01 EDT 2023

% Result   : Theorem 10.80s 11.04s
% Output   : Proof 10.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU008+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Wed Aug 23 20:45:47 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.46  %----Proving TF0_NAR, FOF, or CNF
% 10.80/11.04  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.lxM2RGQNZ4/cvc5---1.0.5_17462.p...
% 10.80/11.04  ------- get file name : TPTP file name is SEU008+1
% 10.80/11.04  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17462.smt2...
% 10.80/11.04  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.80/11.04  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.80/11.04  % SZS status Theorem for SEU008+1
% 10.80/11.04  % SZS output start Proof for SEU008+1
% 10.80/11.04  (
% 10.80/11.04  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B (tptp.set_intersection2 (tptp.relation_dom C) A)) (= (tptp.apply C B) (tptp.apply (tptp.relation_composition (tptp.identity_relation A) C) B)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) C))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom B)) (= (tptp.apply (tptp.relation_composition B C) A) (tptp.apply C (tptp.apply B A)))))))))) (let ((_let_4 (tptp.relation tptp.empty_set))) (let ((_let_5 (tptp.empty tptp.empty_set))) (let ((_let_6 (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (tptp.relation _let_1) (tptp.function _let_1)))))) (let ((_let_7 (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))))) (let ((_let_9 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_10 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_11 (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_12 (tptp.relation _let_11))) (let ((_let_13 (tptp.function _let_11))) (let ((_let_14 (tptp.apply _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_15 (tptp.apply (tptp.relation_composition _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_16 (= _let_15 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_14)))) (let ((_let_17 (not _let_10))) (let ((_let_18 (not _let_9))) (let ((_let_19 (tptp.relation_dom _let_11))) (let ((_let_20 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_19))) (let ((_let_21 (not _let_20))) (let ((_let_22 (not _let_13))) (let ((_let_23 (not _let_12))) (let ((_let_24 (or _let_23 _let_22 _let_21 _let_18 _let_17 _let_16))) (let ((_let_25 (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) _let_15))) (let ((_let_26 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_27 (tptp.set_intersection2 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_28 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_27))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_18 _let_17 _let_29 _let_25))) (let ((_let_31 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (not (tptp.in B (tptp.set_intersection2 (tptp.relation_dom C) A))) (= (tptp.apply C B) (tptp.apply (tptp.relation_composition (tptp.identity_relation A) C) B)))))) (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 (_let_7))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_ENUM))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args _let_40) :args _let_38)) _let_39 :args (_let_12 false _let_7)))) (let ((_let_42 (forall ((BOUND_VARIABLE_1002 $$unsorted)) (tptp.function (tptp.identity_relation BOUND_VARIABLE_1002))))) (let ((_let_43 (_let_42))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_43) :args _let_40) :args _let_43)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_13 false _let_42)))) (let ((_let_45 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1122 $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.in A (tptp.relation_dom B))) (not (tptp.relation BOUND_VARIABLE_1122)) (not (tptp.function BOUND_VARIABLE_1122)) (= (tptp.apply (tptp.relation_composition B BOUND_VARIABLE_1122) A) (tptp.apply BOUND_VARIABLE_1122 (tptp.apply B A))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_14))) (let ((_let_48 (not _let_16))) (let ((_let_49 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_47))) (let ((_let_52 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (= C (tptp.apply (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) C)))))) (let ((_let_53 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_19))) (let ((_let_54 (and _let_53 _let_52))) (let ((_let_55 (or _let_23 _let_22 _let_54))) (let ((_let_56 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= A (tptp.relation_dom B)) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (= C (tptp.apply B C)))))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_23 _let_22 _let_54 (not _let_55)))) _let_41 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_11 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_56)))) _let_57 :args (_let_55 false _let_56)) :args (_let_54 false _let_12 false _let_13 false _let_55)))) (let ((_let_59 (not _let_54))) (let ((_let_60 (_let_52))) (let ((_let_61 (and (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_26) _let_49))) (let ((_let_62 (= _let_28 _let_61))) (let ((_let_63 (forall ((D $$unsorted)) (let ((_let_1 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (= (tptp.in D (tptp.set_intersection2 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (and (tptp.in D _let_1) (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))))) (let ((_let_64 (_let_8))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (_let_63))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_61 1)) :args ((or _let_49 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or _let_29 _let_61 (not _let_62)))) (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_28))) :args _let_34)) :args ((or _let_28 _let_30))) _let_36 :args (_let_28 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_66) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_27 QUANTIFIERS_INST_CBQI_PROP)) :args _let_64))) _let_65 :args (_let_63 false _let_8)) :args (_let_62 false _let_63)) :args (_let_61 false _let_28 false _let_62)) :args (_let_49 false _let_61)))) (let ((_let_68 (not _let_25))) (let ((_let_69 (and _let_68 _let_47))) (let ((_let_70 (ASSUME :args (_let_68)))) (let ((_let_71 (ASSUME :args (_let_47)))) (let ((_let_72 (and _let_53 _let_49))) (let ((_let_73 (ASSUME :args (_let_49)))) (let ((_let_74 (ASSUME :args (_let_53)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_18 _let_17 _let_23 _let_22 _let_21 _let_16 (not _let_24)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_72)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_73 _let_74) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (SYMM _let_74) :args (APPLY_UF tptp.in)) (TRUE_INTRO _let_73))) :args (_let_49 _let_53))) :args (_let_53 _let_49))) :args (true _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_54 0)) :args ((or _let_53 _let_59))) _let_58 :args (_let_53 false _let_54)) _let_67 :args (_let_20 false _let_53 false _let_49)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_69)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_71 _let_70) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (SYMM _let_71) :args (APPLY_UF tptp.apply)) (REFL :args (_let_15)) :args (=)) (FALSE_INTRO _let_70)) :args ((= _let_16 false)))) :args (_let_47 _let_68))) :args (_let_68 _let_47))) :args (true _let_69)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_25))) (REFL :args ((not _let_47))) (REFL :args (_let_48)) :args _let_34)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 3)) _let_36 :args (_let_68 true _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_47 (not _let_51)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_60) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_ENUM)) :args _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_54 1)) :args ((or _let_52 _let_59))) _let_58 :args (_let_52 false _let_54)) :args (_let_51 false _let_52)) :args (_let_47 false _let_49 false _let_51)) :args (_let_48 true _let_25 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_45))) _let_46 :args (_let_24 false _let_45)) _let_44 _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_10))) :args _let_34)) :args ((or _let_10 _let_30))) _let_36 :args (_let_10 true _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_9))) :args _let_34)) :args ((or _let_9 _let_30))) _let_36 :args (_let_9 true _let_30)) :args (false false _let_20 true _let_16 false _let_24 false _let_13 false _let_12 false _let_10 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 $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) _let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))) _let_7 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition B A))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (and _let_5 _let_4 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.relation A) (tptp.function A) (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_5 _let_6 (and _let_5 _let_4) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_3 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.80/11.04  )
% 10.80/11.04  % SZS output end Proof for SEU008+1
% 10.80/11.04  % cvc5---1.0.5 exiting
% 10.80/11.05  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------