TSTP Solution File: ITP010^2 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP010^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% 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 : Wed May 29 17:11:44 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP010^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 26 02:53:09 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.50 %----Proving TH0
% 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.ZoExWmdH3l/cvc5---1.0.5_2090.smt2
% 0.20/0.53 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.ZoExWmdH3l/cvc5---1.0.5_2090.smt2
% 0.20/0.53 (assume a0 (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.20/0.53 (assume a1 (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.20/0.53 (assume a2 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.20/0.53 (assume a3 (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.20/0.53 (assume a4 (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.20/0.53 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.20/0.53 (assume a6 (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.20/0.53 (assume a7 (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.20/0.53 (assume a8 (@ tptp.p tptp.c_2Ebool_2ET))
% 0.20/0.53 (assume a9 (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))))
% 0.20/0.53 (assume a10 (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.20/0.53 (assume a11 (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.20/0.53 (assume a12 (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.bool) tptp.bool))))
% 0.20/0.53 (assume a13 (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))))))))
% 0.20/0.53 (assume a14 (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.bool) tptp.bool))))
% 0.20/0.53 (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_5C_2F) Q)) R)) (or (@ tptp.p Q) (@ tptp.p R))))))))
% 0.20/0.53 (assume a16 (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.bool) tptp.bool))))
% 0.20/0.53 (assume a17 (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))))))))
% 0.20/0.53 (assume a18 (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.20/0.53 (assume a19 (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.20/0.53 (assume a20 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27a) tptp.bool)))))
% 0.20/0.53 (assume a21 (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))))
% 0.20/0.53 (assume a22 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.20/0.53 (assume a23 (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 0.20/0.53 (assume a24 true)
% 0.20/0.53 (assume a25 (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))))
% 0.20/0.53 (assume a26 (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p V0t))) (@ tptp.p V0t)))))
% 0.20/0.53 (assume a27 (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (=> true (@ tptp.p V0t)) (@ tptp.p V0t)) (= (=> (@ tptp.p V0t) true) true) (= (=> false (@ tptp.p V0t)) true) (= (=> (@ tptp.p V0t) (@ tptp.p V0t)) true) (= (=> (@ tptp.p V0t) false) (not (@ tptp.p V0t)))))))
% 0.20/0.53 (assume a28 (and (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not (@ tptp.p V0t))) (@ tptp.p V0t)))) (= (not true) false) (= (not false) true)))
% 0.20/0.53 (assume a29 (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (= V0x V0x) true))))
% 0.20/0.53 (assume a30 (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true (@ tptp.p V0t)) (@ tptp.p V0t)) (= (= (@ tptp.p V0t) true) (@ tptp.p V0t)) (= (= false (@ tptp.p V0t)) (not (@ tptp.p V0t))) (= (= (@ tptp.p V0t) false) (not (@ tptp.p V0t)))))))
% 0.20/0.53 (assume a31 (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27b) A_27a)) V1t)) V0s))))))))
% 0.20/0.53 (assume a32 (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not (@ tptp.p V0t))) (@ tptp.p V0t)))))
% 0.20/0.53 (assume a33 (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (@ tptp.p V0A) (=> (not (@ tptp.p V0A)) false)))))
% 0.20/0.53 (assume a34 (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or (@ tptp.p V0A) (@ tptp.p V1B))) false) (=> (=> (@ tptp.p V0A) false) (=> (not (@ tptp.p V1B)) false))))))))
% 0.20/0.53 (assume a35 (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or (not (@ tptp.p V0A)) (@ tptp.p V1B))) false) (=> (@ tptp.p V0A) (=> (not (@ tptp.p V1B)) false))))))))
