%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ITP012_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 03:14:48 EDT 2023

% Result   : Theorem 2.53s 2.75s
% Output   : Proof 2.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : ITP012_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.03/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n023.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sun Aug 27 14:53:26 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.23/0.52  %----Proving TF0_NAR, FOF, or CNF
% 2.53/2.75  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.XfeVtnuQDM/cvc5---1.0.5_11292.p...
% 2.53/2.75  ------- get file name : TPTP file name is ITP012_2
% 2.53/2.75  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11292.smt2...
% 2.53/2.75  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.53/2.75  % SZS status Theorem for ITP012_2
% 2.53/2.75  % SZS output start Proof for ITP012_2
% 2.53/2.75  (
% 2.53/2.75  (let ((_let_1 (not (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint V0p)))) (let ((_let_3 (tptp.inj__ty_2Einteger_2Eint V1q))) (=> (tptp.p (tptp.ap _let_2 _let_3)) (= (tptp.p (tptp.ap _let_2 (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__sub _let_1) _let_3))) (tptp.p (tptp.ap _let_2 _let_1))))))))))) (let ((_let_2 (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (tptp.inj__ty_2Einteger_2Eint V1q))) (let ((_let_2 (tptp.inj__ty_2Einteger_2Eint V0p))) (let ((_let_3 (tptp.ap tptp.c_2Einteger_2Eint__divides _let_2))) (let ((_let_4 (tptp.p (tptp.ap _let_3 _let_1)))) (and (= (tptp.p (tptp.ap _let_3 (tptp.ap tptp.c_2Einteger_2Eint__neg _let_1))) _let_4) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.ap tptp.c_2Einteger_2Eint__neg _let_2)) _let_1)) _let_4))))))))) (let ((_let_3 (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint V0p)))) (let ((_let_3 (tptp.inj__ty_2Einteger_2Eint V1q))) (=> (tptp.p (tptp.ap _let_2 _let_3)) (= (tptp.p (tptp.ap _let_2 (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__add _let_1) _let_3))) (tptp.p (tptp.ap _let_2 _let_1)))))))))) (let ((_let_4 (forall ((V0x tptp.tp__ty_2Einteger_2Eint) (V1y tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (tptp.inj__ty_2Einteger_2Eint V1y))) (let ((_let_2 (tptp.inj__ty_2Einteger_2Eint V0x))) (= (tptp.surj__ty_2Einteger_2Eint (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__sub _let_2) _let_1)) (tptp.surj__ty_2Einteger_2Eint (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__add _let_2) (tptp.ap tptp.c_2Einteger_2Eint__neg _let_1))))))))) (let ((_let_5 (tptp.arr tptp.bool tptp.bool))) (let ((_let_6 (tptp.arr tptp.bool _let_5))) (let ((_let_7 (forall ((X0 tptp.tp__ty_2Einteger_2Eint)) (= (tptp.inj__ty_2Einteger_2Eint (tptp.fo__c_2Einteger_2Eint__neg X0)) (tptp.ap tptp.c_2Einteger_2Eint__neg (tptp.inj__ty_2Einteger_2Eint X0)))))) (let ((_let_8 (tptp.arr tptp.ty_2Einteger_2Eint tptp.ty_2Einteger_2Eint))) (let ((_let_9 (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (tptp.inj__ty_2Einteger_2Eint (tptp.fo__c_2Einteger_2Eint__add X0 X1)) (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__add (tptp.inj__ty_2Einteger_2Eint X0)) (tptp.inj__ty_2Einteger_2Eint X1)))))) (let ((_let_10 (tptp.arr tptp.ty_2Einteger_2Eint _let_8))) (let ((_let_11 (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (tptp.inj__ty_2Einteger_2Eint (tptp.fo__c_2Einteger_2Eint__sub X0 X1)) (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__sub (tptp.inj__ty_2Einteger_2Eint X0)) (tptp.inj__ty_2Einteger_2Eint