TSTP Solution File: ITP001_5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP001_5 : 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 03:13:50 EDT 2023
% Result : Theorem 0.40s 0.61s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : ITP001_5 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.11/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n009.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun Aug 27 12:46:20 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.52 %----Proving TF0_NAR, FOF, or CNF
% 0.40/0.61 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.sDQRA8lKFh/cvc5---1.0.5_463.p...
% 0.40/0.61 ------- get file name : TPTP file name is ITP001_5
% 0.40/0.61 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_463.smt2...
% 0.40/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.40/0.61 % SZS status Theorem for ITP001_5
% 0.40/0.61 % SZS output start Proof for ITP001_5
% 0.40/0.61 (
% 0.40/0.61 (let ((_let_1 (not true))) (let ((_let_2 (tptp.i tptp.bool))) (let ((_let_3 (tptp.arr tptp.bool tptp.bool))) (let ((_let_4 (tptp.arr tptp.bool _let_3))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :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 $$unsorted)) (=> (tptp.mem X tptp.bool) (= X (tptp.inj__o (tptp.surj__o X))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Emin_2E_3D A_27a) (tptp.arr A_27a (tptp.arr A_27a tptp.bool)))) (forall ((A tptp.del) (X $$unsorted)) (=> (tptp.mem X A) (forall ((Y $$unsorted)) (=> (tptp.mem Y A) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A) X) Y)) (= X Y)))))) (tptp.mem tptp.c_2Emin_2E_3D_3D_3E _let_4) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Emin_2E_3D_3D_3E X0 X1)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E Q) R)) (=> (tptp.p Q) (tptp.p R))))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Emin_2E_40 A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) A_27a))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2E_21 A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool))) (forall ((A tptp.del) (Q $$unsorted)) (=> (tptp.mem Q (tptp.arr A tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 A) Q)) (forall ((X $$unsorted)) (=> (tptp.mem X A) (tptp.p (tptp.ap Q X))))))) (tptp.mem tptp.c_2Ebool_2E_2F_5C _let_4) (forall ((X0 tptp.tp__o) (X1 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_2F_5C X0 X1)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.inj__o X0)) (tptp.inj__o X1)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (forall ((R $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C Q) R)) (and (tptp.p Q) (tptp.p R))))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2E_3F A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool))) (forall ((A tptp.del) (Q $$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))))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2E_3F_21 A_27a) (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2EARB A_27a) A_27a)) (tptp.mem tptp.c_2Ebool_2EBOUNDED _let_3) (forall ((X0 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2EBOUNDED X0)) (tptp.ap tptp.c_2Ebool_2EBOUNDED (tptp.inj__o X0)))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2ECOND A_27a) (tptp.arr tptp.bool (tptp.arr A_27a (tptp.arr A_27a A_27a))))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2EDATATYPE