%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 16:29:05 EDT 2023

% Result   : Theorem 0.23s 0.61s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Wed Aug 23 12:23:42 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.23/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8X2c4HYEKW/cvc5---1.0.5_942.p...
% 0.23/0.61  ------- get file name : TPTP file name is SEU032+1
% 0.23/0.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_942.smt2...
% 0.23/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.61  % SZS status Theorem for SEU032+1
% 0.23/0.61  % SZS output start Proof for SEU032+1
% 0.23/0.61  (
% 0.23/0.61  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (= (tptp.function_inverse (tptp.function_inverse A)) A))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (and (tptp.one_to_one A) (= (tptp.relation_rng A) (tptp.relation_dom B)) (= (tptp.relation_composition A B) (tptp.identity_relation (tptp.relation_dom A)))) (= B (tptp.function_inverse A))))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (tptp.one_to_one (tptp.function_inverse A))))))) (let ((_let_4 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (and (= (tptp.relation_composition A _let_1) (tptp.identity_relation (tptp.relation_dom A))) (= (tptp.relation_composition _let_1 A) (tptp.identity_relation (tptp.relation_rng A)))))))))) (let ((_let_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (and (= (tptp.relation_rng A) (tptp.relation_dom _let_1)) (= (tptp.relation_dom A) (tptp.relation_rng _let_1))))))))) (let ((_let_6 (tptp.relation tptp.empty_set))) (let ((_let_7 (tptp.empty tptp.empty_set))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))))) (let ((_let_9 (tptp.function_inverse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_10 (tptp.relation_dom _let_9))) (let ((_let_11 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (tptp.relation_composition _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_14 (= _let_13 (tptp.identity_relation _let_11)))) (let ((_let_15 (= _let_13 (tptp.identity_relation _let_10)))) (let ((_let_16 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_17 (= _let_16 (tptp.relation_rng _let_9)))) (let ((_let_18 (and _let_12 _let_17))) (let ((_let_19 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_20 _let_18))) (let ((_let_26 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.one_to_one A)) (and (= (tptp.relation_rng A) (tptp.relation_dom _let_1)) (= (tptp.relation_dom A) (tptp.relation_rng _let_1)))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.function_inverse _let_9)))) (let ((_let_29 (or _let_24 _let_22 _let_20 _let_28))) (let ((_let_30 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.one_to_one A)) (= A (tptp.function_inverse (tptp.function_inverse A))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_32) :args (_let_34))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_33)) :args ((or _let_19 _let_29))) _let_35 :args (_let_19 true _let_29)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_33)) :args ((or _let_21 _let_29))) _let_35 :args (_let_21 true _let_29)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_33)) :args ((or _let_23 _let_29))) _let_35 :args (_let_23 true _let_29)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_22 _let_20 _let_18 (not _let_25)))) _let_39 _let_38 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_26))) _let_27 :args (_let_25 false _let_26)) :args (_let_18 false _let_23 false _let_21 false _let_19 false _let_25)))) (let ((_let_41 (not _let_18))) (let ((_let_42 (and (= (tptp.relation_composition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_9) (tptp.identity_relation _let_16)) _let_14))) (let ((_let_43 (or _let_24 _let_22 _let_20 _let_42))) (let ((_let_44 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.one_to_one A)) (and (= (tptp.relation_composition A _let_1) (tptp.identity_relation (tptp.relation_dom A))) (= (tptp.relation_composition _let_1 A) (tptp.identity_relation (tptp.relation_rng A))))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (not _let_15))) (let ((_let_47 (not _let_17))) (let ((_let_48 (tptp.one_to_one _let_9))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.function _let_9))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.relation _let_9))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51 _let_49 _let_24 _let_22 _let_47 _let_46 _let_28))) (let ((_let_55 (forall ((A $$unsorted) (BOUND_VARIABLE_1238 $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.one_to_one A)) (not (tptp.relation BOUND_VARIABLE_1238)) (not (tptp.function BOUND_VARIABLE_1238)) (not (= (tptp.relation_rng A) (tptp.relation_dom BOUND_VARIABLE_1238))) (not (= (tptp.identity_relation (tptp.relation_dom A)) (tptp.relation_composition A BOUND_VARIABLE_1238))) (= (tptp.function_inverse A) BOUND_VARIABLE_1238))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or _let_24 _let_22 _let_20 _let_48))) (let ((_let_58 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.one_to_one A)) (tptp.one_to_one (tptp.function_inverse A)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (and _let_52 _let_50))) (let ((_let_61 (or _let_24 _let_22 _let_60))) (let ((_let_62 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (or (not (tptp.relation A)) (not (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_24 _let_22 _let_60 (not _let_61)))) _let_39 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.function_inverse A)))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_60 false _let_23 false _let_21 false _let_61)))) (let ((_let_65 (not _let_60))) (let ((_let_66 (ASSUME :args (_let_46)))) (let ((_let_67 (ASSUME :args (_let_12)))) (let ((_let_68 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_66 (MODUS_PONENS (AND_INTRO _let_67 _let_68) (SCOPE (TRANS (SYMM (SYMM _let_68)) (CONG (SYMM (SYMM _let_67)) :args (APPLY_UF tptp.identity_relation))) :args (_let_12 _let_14)))) :args (_let_12 _let_14 _let_46)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_15)))))) (FALSE_INTRO _let_66))) :args (_let_46 _let_15)) :args ((not (and _let_12 _let_14 _let_46)) SB_LITERAL))) (CONG (REFL :args ((not _let_12))) (REFL :args ((not _let_14))) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_15))) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_24 _let_22 _let_28 _let_53 _let_51 _let_49 _let_47 _let_46 (not _let_54)))) _let_39 _let_38 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 3)) _let_35 :args ((not _let_28) true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 0)) :args ((or _let_52 _let_65))) _let_64 :args (_let_52 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_60 1)) :args ((or _let_50 _let_65))) _let_64 :args (_let_50 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_24 _let_22 _let_20 _let_48 (not _let_57)))) _let_39 _let_38 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_48 false _let_23 false _let_21 false _let_19 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_18 1)) :args ((or _let_17 _let_41))) _let_40 :args (_let_17 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_composition A BOUND_VARIABLE_1238)))) :args (_let_55)))) _let_56 :args (_let_54 false _let_55)) :args (_let_46 false _let_23 false _let_21 true _let_28 false _let_52 false _let_50 false _let_48 false _let_17 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 1)) :args ((or _let_14 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_24 _let_22 _let_20 _let_42 (not _let_43)))) _let_39 _let_38 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_42 false _let_23 false _let_21 false _let_19 false _let_43)) :args (_let_14 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_18 0)) :args ((or _let_12 _let_41))) _let_40 :args (_let_12 false _let_18)) :args (false true _let_15 false _let_14 false _let_12)) :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 $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) _let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))) (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))) (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_7 _let_6 (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 $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (tptp.relation _let_1) (tptp.function _let_1)))) (and _let_7 _let_6) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$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))))) (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))))) (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 (tptp.relation A) (tptp.empty A) (tptp.function 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 $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$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))) (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))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) _let_4 _let_3 _let_2 _let_1 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.61  )
% 0.23/0.61  % SZS output end Proof for SEU032+1
% 0.23/0.61  % cvc5---1.0.5 exiting
% 0.23/0.61  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------