X1)))))) (let ((_let_12 (forall ((X tptp.tp__ty_2Einteger_2Eint)) (= (tptp.surj__ty_2Einteger_2Eint (tptp.inj__ty_2Einteger_2Eint X)) X)))) (let ((_let_13 (tptp.fo__c_2Einteger_2Eint__sub SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_14 (tptp.inj__ty_2Einteger_2Eint _let_13))) (let ((_let_15 (tptp.inj__ty_2Einteger_2Eint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.inj__ty_2Einteger_2Eint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__sub _let_16) _let_15))) (let ((_let_18 (= _let_17 _let_14))) (let ((_let_19 (tptp.ap tptp.c_2Einteger_2Eint__neg _let_15))) (let ((_let_20 (tptp.ap tptp.c_2Einteger_2Eint__add _let_16))) (let ((_let_21 (= (tptp.surj__ty_2Einteger_2Eint _let_17) (tptp.surj__ty_2Einteger_2Eint (tptp.ap _let_20 _let_19))))) (let ((_let_22 (= _let_13 (tptp.surj__ty_2Einteger_2Eint _let_14)))) (let ((_let_23 (tptp.fo__c_2Einteger_2Eint__neg SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_24 (tptp.inj__ty_2Einteger_2Eint _let_23))) (let ((_let_25 (= _let_19 _let_24))) (let ((_let_26 (tptp.ap _let_20 _let_24))) (let ((_let_27 (tptp.fo__c_2Einteger_2Eint__add SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_23))) (let ((_let_28 (tptp.inj__ty_2Einteger_2Eint _let_27))) (let ((_let_29 (= _let_28 _let_26))) (let ((_let_30 (= _let_27 (tptp.surj__ty_2Einteger_2Eint _let_28)))) (let ((_let_31 (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_32 (tptp.p (tptp.ap _let_31 _let_17)))) (let ((_let_33 (tptp.p (tptp.ap _let_31 _let_26)))) (let ((_let_34 (_let_11))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__sub (tptp.inj__ty_2Einteger_2Eint X0)) (tptp.inj__ty_2Einteger_2Eint X1))))) :args _let_34))) _let_35 :args (_let_18 false _let_11)))) (let ((_let_37 (_let_4))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__sub (tptp.inj__ty_2Einteger_2Eint V0x)) (tptp.inj__ty_2Einteger_2Eint V1y))))) :args _let_37)) _let_38 :args (_let_21 false _let_4)))) (let ((_let_40 (forall ((X tptp.tp__ty_2Einteger_2Eint)) (= X (tptp.surj__ty_2Einteger_2Eint (tptp.inj__ty_2Einteger_2Eint X)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 ((tptp.inj__ty_2Einteger_2Eint X)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_43)) :args _let_42)) _let_41 :args (_let_22 false _let_40)))) (let ((_let_45 (_let_7))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.ap tptp.c_2Einteger_2Eint__neg (tptp.inj__ty_2Einteger_2Eint X0))))) :args _let_45))) _let_46 :args (_let_25 false _let_7)))) (let ((_let_48 (_let_9))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_23 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__add (tptp.inj__ty_2Einteger_2Eint X0)) (tptp.inj__ty_2Einteger_2Eint X1))))) :args _let_48)) _let_49 :args (_let_29 false _let_9)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_43)) :args _let_42)) _let_41 :args (_let_30 false _let_40)))) (let ((_let_52 (tptp.p (tptp.ap _let_31 _let_16)))) (let ((_let_53 (= _let_32 _let_52))) (let ((_let_54 (not _let_32))) (let ((_let_55 (= _let_52 _let_33))) (let ((_let_56 (tptp.p (tptp.ap _let_31 _let_15)))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_53))) (let ((_let_59 (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint V0p)))) (let ((_let_3 (tptp.inj__ty_2Einteger_2Eint V1q))) (or (not (tptp.p (tptp.ap _let_2 _let_3))) (= (tptp.p (tptp.ap _let_2 (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__sub _let_1) _let_3))) (tptp.p (tptp.ap _let_2 _let_1)))))))))) (let ((_let_60 (not _let_58))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (or))) (let ((_let_63 (not _let_59))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_61) :args (_let_63))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_59))) (REFL :args (_let_60)) :args _let_62)) _let_61 :args (_let_60 true _let_59)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_58 1)) _let_64 :args ((not _let_53) true _let_58)))) (let ((_let_66 (_let_53))) (let ((_let_67 (tptp.p (tptp.ap _let_31 _let_24)))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_55))) (let ((_let_70 (forall ((V0p tptp.tp__ty_2Einteger_2Eint) (V1q tptp.tp__ty_2Einteger_2Eint) (V2r tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (tptp.inj__ty_2Einteger_2Eint V2r))) (let ((_let_2 (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint V0p)))) (let ((_let_3 (tptp.inj__ty_2Einteger_2Eint V1q))) (or (not (tptp.p (tptp.ap _let_2 _let_3))) (= (tptp.p (tptp.ap _let_2 (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__add _let_1) _let_3))) (tptp.p (tptp.ap _let_2 _let_1)))))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (tptp.p (tptp.ap _let_31 _let_19)))) (let ((_let_73 (= _let_56 _let_72))) (let ((_let_74 (forall ((BOUND_VARIABLE_1749 tptp.tp__ty_2Einteger_2Eint) (BOUND_VARIABLE_1751 tptp.tp__ty_2Einteger_2Eint)) (let ((_let_1 (tptp.inj__ty_2Einteger_2Eint BOUND_VARIABLE_1751))) (let ((_let_2 (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint BOUND_VARIABLE_1749)))) (= (tptp.p (tptp.ap _let_2 _let_1)) (tptp.p (tptp.ap _let_2 (tptp.ap tptp.c_2Einteger_2Eint__neg _let_1))))))))) (let ((_let_75 (_let_74))) (let ((_let_76 (and _let_72 _let_25))) (let ((_let_77 (_let_72 _let_25))) (let ((_let_78 (ASSUME :args (_let_72)))) (let ((_let_79 (APPLY_UF tptp.p))) (let ((_let_80 (APPLY_UF tptp.ap))) (let ((_let_81 (ASSUME :args (_let_25)))) (let ((_let_82 (SYMM _let_81))) (let ((_let_83 (REFL :args (_let_31)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_55 (not _let_69)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_76)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_78 _let_81) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG _let_83 _let_82 :args _let_80) :args _let_79) (TRUE_INTRO _let_78))) :args _let_77)) :args _let_77)) :args (true _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_73)) :args ((or _let_57 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG (REFL :args (_let_58)) (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_62)) :args ((or _let_56 _let_58))) _let_64 :args (_let_56 true _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_75) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint BOUND_VARIABLE_1749)) (tptp.inj__ty_2Einteger_2Eint BOUND_VARIABLE_1751))))) :args _let_75)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (_let_73 false _let_74)) :args (_let_72 false _let_56 false _let_73)) _let_47 :args (_let_67 false _let_72 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint V0p)) (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__add (tptp.inj__ty_2Einteger_2Eint V2r)) (tptp.inj__ty_2Einteger_2Eint V1q)))))) :args (_let_70)))) _let_71 :args (_let_69 false _let_70)) :args (_let_55 false _let_67 false _let_69)))) (let ((_let_85 (not _let_55))) (let ((_let_86 (not _let_33))) (let ((_let_87 (_let_55))) (let ((_let_88 (and _let_32 _let_18 _let_21 _let_22 _let_25 _let_29 _let_30))) (let ((_let_89 (ASSUME :args (_let_32)))) (let ((_let_90 (ASSUME :args (_let_18)))) (let ((_let_91 (APPLY_UF tptp.inj__ty_2Einteger_2Eint))) (let ((_let_92 (ASSUME :args (_let_22)))) (let ((_let_93 (APPLY_UF tptp.surj__ty_2Einteger_2Eint))) (let ((_let_94 (ASSUME :args (_let_21)))) (let ((_let_95 (ASSUME :args (_let_29)))) (let ((_let_96 (SYMM _let_95))) (let ((_let_97 (ASSUME :args (_let_30)))) (let ((_let_98 (CONG (CONG _let_83 (TRANS _let_96 (CONG (TRANS (SYMM (SYMM _let_97)) (CONG (TRANS (SYMM _let_96) (CONG (REFL :args (_let_20)) _let_82 :args _let_80)) :args _let_93)) :args _let_91) (CONG (TRANS (SYMM _let_94) (CONG _let_90 :args _let_93) (SYMM _let_92)) :args _let_91) (SYMM _let_90)) :args _let_80) :args _let_79))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_88)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_89 _let_90 _let_92 _let_94 _let_81 _let_95 _let_97) (SCOPE (TRUE_ELIM (TRANS _let_98 (TRUE_INTRO _let_89))) :args (_let_32 _let_18 _let_22 _let_21 _let_25 _let_29 _let_30))) :args (_let_32 _let_18 _let_21 _let_22 _let_25 _let_29 _let_30))) :args (true _let_88)) _let_51 _let_50 _let_47 _let_44 _let_39 _let_36 (REORDERING (CNF_EQUIV_POS2 :args _let_87) :args ((or _let_52 _let_86 _let_85))) _let_84 (REORDERING (CNF_EQUIV_NEG1 :args _let_66) :args ((or _let_32 _let_52 _let_53))) _let_65 :args (_let_52 false _let_30 false _let_29 false _let_25 false _let_22 false _let_21 false _let_18 true _let_33 false _let_55 false _let_32 true _let_53)))) (let ((_let_100 (and _let_54 _let_18 _let_21 _let_22 _let_25 _let_29 _let_30))) (let ((_let_101 (ASSUME :args (_let_54)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_100)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_101 _let_90 _let_92 _let_94 _let_81 _let_95 _let_97) (SCOPE (FALSE_ELIM (TRANS _let_98 (FALSE_INTRO _let_101))) :args (_let_54 _let_18 _let_22 _let_21 _let_25 _let_29 _let_30))) :args (_let_54 _let_18 _let_21 _let_22 _let_25 _let_29 _let_30))) :args (true _let_100)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_32))) (REFL :args ((not _let_18))) (REFL :args ((not _let_21))) (REFL :args ((not _let_22))) (REFL :args ((not _let_25))) (REFL :args ((not _let_29))) (REFL :args ((not _let_30))) (REFL :args (_let_86)) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_87) :args ((or (not _let_52) _let_33 _let_85))) _let_99 _let_84 :args (_let_33 false _let_52 false _let_55)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_66) _let_65 _let_99 :args (_let_54 true _let_53 false _let_52)) _let_51 _let_50 _let_47 _let_44 _let_39 _let_36 :args (false false _let_33 true _let_32 false _let_30 false _let_29 false _let_25 false _let_22 false _let_21 false _let_18)) :args ((forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.mem (tptp.ap F X) B))))) (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 tptp.del) (B tptp.del) (F $$unsorted)) (=> (tptp.mem F (tptp.arr A B)) (forall ((G $$unsorted)) (=> (tptp.mem G (tptp.arr A B)) (=> (forall ((X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap F X) (tptp.ap G X)))) (= F G)))))) (forall ((A tptp.del) (Y $$unsorted) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.k A Y) X) Y))) (forall ((A tptp.del) (X $$unsorted)) (=> (tptp.mem X A) (= (tptp.ap (tptp.i A) X) X))) (forall ((X tptp.tp__o)) (= (tptp.surj__o (tptp.inj__o X)) X)) (forall ((X tptp.tp__o)) (tptp.mem (tptp.inj__o X) tptp.bool)) (forall ((X $$unsorted)) (=> (tptp.mem X tptp.bool) (= X (tptp.inj__o (tptp.surj__o X))))) (tptp.mem tptp.c_2Ebool_2ET tptp.bool) (= (tptp.inj__o tptp.fo__c_2Ebool_2ET) tptp.c_2Ebool_2ET) (tptp.p tptp.c_2Ebool_2ET) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2E_3F