A_27a) (tptp.arr A_27a tptp.bool))) (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)) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2EIN A_27a) (tptp.arr A_27a (tptp.arr (tptp.arr A_27a tptp.bool) tptp.bool)))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (tptp.arr A_27a A_27b))) (tptp.mem (tptp.c_2Ebool_2ELET A_27a A_27b) (tptp.arr _let_1 _let_1)))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (tptp.mem (tptp.c_2Ebool_2EONE__ONE A_27a A_27b) (tptp.arr (tptp.arr A_27a A_27b) tptp.bool))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (tptp.mem (tptp.c_2Ebool_2EONTO A_27a A_27b) (tptp.arr (tptp.arr A_27a A_27b) tptp.bool))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (tptp.arr A_27a A_27b))) (tptp.mem (tptp.c_2Ebool_2ERES__ABSTRACT A_27a A_27b) (tptp.arr (tptp.arr A_27a tptp.bool) (tptp.arr _let_1 _let_1))))) (forall ((A_27a tptp.del)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (tptp.mem (tptp.c_2Ebool_2ERES__EXISTS A_27a) (tptp.arr _let_1 (tptp.arr _let_1 tptp.bool))))) (forall ((A_27a tptp.del)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (tptp.mem (tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a) (tptp.arr _let_1 (tptp.arr _let_1 tptp.bool))))) (forall ((A_27a tptp.del)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (tptp.mem (tptp.c_2Ebool_2ERES__FORALL A_27a) (tptp.arr _let_1 (tptp.arr _let_1 tptp.bool))))) (forall ((A_27a tptp.del)) (let ((_let_1 (tptp.arr A_27a tptp.bool))) (tptp.mem (tptp.c_2Ebool_2ERES__SELECT A_27a) (tptp.arr _let_1 (tptp.arr _let_1 A_27a))))) (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) (A_27b tptp.del)) (tptp.mem (tptp.c_2Ebool_2ETYPE__DEFINITION A_27a A_27b) (tptp.arr (tptp.arr A_27a tptp.bool) (tptp.arr (tptp.arr A_27b A_27a) tptp.bool)))) (tptp.mem tptp.c_2Ebool_2E_5C_2F _let_4) (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 $$unsorted)) (=> (tptp.mem R tptp.bool) (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F Q) R)) (or (tptp.p Q) (tptp.p R))))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (tptp.mem (tptp.c_2Ebool_2Eitself__case A_27a A_27b) (tptp.arr (tptp.ty_2Ebool_2Eitself A_27a) (tptp.arr A_27b A_27b)))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (tptp.arr A_27a A_27b))) (tptp.mem (tptp.c_2Ebool_2Eliteral__case A_27a A_27b) (tptp.arr _let_1 _let_1)))) (forall ((A_27a tptp.del)) (tptp.mem (tptp.c_2Ebool_2Ethe__value A_27a) (tptp.ty_2Ebool_2Eitself A_27a))) (tptp.mem tptp.c_2Ebool_2E_7E _let_3) (forall ((X0 tptp.tp__o)) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_7E X0)) (tptp.ap tptp.c_2Ebool_2E_7E (tptp.inj__o X0)))) (forall ((Q $$unsorted)) (=> (tptp.mem Q tptp.bool) (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E Q)) (not (tptp.p Q))))) (= true (= _let_2 _let_2)) (forall ((A_27a tptp.del) (V0P $$unsorted)) (= (tptp.ap (tptp.f1 A_27a) V0P) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D (tptp.arr A_27a tptp.bool)) V0P) (tptp.k A_27a tptp.c_2Ebool_2ET)))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2E_21 A_27a) (tptp.f1 A_27a))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (= (tptp.ap (tptp.f2 A_27a) V0P) (tptp.ap V0P (tptp.ap (tptp.c_2Emin_2E_40 A_27a) V0P)))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2E_3F A_27a) (tptp.f2 A_27a))) (forall ((V1t2 tptp.tp__o) (V0t1 tptp.tp__o) (V2t tptp.tp__o)) (let ((_let_1 (tptp.inj__o V2t))) (= (tptp.ap (tptp.f3 V1t2 V0t1) _let_1) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o V0t1)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o V1t2)) _let_1))) _let_1)))) (forall ((V0t1 tptp.tp__o) (V1t2 tptp.tp__o)) (= (tptp.ap (tptp.f4 V0t1) (tptp.inj__o V1t2)) (tptp.ap (tptp.c_2Ebool_2E_21 tptp.bool) (tptp.f3 V1t2 V0t1)))) (forall ((V0t1 tptp.tp__o)) (= (tptp.ap tptp.f5 (tptp.inj__o V0t1)) (tptp.f4 V0t1))) (= tptp.c_2Ebool_2E_2F_5C tptp.f5) (forall ((V0t1 tptp.tp__o) (V1t2 tptp.tp__o) (V2t tptp.tp__o)) (let ((_let_1 (tptp.inj__o V2t))) (= (tptp.ap (tptp.f6 V0t1 V1t2) _let_1) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o V0t1)) _let_1)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.inj__o V1t2)) _let_1)) _let_1))))) (forall ((V0t1 tptp.tp__o) (V1t2 tptp.tp__o)) (= (tptp.ap (tptp.f7 V0t1) (tptp.inj__o V1t2)) (tptp.ap (tptp.c_2Ebool_2E_21 tptp.bool) (tptp.f6 V0t1 V1t2)))) (forall ((V0t1 tptp.tp__o)) (= (tptp.ap tptp.f8 (tptp.inj__o V0t1)) (tptp.f7 V0t1))) (= tptp.c_2Ebool_2E_5C_2F tptp.f8) (= false (forall ((V0t tptp.tp__o)) (tptp.p (tptp.inj__o V0t)))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.inj__o V0t))) (= (tptp.ap tptp.f9 _let_1) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E _let_1) (tptp.inj__o tptp.fo__c_2Ebool_2EF))))) (= tptp.c_2Ebool_2E_7E tptp.f9) (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (tptp.mem V0P (tptp.arr A_27a tptp.bool)) (forall ((V1x $$unsorted)) (=> (tptp.mem V1x A_27a) (forall ((V2y $$unsorted)) (= (tptp.ap (tptp.f10 A_27a V0P V1x) V2y) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.ap V0P V1x)) (tptp.ap V0P V2y))) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27a) V1x) V2y)))))))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (tptp.mem V0P (tptp.arr A_27a tptp.bool)) (forall ((V1x $$unsorted)) (= (tptp.ap (tptp.f11 A_27a V0P) V1x) (tptp.ap (tptp.c_2Ebool_2E_21 A_27a) (tptp.f10 A_27a V0P V1x)))))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (= (tptp.ap (tptp.f12 A_27a) V0P) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.ap (tptp.c_2Ebool_2E_3F A_27a) V0P)) (tptp.ap (tptp.c_2Ebool_2E_21 A_27a) (tptp.f11 A_27a V0P))))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2E_3F_21 A_27a) (tptp.f12 A_27a))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0f $$unsorted)) (=> (tptp.mem V0f (tptp.arr A_27a A_27b)) (forall ((V1x $$unsorted)) (= (tptp.ap (tptp.f13 A_27b A_27a V0f) V1x) (tptp.ap V0f V1x))))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0f $$unsorted)) (= (tptp.ap (tptp.f14 A_27b A_27a) V0f) (tptp.f13 A_27b A_27a V0f))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (tptp.c_2Ebool_2ELET A_27a A_27b) (tptp.f14 A_27b A_27a))) (forall ((A_27a tptp.del) (V1t1 $$unsorted)) (=> (tptp.mem V1t1 A_27a) (forall ((V2t2 $$unsorted)) (=> (tptp.mem V2t2 A_27a) (forall ((V0t tptp.tp__o) (V3x $$unsorted)) (let ((_let_1 (tptp.ap (tptp.c_2Emin_2E_3D A_27a) V3x))) (let ((_let_2 (tptp.ap (tptp.c_2Emin_2E_3D tptp.bool) (tptp.inj__o V0t)))) (= (tptp.ap (tptp.f15 A_27a V1t1 V2t2 V0t) V3x) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap _let_2 (tptp.inj__o tptp.fo__c_2Ebool_2ET))) (tptp.ap _let_1 V1t1))) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap _let_2 (tptp.inj__o tptp.fo__c_2Ebool_2EF))) (tptp.ap _let_1 V2t2))))))))))) (forall ((A_27a tptp.del) (V0t tptp.tp__o) (V1t1 $$unsorted)) (=> (tptp.mem V1t1 A_27a) (forall ((V2t2 $$unsorted)) (= (tptp.ap (tptp.f16 A_27a V0t V1t1) V2t2) (tptp.ap (tptp.c_2Emin_2E_40 A_27a) (tptp.f15 A_27a V1t1 V2t2 V0t)))))) (forall ((A_27a tptp.del) (V0t tptp.tp__o) (V1t1 $$unsorted)) (= (tptp.ap (tptp.f17 A_27a V0t) V1t1) (tptp.f16 A_27a V0t V1t1))) (forall ((A_27a tptp.del) (V0t tptp.tp__o)) (= (tptp.ap (tptp.f18 A_27a) (tptp.inj__o V0t)) (tptp.f17 A_27a V0t))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2ECOND A_27a) (tptp.f18 A_27a))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0f $$unsorted)) (=> (tptp.mem V0f (tptp.arr A_27a A_27b)) (forall ((V1x1 $$unsorted)) (=> (tptp.mem V1x1 A_27a) (forall ((V2x2 $$unsorted)) (= (tptp.ap (tptp.f19 A_27b A_27a V0f V1x1) V2x2) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27b) (tptp.ap V0f V1x1)) (tptp.ap V0f V2x2))) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27a) V1x1) V2x2)))))))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0f $$unsorted)) (=> (tptp.mem V0f (tptp.arr A_27a A_27b)) (forall ((V1x1 $$unsorted)) (= (tptp.ap (tptp.f20 A_27b A_27a V0f) V1x1) (tptp.ap (tptp.c_2Ebool_2E_21 A_27a) (tptp.f19 A_27b A_27a V0f V1x1)))))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0f $$unsorted)) (= (tptp.ap (tptp.f21 A_27b A_27a) V0f) (tptp.ap (tptp.c_2Ebool_2E_21 A_27a) (tptp.f20 A_27b A_27a V0f)))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (tptp.c_2Ebool_2EONE__ONE A_27a A_27b) (tptp.f21 A_27b A_27a))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0f $$unsorted)) (=> (tptp.mem V0f (tptp.arr A_27a A_27b)) (forall ((V1y $$unsorted)) (=> (tptp.mem V1y A_27b) (forall ((V2x $$unsorted)) (= (tptp.ap (tptp.f22 A_27b A_27a V0f V1y) V2x) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27b) V1y) (tptp.ap V0f V2x)))))))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (tptp.mem V0f (tptp.arr A_27a A_27b)) (forall ((V1y $$unsorted)) (= (tptp.ap (tptp.f23 A_27a A_27b V0f) V1y) (tptp.ap (tptp.c_2Ebool_2E_3F A_27a) (tptp.f22 A_27b A_27a V0f V1y)))))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (= (tptp.ap (tptp.f24 A_27a A_27b) V0f) (tptp.ap (tptp.c_2Ebool_2E_21 A_27b) (tptp.f23 A_27a A_27b V0f)))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (tptp.c_2Ebool_2EONTO A_27a A_27b) (tptp.f24 A_27a A_27b))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V1rep $$unsorted)) (=> (tptp.mem V1rep (tptp.arr A_27b A_27a)) (forall ((V2x_27 $$unsorted)) (=> (tptp.mem V2x_27 A_27b) (forall ((V3x_27_27 $$unsorted)) (= (tptp.ap (tptp.f25 A_27a A_27b V1rep V2x_27) V3x_27_27) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27a) (tptp.ap V1rep V2x_27)) (tptp.ap V1rep V3x_27_27))) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27b) V2x_27) V3x_27_27)))))))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V1rep $$unsorted)) (=> (tptp.mem V1rep (tptp.arr A_27b A_27a)) (forall ((V2x_27 $$unsorted)) (= (tptp.ap (tptp.f26 A_27a A_27b V1rep) V2x_27) (tptp.ap (tptp.c_2Ebool_2E_21 A_27b) (tptp.f25 A_27a A_27b V1rep V2x_27)))))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V1rep $$unsorted)) (=> (tptp.mem V1rep (tptp.arr A_27b A_27a)) (forall ((V4x $$unsorted)) (=> (tptp.mem