% 0.20/0.53 (assume a36 (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (=> (not (@ tptp.p V0A)) false) (=> (=> (@ tptp.p V0A) false) false)))))
% 0.20/0.53 (assume a37 (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= (@ tptp.p V0p) (= (@ tptp.p V1q) (@ tptp.p V2r))) (and (or (@ tptp.p V0p) (@ tptp.p V1q) (@ tptp.p V2r)) (or (@ tptp.p V0p) (not (@ tptp.p V2r)) (not (@ tptp.p V1q))) (or (@ tptp.p V1q) (not (@ tptp.p V2r)) (not (@ tptp.p V0p))) (or (@ tptp.p V2r) (not (@ tptp.p V1q)) (not (@ tptp.p V0p))))))))))))
% 0.20/0.53 (assume a38 (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (= (= (@ tptp.p V0p) (not (@ tptp.p V1q))) (and (or (@ tptp.p V0p) (@ tptp.p V1q)) (or (not (@ tptp.p V1q)) (not (@ tptp.p V0p))))))))))
% 0.20/0.53 (assume a39 (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))))))))
% 0.20/0.53 (assume a40 true)
% 0.20/0.53 (step t1 (cl (not (= (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))))))) false)) (not (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)))))))))) false) :rule equiv_pos2)
% 0.20/0.53 (anchor :step t2 :args ((A_27a tptp.del) (:= A_27a A_27a) (A_27b tptp.del) (:= A_27b A_27b) (V0s $$unsorted) (:= V0s V0s)))
% 0.20/0.53 (step t2.t1 (cl (= A_27a A_27a)) :rule refl)
% 0.20/0.53 (step t2.t2 (cl (= A_27b A_27b)) :rule refl)
% 0.20/0.53 (step t2.t3 (cl (= V0s V0s)) :rule refl)
% 0.20/0.53 (step t2.t4 (cl (= (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)))) :rule refl)
% 0.20/0.53 (anchor :step t2.t5 :args ((V1t $$unsorted) (:= V1t V1t)))
% 0.20/0.53 (step t2.t5.t1 (cl (= V1t V1t)) :rule refl)
% 0.20/0.53 (step t2.t5.t2 (cl (= (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)))) :rule refl)
% 0.20/0.53 (step t2.t5.t3 (cl (= (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)))) true)) :rule all_simplify)
% 0.20/0.53 (step t2.t5.t4 (cl (= (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) true))) :rule cong :premises (t2.t5.t2 t2.t5.t3))
% 0.20/0.53 (step t2.t5.t5 (cl (= (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) true) true)) :rule all_simplify)
% 0.20/0.53 (step t2.t5.t6 (cl (= (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))) true)) :rule trans :premises (t2.t5.t4 t2.t5.t5))
% 0.20/0.53 (step t2.t5 (cl (= (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)))))) (forall ((V1t $$unsorted)) true))) :rule bind)
% 0.20/0.53 (step t2.t6 (cl (= (forall ((V1t $$unsorted)) true) true)) :rule all_simplify)
% 0.20/0.53 (step t2.t7 (cl (= (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)))))) true)) :rule trans :premises (t2.t5 t2.t6))
% 0.20/0.53 (step t2.t8 (cl (= (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) true))) :rule cong :premises (t2.t4 t2.t7))
% 0.20/0.53 (step t2.t9 (cl (= (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) true) true)) :rule all_simplify)
% 0.20/0.53 (step t2.t10 (cl (= (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))))) true)) :rule trans :premises (t2.t8 t2.t9))
% 0.20/0.53 (step t2 (cl (= (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)))))))) (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) true))) :rule bind)
% 0.37/0.53 (step t3 (cl (= (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) true) true)) :rule all_simplify)
% 0.37/0.53 (step t4 (cl (= (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t)))))))) true)) :rule trans :premises (t2 t3))
% 0.37/0.53 (step t5 (cl (= (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))))))) (not true))) :rule cong :premises (t4))
% 0.37/0.53 (step t6 (cl (= (not true) false)) :rule all_simplify)
% 0.37/0.53 (step t7 (cl (= (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecardinal_2Ecardleq A_27a) A_27b)) V0s)) V1t))))))))) false)) :rule trans :premises (t5 t6))
% 0.37/0.53 (step t8 (cl false) :rule resolution :premises (t1 t7 a39))
% 0.37/0.53 (step t9 (cl (not false)) :rule false)
% 0.37/0.53 (step t10 (cl) :rule resolution :premises (t8 t9))
% 0.37/0.53
% 0.37/0.53 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.ZoExWmdH3l/cvc5---1.0.5_2090.smt2
% 0.37/0.53 % cvc5---1.0.5 exiting
% 0.37/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------