A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool))) (forall ((A tptp.del) (Q $$unsorted)) (=> (tptp.mem Q (tptp.arr A tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_3F A) Q)) (exists ((X $$unsorted)) (and (tptp.mem X A) (tptp.p (tptp.ap Q X))))))) _let_12 (forall ((X tptp.tp__ty_2Einteger_2Eint)) (tptp.mem (tptp.inj__ty_2Einteger_2Eint X) tptp.ty_2Einteger_2Eint)) (forall ((X $$unsorted)) (=> (tptp.mem X tptp.ty_2Einteger_2Eint) (= X (tptp.inj__ty_2Einteger_2Eint (tptp.surj__ty_2Einteger_2Eint X))))) (tptp.mem tptp.c_2Einteger_2Eint__sub _let_10) _let_11 (tptp.mem tptp.c_2Einteger_2Eint__add _let_10) _let_9 (tptp.mem tptp.c_2Einteger_2Eint__neg _let_8) _let_7 (tptp.mem tptp.c_2Einteger_2Eint__divides (tptp.arr tptp.ty_2Einteger_2Eint (tptp.arr tptp.ty_2Einteger_2Eint tptp.bool))) (forall ((X0 tptp.tp__ty_2Einteger_2Eint) (X1 tptp.tp__ty_2Einteger_2Eint)) (= (tptp.inj__o (tptp.fo__c_2Einteger_2Eint__divides X0 X1)) (tptp.ap (tptp.ap tptp.c_2Einteger_2Eint__divides (tptp.inj__ty_2Einteger_2Eint X0)) (tptp.inj__ty_2Einteger_2Eint X1)))) (tptp.mem tptp.c_2Ebool_2EF tptp.bool) (= (tptp.inj__o tptp.fo__c_2Ebool_2EF) tptp.c_2Ebool_2EF) (not (tptp.p tptp.c_2Ebool_2EF)) (tptp.mem tptp.c_2Emin_2E_3D_3D_3E _let_6) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Emin_2E_3D_3D_3E X0 X1)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E Q) R)) (=> (tptp.p Q) (tptp.p R))))))) (tptp.mem tptp.c_2Ebool_2E_5C_2F _let_6) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_5C_2F X0 X1)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F Q) R)) (or (tptp.p Q) (tptp.p R))))))) (tptp.mem tptp.c_2Ebool_2E_2F_5C _let_6) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_2F_5C X0 X1)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C Q) R)) (and (tptp.p Q) (tptp.p R))))))) (tptp.mem tptp.c_2Ebool_2E_7E _let_5) (forall ((X0 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_7E X0)) (tptp.ap tptp.c_2Ebool_2E_7E (tptp.inj__o X0)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E Q)) (not (tptp.p Q))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Emin_2E_3D A_27a) (tptp.arr A_27a (tptp.arr A_27a tptp.bool)))) (forall ((A tptp.del) (X $$unsorted)) (=> (tptp.mem X A) (forall ((Y $$unsorted)) (=> (tptp.mem Y A) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A) X) Y)) (= X Y)))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2E_21 A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool))) (forall ((A tptp.del) (Q $$unsorted)) (=> (tptp.mem Q (tptp.arr A tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 A) Q)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.p (tptp.ap Q X))))))) true (forall ((V0t1 tptp.tp__o) (V1t2 tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1t2)))) (let ((_let_2 (tptp.p (tptp.inj__o V0t1)))) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1)))))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (=> (=> _let_1 false) (not _let_1)))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (=> (not _let_1) (=> _let_1 false)))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (and (= (=> true _let_1) _let_1) (= (=> _let_1 true) true) (= (=> false _let_1) true) (= (=> _let_1 _let_1) true) (= (=> _let_1 false) (not _let_1))))) (and (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (= (not (not _let_1)) _let_1))) (= (not true) false) (= (not false) true)) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (let ((_let_2 (not _let_1))) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2))))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (tptp.mem