%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP018+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.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 03:15:50 EDT 2023

% Result   : Theorem 0.41s 0.58s
% Output   : Proof 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : ITP018+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n009.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun Aug 27 10:18:50 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.41/0.58  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.6tjGXXmE9n/cvc5---1.0.5_7667.p...
% 0.41/0.58  ------- get file name : TPTP file name is ITP018+2
% 0.41/0.58  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7667.smt2...
% 0.41/0.58  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.41/0.58  % SZS status Theorem for ITP018+2
% 0.41/0.58  % SZS output start Proof for ITP018+2
% 0.41/0.58  (
% 0.41/0.58  (let ((_let_1 (not (forall ((A_27t $$unsorted)) (=> (tptp.ne A_27t) (forall ((A_27w $$unsorted)) (let ((_let_1 (tptp.c_2Ebool_2Ethe__value (tptp.ty_2Epair_2Eprod A_27t A_27w)))) (=> (tptp.ne A_27w) (= (tptp.ap tptp.c_2Erealax_2Ereal__neg (tptp.ap (tptp.c_2Ebinary__ieee_2Eulp A_27t A_27w) _let_1)) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__to__real A_27t A_27w) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__negate A_27t A_27w) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__plus__min A_27t A_27w) _let_1)))))))))))) (let ((_let_2 (forall ((A_27t $$unsorted)) (=> (tptp.ne A_27t) (forall ((A_27w $$unsorted)) (let ((_let_1 (tptp.c_2Ebool_2Ethe__value (tptp.ty_2Epair_2Eprod A_27t A_27w)))) (=> (tptp.ne A_27w) (= (tptp.ap (tptp.c_2Ebinary__ieee_2Eulp A_27t A_27w) _let_1) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__to__real A_27t A_27w) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__plus__min A_27t A_27w) _let_1)))))))))) (let ((_let_3 (forall ((A_27a $$unsorted)) (=> (tptp.ne A_27a) (forall ((A_27b $$unsorted)) (=> (tptp.ne A_27b) (forall ((V0x $$unsorted)) (let ((_let_1 (tptp.c_2Ebinary__ieee_2Efloat__to__real A_27a A_27b))) (=> (tptp.mem V0x (tptp.ty_2Ebinary__ieee_2Efloat A_27a A_27b)) (= (tptp.ap _let_1 (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__negate A_27a A_27b) V0x)) (tptp.ap tptp.c_2Erealax_2Ereal__neg (tptp.ap _let_1 V0x)))))))))))) (let ((_let_4 (forall ((A_27a $$unsorted)) (=> (tptp.ne A_27a) (tptp.mem (tptp.c_2Ebool_2Ethe__value A_27a) (tptp.ty_2Ebool_2Eitself A_27a)))))) (let ((_let_5 (forall ((A_27t $$unsorted)) (=> (tptp.ne A_27t) (forall ((A_27w $$unsorted)) (=> (tptp.ne A_27w) (tptp.mem (tptp.c_2Ebinary__ieee_2Efloat__plus__min A_27t A_27w) (tptp.arr (tptp.ty_2Ebool_2Eitself (tptp.ty_2Epair_2Eprod A_27t A_27w)) (tptp.ty_2Ebinary__ieee_2Efloat A_27t A_27w))))))))) (let ((_let_6 (forall ((A0 $$unsorted)) (=> (tptp.ne A0) (forall ((A1 $$unsorted)) (=> (tptp.ne A1) (tptp.ne (tptp.ty_2Epair_2Eprod A0 A1)))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.mem (tptp.ap F X) B))))))) (let ((_let_8 (tptp.ty_2Epair_2Eprod SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (tptp.c_2Ebool_2Ethe__value _let_8))) (let ((_let_10 (tptp.c_2Ebinary__ieee_2Efloat__plus__min SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (tptp.ap _let_10 _let_9))) (let ((_let_12 (tptp.c_2Ebinary__ieee_2Efloat__to__real SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (tptp.ap _let_12 (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__negate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_11)))) (let ((_let_14 (tptp.ap (tptp.c_2Ebinary__ieee_2Eulp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_9))) (let ((_let_15 (= (tptp.ap tptp.c_2Erealax_2Ereal__neg _let_14) _let_13))) (let ((_let_16 (tptp.ap _let_12 _let_11))) (let ((_let_17 (= _let_14 _let_16))) (let ((_let_18 (= _let_13 (tptp.ap tptp.c_2Erealax_2Ereal__neg _let_16)))) (let ((_let_19 (tptp.ne SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.ne SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_15))) (let ((_let_24 (forall ((A_27t $$unsorted) (BOUND_VARIABLE_1370 $$unsorted)) (let ((_let_1 (tptp.c_2Ebool_2Ethe__value (tptp.ty_2Epair_2Eprod A_27t BOUND_VARIABLE_1370)))) (or (not (tptp.ne A_27t)) (not (tptp.ne BOUND_VARIABLE_1370)) (= (tptp.ap tptp.c_2Erealax_2Ereal__neg (tptp.ap (tptp.c_2Ebinary__ieee_2Eulp A_27t BOUND_VARIABLE_1370) _let_1)) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__to__real A_27t BOUND_VARIABLE_1370) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__negate A_27t BOUND_VARIABLE_1370) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__plus__min A_27t BOUND_VARIABLE_1370) _let_1))))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (not _let_24))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_27)) _let_26 :args (_let_25 true _let_24)))) (let ((_let_30 (or _let_22 _let_20 _let_17))) (let ((_let_31 (forall ((A_27t $$unsorted) (BOUND_VARIABLE_1337 $$unsorted)) (let ((_let_1 (tptp.c_2Ebool_2Ethe__value (tptp.ty_2Epair_2Eprod A_27t BOUND_VARIABLE_1337)))) (or (not (tptp.ne A_27t)) (not (tptp.ne BOUND_VARIABLE_1337)) (= (tptp.ap (tptp.c_2Ebinary__ieee_2Eulp A_27t BOUND_VARIABLE_1337) _let_1) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__to__real A_27t BOUND_VARIABLE_1337) (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__plus__min A_27t BOUND_VARIABLE_1337) _let_1)))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (REFL :args (_let_23)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_27)) :args ((or _let_19 _let_23))) _let_29 :args (_let_19 true _let_23)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_27)) :args ((or _let_21 _let_23))) _let_29 :args (_let_21 true _let_23)))) (let ((_let_36 (tptp.ty_2Ebinary__ieee_2Efloat SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_37 (tptp.mem _let_11 _let_36))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_22 _let_20 _let_38 _let_18))) (let ((_let_40 (forall ((A_27a $$unsorted) (BOUND_VARIABLE_1308 $$unsorted) (BOUND_VARIABLE_1306 $$unsorted)) (let ((_let_1 (tptp.c_2Ebinary__ieee_2Efloat__to__real A_27a BOUND_VARIABLE_1306))) (or (not (tptp.ne A_27a)) (not (tptp.ne BOUND_VARIABLE_1306)) (not (tptp.mem BOUND_VARIABLE_1308 (tptp.ty_2Ebinary__ieee_2Efloat A_27a BOUND_VARIABLE_1306))) (= (tptp.ap _let_1 (tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__negate A_27a BOUND_VARIABLE_1306) BOUND_VARIABLE_1308)) (tptp.ap tptp.c_2Erealax_2Ereal__neg (tptp.ap _let_1 BOUND_VARIABLE_1308)))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (tptp.ty_2Ebool_2Eitself _let_8))) (let ((_let_43 (tptp.mem _let_9 _let_42))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.mem _let_10 (tptp.arr _let_42 _let_36)))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_37))) (let ((_let_48 (forall ((A $$unsorted) (B $$unsorted) (F $$unsorted) (BOUND_VARIABLE_955 $$unsorted)) (or (not (tptp.mem F (tptp.arr A B))) (not (tptp.mem BOUND_VARIABLE_955 A)) (tptp.mem (tptp.ap F BOUND_VARIABLE_955) B))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (tptp.ne _let_8))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_43))) (let ((_let_53 (forall ((A_27a $$unsorted)) (or (not (tptp.ne A_27a)) (tptp.mem (tptp.c_2Ebool_2Ethe__value A_27a) (tptp.ty_2Ebool_2Eitself A_27a)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (or _let_22 _let_20 _let_50))) (let ((_let_56 (forall ((A0 $$unsorted) (BOUND_VARIABLE_1098 $$unsorted)) (or (not (tptp.ne A0)) (not (tptp.ne BOUND_VARIABLE_1098)) (tptp.ne (tptp.ty_2Epair_2Eprod A0 BOUND_VARIABLE_1098)))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (or _let_22 _let_20 _let_45))) (let ((_let_59 (forall ((A_27t $$unsorted) (BOUND_VARIABLE_1123 $$unsorted)) (or (not (tptp.ne A_27t)) (not (tptp.ne BOUND_VARIABLE_1123)) (tptp.mem (tptp.c_2Ebinary__ieee_2Efloat__plus__min A_27t BOUND_VARIABLE_1123) (tptp.arr (tptp.ty_2Ebool_2Eitself (tptp.ty_2Epair_2Eprod A_27t BOUND_VARIABLE_1123)) (tptp.ty_2Ebinary__ieee_2Efloat A_27t BOUND_VARIABLE_1123))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (and _let_18 _let_17))) (let ((_let_62 (_let_18 _let_17))) (let ((_let_63 (ASSUME :args (_let_18)))) (let ((_let_64 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_61)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_63 _let_64) (SCOPE (TRANS (CONG (REFL :args (tptp.c_2Erealax_2Ereal__neg)) (SYMM (SYMM _let_64)) :args (APPLY_UF tptp.ap)) (SYMM _let_63)) :args _let_62)) :args _let_62)) :args (true _let_61)) :args ((or _let_15 (not _let_18) (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_22 _let_20 _let_38 _let_18 (not _let_39)))) _let_35 _let_34 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_37 _let_46 _let_44 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_22 _let_20 _let_45 (not _let_58)))) _let_35 _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_2Ebinary__ieee_2Efloat__plus__min A_27t BOUND_VARIABLE_1123)))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_45 false _let_21 false _let_19 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_43 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_22 _let_20 _let_50 (not _let_55)))) _let_35 _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ty_2Epair_2Eprod A0 BOUND_VARIABLE_1098)))) :args (_let_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_50 false _let_21 false _let_19 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_2Ebool_2Ethe__value A_27a)))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_43 false _let_50 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_42 _let_36 _let_10 _let_9 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.mem F (tptp.arr A B)) false)) (not (= (tptp.mem BOUND_VARIABLE_955 A) false))))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_37 false _let_45 false _let_43 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.c_2Ebinary__ieee_2Efloat__negate A_27a BOUND_VARIABLE_1306) BOUND_VARIABLE_1308)))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_18 false _let_21 false _let_19 false _let_37 false _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_22 _let_20 _let_17 (not _let_30)))) _let_35 _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_2Ebinary__ieee_2Eulp A_27t BOUND_VARIABLE_1337)))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_17 false _let_21 false _let_19 false _let_30)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 2)) _let_29 :args ((not _let_15) true _let_23)) :args (false false _let_18 false _let_17 true _let_15)) :args ((tptp.ne tptp.bool) (tptp.ne tptp.ind) (forall ((A $$unsorted)) (=> (tptp.ne A) (forall ((B $$unsorted)) (=> (tptp.ne B) (tptp.ne (tptp.arr A B)))))) _let_7 (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (=> (= (tptp.p Q) (tptp.p R)) (= Q R)))))) (forall ((A $$unsorted) (B $$unsorted) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((G $$unsorted)) (=> (tptp.mem G (tptp.arr A B)) (=> (forall ((X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap F X) (tptp.ap G X)))) (= F G)))))) (forall ((A $$unsorted) (Y $$unsorted) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.k A Y) X) Y))) (forall ((A $$unsorted) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.i A) X) X))) (tptp.ne tptp.ty_2Erealax_2Ereal) (tptp.mem tptp.c_2Erealax_2Ereal__neg (tptp.arr tptp.ty_2Erealax_2Ereal tptp.ty_2Erealax_2Ereal)) (forall ((A0 $$unsorted)) (=> (tptp.ne A0) (forall ((A1 $$unsorted)) (=> (tptp.ne A1) (tptp.ne (tptp.ty_2Ebinary__ieee_2Efloat A0 A1)))))) (forall ((A_27t $$unsorted)) (=> (tptp.ne A_27t) (forall ((A_27w $$unsorted)) (let ((_let_1 (tptp.ty_2Ebinary__ieee_2Efloat A_27t A_27w))) (=> (tptp.ne A_27w) (tptp.mem (tptp.c_2Ebinary__ieee_2Efloat__negate A_27t A_27w) (tptp.arr _let_1 _let_1))))))) _let_6 (forall ((A0 $$unsorted)) (=> (tptp.ne A0) (tptp.ne (tptp.ty_2Ebool_2Eitself A0)))) _let_5 (forall ((A_27t $$unsorted)) (=> (tptp.ne A_27t) (forall ((A_27w $$unsorted)) (=> (tptp.ne A_27w) (tptp.mem (tptp.c_2Ebinary__ieee_2Efloat__to__real A_27t A_27w) (tptp.arr (tptp.ty_2Ebinary__ieee_2Efloat A_27t A_27w) tptp.ty_2Erealax_2Ereal)))))) _let_4 (forall ((A_27t $$unsorted)) (=> (tptp.ne A_27t) (forall ((A_27w $$unsorted)) (=> (tptp.ne A_27w) (tptp.mem (tptp.c_2Ebinary__ieee_2Eulp A_27t A_27w) (tptp.arr (tptp.ty_2Ebool_2Eitself (tptp.ty_2Epair_2Eprod A_27t A_27w)) tptp.ty_2Erealax_2Ereal)))))) (tptp.mem tptp.c_2Ebool_2ET tptp.bool) (tptp.p tptp.c_2Ebool_2ET) (forall ((A_27a $$unsorted)) (=> (tptp.ne A_27a) (tptp.mem (tptp.c_2Emin_2E_3D A_27a) (tptp.arr A_27a (tptp.arr A_27a tptp.bool))))) (forall ((A $$unsorted)) (=> (tptp.ne A) (forall ((X $$unsorted)) (=> (tptp.mem X A) (forall ((Y $$unsorted)) (=> (tptp.mem Y A) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A) X) Y)) (= X Y)))))))) (forall ((A_27a $$unsorted)) (=> (tptp.ne A_27a) (tptp.mem (tptp.c_2Ebool_2E_21 A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool)))) (forall ((A $$unsorted)) (=> (tptp.ne A) (forall ((Q $$unsorted)) (=> (tptp.mem Q (tptp.arr A tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 A) Q)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.p (tptp.ap Q X))))))))) _let_3 _let_2 true (forall ((A_27a $$unsorted)) (=> (tptp.ne A_27a) (forall ((V0x $$unsorted)) (=> (tptp.mem V0x A_27a) (= (= V0x V0x) true))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.41/0.58  )
% 0.41/0.58  % SZS output end Proof for ITP018+2
% 0.41/0.58  % cvc5---1.0.5 exiting
% 0.41/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------