V4x A_27a) (forall ((V5x_27 $$unsorted)) (= (tptp.ap (tptp.f27 A_27a A_27b V1rep V4x) V5x_27) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27a) V4x) (tptp.ap V1rep V5x_27)))))))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0P $$unsorted)) (=> (tptp.mem V0P (tptp.arr A_27a tptp.bool)) (forall ((V1rep $$unsorted)) (=> (tptp.mem V1rep (tptp.arr A_27b A_27a)) (forall ((V4x $$unsorted)) (= (tptp.ap (tptp.f28 A_27b A_27a V0P V1rep) V4x) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D tptp.bool) (tptp.ap V0P V4x)) (tptp.ap (tptp.c_2Ebool_2E_3F A_27b) (tptp.f27 A_27a A_27b V1rep V4x))))))))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0P $$unsorted)) (=> (tptp.mem V0P (tptp.arr A_27a tptp.bool)) (forall ((V1rep $$unsorted)) (= (tptp.ap (tptp.f29 A_27b A_27a V0P) V1rep) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.ap (tptp.c_2Ebool_2E_21 A_27b) (tptp.f26 A_27a A_27b V1rep))) (tptp.ap (tptp.c_2Ebool_2E_21 A_27a) (tptp.f28 A_27b A_27a V0P V1rep))))))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0P $$unsorted)) (= (tptp.ap (tptp.f30 A_27b A_27a) V0P) (tptp.f29 A_27b A_27a V0P))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (tptp.c_2Ebool_2ETYPE__DEFINITION A_27a A_27b) (tptp.f30 A_27b A_27a))) (forall ((V0t tptp.tp__o)) (let ((_let_1 (tptp.p (tptp.inj__o V0t)))) (or (= _let_1 true) (= _let_1 false)))) (forall ((A_27b tptp.del) (A_27a tptp.del) (V0t $$unsorted)) (=> (tptp.mem V0t (tptp.arr A_27a A_27b)) (forall ((V1x $$unsorted)) (= (tptp.ap (tptp.f31 A_27b A_27a V0t) V1x) (tptp.ap V0t V1x))))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V0t $$unsorted)) (=> (tptp.mem V0t (tptp.arr A_27a A_27b)) (= (tptp.f31 A_27b A_27a V0t) V0t))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (tptp.mem V0P (tptp.arr A_27a tptp.bool)) (forall ((V1x $$unsorted)) (=> (tptp.mem V1x A_27a) (=> (tptp.p (tptp.ap V0P V1x)) (tptp.p (tptp.ap V0P (tptp.ap (tptp.c_2Emin_2E_40 A_27a) V0P)))))))) (forall ((X tptp.tp__i)) (= (tptp.surj__i (tptp.inj__i X)) X)) (forall ((X tptp.tp__i)) (tptp.mem (tptp.inj__i X) tptp.ind)) (forall ((X $$unsorted)) (=> (tptp.mem X tptp.ind) (= X (tptp.inj__i (tptp.surj__i X))))) (exists ((V0f $$unsorted)) (and (tptp.mem V0f (tptp.arr tptp.ind tptp.ind)) (tptp.p (tptp.ap (tptp.c_2Ebool_2EONE__ONE tptp.ind tptp.ind) V0f)) (not (tptp.p (tptp.ap (tptp.c_2Ebool_2EONTO tptp.ind tptp.ind) V0f))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (tptp.c_2Ebool_2Eliteral__case A_27a A_27b) (tptp.f14 A_27b A_27a))) (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (tptp.mem V0x A_27a) (forall ((V1f $$unsorted)) (= (tptp.ap (tptp.f32 A_27a V0x) V1f) (tptp.ap V1f V0x))))) (forall ((A_27a tptp.del) (V0x $$unsorted)) (= (tptp.ap (tptp.f33 A_27a) V0x) (tptp.f32 A_27a V0x))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2EIN A_27a) (tptp.f33 A_27a))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (tptp.mem V0p (tptp.arr A_27a tptp.bool)) (forall ((V1m $$unsorted)) (=> (tptp.mem V1m (tptp.arr A_27a tptp.bool)) (forall ((V2x $$unsorted)) (= (tptp.ap (tptp.f34 A_27a V0p V1m) V2x) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap (tptp.c_2Ebool_2EIN A_27a) V2x) V0p)) (tptp.ap V1m V2x)))))))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (tptp.mem V0p (tptp.arr A_27a tptp.bool)) (forall ((V1m $$unsorted)) (= (tptp.ap (tptp.f35 A_27a V0p) V1m) (tptp.ap (tptp.c_2Ebool_2E_21 A_27a) (tptp.f34 A_27a V0p V1m)))))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (= (tptp.ap (tptp.f36 A_27a) V0p) (tptp.f35 A_27a V0p))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2ERES__FORALL A_27a) (tptp.f36 A_27a))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (tptp.mem V0p (tptp.arr A_27a tptp.bool)) (forall ((V1m $$unsorted)) (=> (tptp.mem V1m (tptp.arr A_27a tptp.bool)) (forall ((V2x $$unsorted)) (= (tptp.ap (tptp.f37 A_27a V0p V1m) V2x) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.ap (tptp.ap (tptp.c_2Ebool_2EIN A_27a) V2x) V0p)) (tptp.ap V1m V2x)))))))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (tptp.mem V0p (tptp.arr A_27a tptp.bool)) (forall ((V1m $$unsorted)) (= (tptp.ap (tptp.f38 A_27a V0p) V1m) (tptp.ap (tptp.c_2Ebool_2E_3F A_27a) (tptp.f37 A_27a V0p V1m)))))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (= (tptp.ap (tptp.f39 A_27a) V0p) (tptp.f38 A_27a V0p))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2ERES__EXISTS A_27a) (tptp.f39 A_27a))) (forall ((A_27a tptp.del) (V1m $$unsorted)) (=> (tptp.mem V1m (tptp.arr A_27a tptp.bool)) (forall ((V2x $$unsorted)) (= (tptp.ap (tptp.f40 A_27a V1m) V2x) (tptp.ap V1m V2x))))) (forall ((A_27a tptp.del) (V1m $$unsorted)) (=> (tptp.mem V1m (tptp.arr A_27a tptp.bool)) (forall ((V3x $$unsorted)) (=> (tptp.mem V3x A_27a) (forall ((V4y $$unsorted)) (= (tptp.ap (tptp.f41 A_27a V1m V3x) V4y) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.ap V1m V3x)) (tptp.ap V1m V4y))) (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D A_27a) V3x) V4y)))))))) (forall ((A_27a tptp.del) (V1m $$unsorted)) (=> (tptp.mem V1m (tptp.arr A_27a tptp.bool)) (forall ((V0p $$unsorted)) (=> (tptp.mem V0p (tptp.arr A_27a tptp.bool)) (forall ((V3x $$unsorted)) (= (tptp.ap (tptp.f42 A_27a V1m V0p) V3x) (tptp.ap (tptp.ap (tptp.c_2Ebool_2ERES__FORALL A_27a) V0p) (tptp.f41 A_27a V1m V3x)))))))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (tptp.mem V0p (tptp.arr A_27a tptp.bool)) (forall ((V1m $$unsorted)) (= (tptp.ap (tptp.f43 A_27a V0p) V1m) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C (tptp.ap (tptp.ap (tptp.c_2Ebool_2ERES__EXISTS A_27a) V0p) (tptp.f40 A_27a V1m))) (tptp.ap (tptp.ap (tptp.c_2Ebool_2ERES__FORALL A_27a) V0p) (tptp.f42 A_27a V1m V0p))))))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (= (tptp.ap (tptp.f44 A_27a) V0p) (tptp.f43 A_27a V0p))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a) (tptp.f44 A_27a))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (tptp.mem V0p (tptp.arr A_27a tptp.bool)) (forall ((V1m $$unsorted)) (= (tptp.ap (tptp.f45 A_27a V0p) V1m) (tptp.ap (tptp.c_2Emin_2E_40 A_27a) (tptp.f37 A_27a V0p V1m)))))) (forall ((A_27a tptp.del) (V0p $$unsorted)) (= (tptp.ap (tptp.f46 A_27a) V0p) (tptp.f45 A_27a V0p))) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2ERES__SELECT A_27a) (tptp.f46 A_27a))) (= tptp.c_2Ebool_2EBOUNDED (tptp.k tptp.bool tptp.c_2Ebool_2ET)) (forall ((A_27a tptp.del)) (= (tptp.c_2Ebool_2EDATATYPE A_27a) (tptp.k A_27a tptp.c_2Ebool_2ET))) _let_1 true)))))))
% 0.40/0.62 )
% 0.40/0.62 % SZS output end Proof for ITP001_5
% 0.40/0.62 % cvc5---1.0.5 exiting
% 0.40/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------