V0P (tptp.arr A_27a tptp.bool)) (= (not (forall ((V1x $$unsorted)) (=> (tptp.mem V1x A_27a) (tptp.p (tptp.ap V0P V1x))))) (exists ((V2x $$unsorted)) (and (tptp.mem V2x A_27a) (not (tptp.p (tptp.ap V0P V2x)))))))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (tptp.mem V0P (tptp.arr A_27a tptp.bool)) (forall ((V1Q $$unsorted)) (=> (tptp.mem V1Q (tptp.arr A_27a tptp.bool)) (= (forall ((V2x $$unsorted)) (=> (tptp.mem V2x A_27a) (and (tptp.p (tptp.ap V0P V2x)) (tptp.p (tptp.ap V1Q V2x))))) (and (forall ((V3x $$unsorted)) (=> (tptp.mem V3x A_27a) (tptp.p (tptp.ap V0P V3x)))) (forall ((V4x $$unsorted)) (=> (tptp.mem V4x A_27a) (tptp.p (tptp.ap V1Q V4x)))))))))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o) (V2C tptp.tp__o)) (let ((_let_1 (or (tptp.p (tptp.inj__o V0A)) (tptp.p (tptp.inj__o V1B)) (tptp.p (tptp.inj__o V2C))))) (= _let_1 _let_1))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0A)))) (let ((_let_2 (tptp.p (tptp.inj__o V1B)))) (= (or _let_1 _let_2) (or _let_2 _let_1))))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1B)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p (tptp.inj__o V0A)))) (let ((_let_4 (not _let_3))) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2)))))))) _let_4 _let_3 _let_2 (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (= (not (not _let_1)) _let_1))) (forall ((V0A tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0A)))) (=> _let_1 (=> (not _let_1) false)))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1B)))) (let ((_let_2 (tptp.p (tptp.inj__o V0A)))) (= (=> (not (or _let_2 _let_1)) false) (=> (=> _let_2 false) (=> (not _let_1) false)))))) (forall ((V0A tptp.tp__o) (V1B tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V1B)))) (let ((_let_2 (tptp.p (tptp.inj__o V0A)))) (= (=> (not (or (not _let_2) _let_1)) false) (=> _let_2 (=> (not _let_1) false)))))) (forall ((V0A tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0A)))) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false)))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p (tptp.inj__o V1q)))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.p (tptp.inj__o V2r)))) (let ((_let_6 (not _let_5))) (= (= _let_1 (= _let_3 _let_5)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2)))))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p (tptp.inj__o V2r)))) (let ((_let_4 (tptp.p (tptp.inj__o V1q)))) (= (= _let_1 (and _let_4 _let_3)) (and (or _let_1 (not _let_4) (not _let_3)) (or _let_4 _let_2) (or _let_3 _let_2)))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (tptp.p (tptp.inj__o V2r)))) (let ((_let_3 (tptp.p (tptp.inj__o V1q)))) (= (= _let_1 (or _let_3 _let_2)) (and (or _let_1 (not _let_3)) (or _let_1 (not _let_2)) (or _let_3 _let_2 (not _let_1)))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o) (V2r tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (tptp.p (tptp.inj__o V2r)))) (let ((_let_3 (tptp.p (tptp.inj__o V1q)))) (= (= _let_1 (=> _let_3 _let_2)) (and (or _let_1 _let_3) (or _let_1 (not _let_2)) (or (not _let_3) _let_2 (not _let_1)))))))) (forall ((V0p tptp.tp__o) (V1q tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0p)))) (let ((_let_2 (tptp.p (tptp.inj__o V1q)))) (let ((_let_3 (not _let_2))) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.53/2.75  )
% 2.53/2.75  % SZS output end Proof for ITP012_2
% 2.53/2.75  % cvc5---1.0.5 exiting
% 2.53/2.76  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------