TSTP Solution File: ITP001^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP001^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n022.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 : Wed May 29 17:11:33 EDT 2024
% Result : Theorem 0.23s 0.58s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : ITP001^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.16 % Command : do_cvc5 %s %d
% 0.17/0.37 % Computer : n022.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sun May 26 03:27:54 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.23/0.54 %----Proving TH0
% 0.23/0.58 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.58 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.RsaJ8M44qE/cvc5---1.0.5_9056.smt2
% 0.23/0.58 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.RsaJ8M44qE/cvc5---1.0.5_9056.smt2
% 0.23/0.58 (assume a0 (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.23/0.58 (assume a1 (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.23/0.58 (assume a2 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.23/0.58 (assume a3 (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.23/0.58 (assume a4 (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.23/0.58 (assume a5 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.23/0.58 (assume a6 (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.23/0.58 (assume a7 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27a) tptp.bool)))))
% 0.23/0.58 (assume a8 (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)))))))
% 0.23/0.58 (assume a9 (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.bool) tptp.bool))))
% 0.23/0.58 (assume a10 (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))))))))
% 0.23/0.58 (assume a11 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) A_27a))))
% 0.23/0.58 (assume a12 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.23/0.58 (assume a13 (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))))))))
% 0.23/0.58 (assume a14 (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.bool) tptp.bool))))
% 0.23/0.58 (assume a15 (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))))))))
% 0.23/0.58 (assume a16 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.23/0.58 (assume a17 (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))))))))
% 0.23/0.58 (assume a18 (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))))
% 0.23/0.58 (assume a19 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EARB A_27a)) A_27a)))
% 0.23/0.58 (assume a20 (@ (@ tptp.mem tptp.c_2Ebool_2EBOUNDED) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.23/0.58 (assume a21 (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))))))
% 0.23/0.58 (assume a22 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EDATATYPE A_27a)) (@ (@ tptp.arr A_27a) tptp.bool))))
% 0.23/0.58 (assume a23 (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.23/0.58 (assume a24 (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.23/0.58 (assume a25 (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)))))
% 0.23/0.58 (assume a26 (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) (@ (@ tptp.arr A_27a) A_27b)))))
% 0.23/0.58 (assume a27 (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))))
% 0.23/0.58 (assume a28 (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))))
% 0.23/0.58 (assume a29 (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) (@ (@ tptp.arr A_27a) A_27b))))))
% 0.23/0.58 (assume a30 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 0.23/0.58 (assume a31 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 0.23/0.58 (assume a32 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 0.23/0.58 (assume a33 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__SELECT A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) A_27a)))))
% 0.23/0.58 (assume a34 (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.23/0.58 (assume a35 (@ tptp.p tptp.c_2Ebool_2ET))
% 0.23/0.58 (assume a36 (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)))))
% 0.23/0.58 (assume a37 (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.bool) tptp.bool))))
% 0.23/0.58 (assume a38 (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))))))))
% 0.23/0.58 (assume a39 (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)))))
% 0.23/0.58 (assume a40 (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) (@ (@ tptp.arr A_27a) A_27b)))))
% 0.23/0.58 (assume a41 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2Ethe__value A_27a)) (@ tptp.ty_2Ebool_2Eitself A_27a))))
% 0.23/0.58 (assume a42 (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.23/0.58 (assume a43 (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.23/0.58 (assume a44 (= true (= (@ (@ tptp.lam tptp.bool) (lambda ((V0x $$unsorted)) V0x)) (@ (@ tptp.lam tptp.bool) (lambda ((V1x $$unsorted)) V1x)))))
% 0.23/0.58 (assume a45 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) tptp.bool))) V0P)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) tptp.c_2Ebool_2ET))))))))
% 0.23/0.58 (assume a46 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P)))))))
% 0.23/0.58 (assume a47 (= tptp.c_2Ebool_2E_2F_5C (@ (@ tptp.lam tptp.bool) (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V0t1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V1t2)) V2t)))) V2t))))))))))
% 0.23/0.58 (assume a48 (= tptp.c_2Ebool_2E_5C_2F (@ (@ tptp.lam tptp.bool) (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V0t1)) V2t))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V1t2)) V2t))) V2t)))))))))))
% 0.23/0.58 (assume a49 (= false (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (@ tptp.p V0t)))))
% 0.23/0.58 (assume a50 (= tptp.c_2Ebool_2E_7E (@ (@ tptp.lam tptp.bool) (lambda ((V0t $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V0t)) tptp.c_2Ebool_2EF)))))
% 0.23/0.58 (assume a51 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) V0P))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap V0P) V1x))) (@ (@ tptp.ap V0P) V2y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V2y))))))))))))))
% 0.23/0.58 (assume a52 (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))))
% 0.23/0.58 (assume a53 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ECOND A_27a) (@ (@ tptp.lam tptp.bool) (lambda ((V0t $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1t1 $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) V0t)) tptp.c_2Ebool_2ET))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V1t1)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) V0t)) tptp.c_2Ebool_2EF))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V2t2)))))))))))))))
% 0.23/0.58 (assume a54 (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x1 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x2 $$unsorted)) (@ (@ 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)))))))))))))
% 0.23/0.58 (assume a55 (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V1y)) (@ (@ tptp.ap V0f) V2x)))))))))))))
% 0.23/0.58 (assume a56 (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27b) A_27a)) (lambda ((V1rep $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V2x_27 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V3x_27_27 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ (@ tptp.ap V1rep) V2x_27))) (@ (@ tptp.ap V1rep) V3x_27_27)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V2x_27)) V3x_27_27)))))))))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ 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.lam A_27b) (lambda ((V5x_27 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V4x)) (@ (@ tptp.ap V1rep) V5x_27)))))))))))))))))
% 0.23/0.58 (assume a57 (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (or (= (@ tptp.p V0t) true) (= (@ tptp.p V0t) false)))))
% 0.23/0.58 (assume a58 (forall ((A_27a tptp.del) (A_27b tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0t) V1x))) V0t))))
% 0.23/0.58 (assume a59 (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)))))))))
% 0.23/0.58 (assume a60 (forall ((X tptp.tp__i)) (= (@ tptp.surj__i (@ tptp.inj__i X)) X)))
% 0.23/0.58 (assume a61 (forall ((X tptp.tp__i)) (@ (@ tptp.mem (@ tptp.inj__i X)) tptp.ind)))
% 0.23/0.58 (assume a62 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ind) (= X (@ tptp.inj__i (@ tptp.surj__i X))))))
% 0.23/0.58 (assume a63 (exists ((V0f $$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))))))
% 0.23/0.58 (assume a64 (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))))
% 0.23/0.58 (assume a65 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EIN A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1f $$unsorted)) (@ (@ tptp.ap V1f) V0x))))))))
% 0.23/0.58 (assume a66 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__FORALL A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))))
% 0.23/0.58 (assume a67 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ 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))))))))))))
% 0.23/0.58 (assume a68 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) V0p)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1m) V2x)))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap V1m) V3x))) (@ (@ tptp.ap V1m) V4y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V4y))))))))))))))))
% 0.23/0.59 (assume a69 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__SELECT A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ 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))))))))))))
% 0.23/0.59 (assume a70 (= tptp.c_2Ebool_2EBOUNDED (@ (@ tptp.lam tptp.bool) (lambda ((V0v $$unsorted)) tptp.c_2Ebool_2ET))))
% 0.23/0.59 (assume a71 (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EDATATYPE A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2ET)))))
% 0.23/0.59 (assume a72 (not true))
% 0.23/0.59 (assume a73 true)
% 0.23/0.59 (step t1 (cl (not (= (not true) false)) (not (not true)) false) :rule equiv_pos2)
% 0.23/0.59 (step t2 (cl (= (not true) false)) :rule all_simplify)
% 0.23/0.59 (step t3 (cl false) :rule resolution :premises (t1 t2 a72))
% 0.23/0.59 (step t4 (cl (not false)) :rule false)
% 0.23/0.59 (step t5 (cl) :rule resolution :premises (t3 t4))
% 0.23/0.59
% 0.23/0.59 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.RsaJ8M44qE/cvc5---1.0.5_9056.smt2
% 0.23/0.59 % cvc5---1.0.5 exiting
% 0.23/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------