TSTP Solution File: LCL581^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LCL581^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% 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 : Wed May 29 17:25:38 EDT 2024
% Result : Theorem 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL581^1 : TPTP v8.2.0. Released v3.6.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n023.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 : Mon May 27 22:10:39 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.54 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.hoNr71nlbK/cvc5---1.0.5_4028.smt2
% 0.22/0.54 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.hoNr71nlbK/cvc5---1.0.5_4028.smt2
% 0.22/0.54 (assume a0 (= tptp.mfalse (lambda ((X $$unsorted)) false)))
% 0.22/0.54 (assume a1 (= tptp.mtrue (lambda ((X $$unsorted)) true)))
% 0.22/0.54 (assume a2 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.22/0.54 (assume a3 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.22/0.54 (assume a4 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.22/0.54 (assume a5 (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.22/0.54 (assume a6 (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))
% 0.22/0.54 (assume a7 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))
% 0.22/0.54 (assume a8 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))
% 0.22/0.54 (assume a9 (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.22/0.54 (assume a10 (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.22/0.54 (assume a11 (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))
% 0.22/0.54 (assume a12 (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))
% 0.22/0.54 (assume a13 (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))
% 0.22/0.54 (assume a14 (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))
% 0.22/0.54 (assume a15 (not (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ tptp.mbox tptp.r) tptp.a)))))
% 0.22/0.54 (assume a16 true)
% 0.22/0.54 (step t1 (cl (not (= (not (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ tptp.mbox tptp.r) tptp.a)))) false)) (not (not (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ tptp.mbox tptp.r) tptp.a))))) false) :rule equiv_pos2)
% 0.22/0.54 (step t2 (cl (and (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))) (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W))))) (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W)))))) (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))) (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W)))))) (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y))))))) (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y))))) (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) (not (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W)))))) (not (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W)))))) (not (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W))))))) (not (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))))) (not (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W))))))) (not (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W))))) (not (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y)))))))) (not (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))))) (not (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0)))))) (not (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) (not (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) (not (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule and_neg)
% 0.22/0.54 (step t3 (cl (not (= (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))) (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W))))))) (not (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W)))))) (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W)))))) :rule equiv_pos2)
% 0.22/0.54 (step t4 (cl (= tptp.mcountersatisfiable tptp.mcountersatisfiable)) :rule refl)
% 0.22/0.54 (anchor :step t5 :args ((P (-> $$unsorted Bool)) (:= P P)))
% 0.22/0.54 (step t5.t1 (cl (= P P)) :rule refl)
% 0.22/0.54 (step t5.t2 (cl (= (exists ((W $$unsorted)) (not (@ P W))) (not (forall ((W $$unsorted)) (@ P W))))) :rule all_simplify)
% 0.22/0.54 (step t5 (cl (= (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W)))) (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W)))))) :rule bind)
% 0.22/0.54 (step t6 (cl (= (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))) (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W))))))) :rule cong :premises (t4 t5))
% 0.22/0.54 (step t7 (cl (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W)))))) :rule resolution :premises (t3 t6 a13))
% 0.22/0.54 (step t8 (cl (not (= (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))) (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W)))))))) (not (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W))))) (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W))))))) :rule equiv_pos2)
% 0.22/0.54 (step t9 (cl (= tptp.msatisfiable tptp.msatisfiable)) :rule refl)
% 0.22/0.54 (anchor :step t10 :args ((P (-> $$unsorted Bool)) (:= P P)))
% 0.22/0.54 (step t10.t1 (cl (= P P)) :rule refl)
% 0.22/0.54 (step t10.t2 (cl (= (exists ((W $$unsorted)) (@ P W)) (not (forall ((W $$unsorted)) (not (@ P W)))))) :rule all_simplify)
% 0.22/0.54 (step t10 (cl (= (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W))) (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W))))))) :rule bind)
% 0.22/0.54 (step t11 (cl (= (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))) (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W)))))))) :rule cong :premises (t9 t10))
% 0.22/0.54 (step t12 (cl (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W))))))) :rule resolution :premises (t8 t11 a12))
% 0.22/0.54 (step t13 (cl (not (= (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))) (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W)))))))) (not (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W))))) (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W))))))) :rule equiv_pos2)
% 0.22/0.54 (step t14 (cl (= tptp.mexists tptp.mexists)) :rule refl)
% 0.22/0.54 (anchor :step t15 :args ((P (-> tptp.individuals $$unsorted Bool)) (:= P P) (W $$unsorted) (:= W W)))
% 0.22/0.54 (step t15.t1 (cl (= P P)) :rule refl)
% 0.22/0.54 (step t15.t2 (cl (= W W)) :rule refl)
% 0.22/0.54 (step t15.t3 (cl (= (exists ((X tptp.individuals)) (@ (@ P X) W)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W)))))) :rule all_simplify)
% 0.22/0.54 (step t15 (cl (= (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W))) (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W))))))) :rule bind)
% 0.22/0.54 (step t16 (cl (= (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))) (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W)))))))) :rule cong :premises (t14 t15))
% 0.22/0.54 (step t17 (cl (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W))))))) :rule resolution :premises (t13 t16 a10))
% 0.22/0.54 (step t18 (cl (not (= (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y))))))))) (not (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y)))))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y)))))))) :rule equiv_pos2)
% 0.22/0.54 (step t19 (cl (= tptp.mdia tptp.mdia)) :rule refl)
% 0.22/0.54 (anchor :step t20 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.22/0.54 (step t20.t1 (cl (= R R)) :rule refl)
% 0.22/0.54 (step t20.t2 (cl (= P P)) :rule refl)
% 0.22/0.54 (step t20.t3 (cl (= X X)) :rule refl)
% 0.22/0.54 (step t20.t4 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))) (not (forall ((Y $$unsorted)) (not (and (@ (@ R X) Y) (@ P Y))))))) :rule all_simplify)
% 0.22/0.54 (step t20.t5 (cl (= (forall ((Y $$unsorted)) (not (and (@ (@ R X) Y) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y)))))) :rule all_simplify)
% 0.22/0.54 (step t20.t6 (cl (= (not (forall ((Y $$unsorted)) (not (and (@ (@ R X) Y) (@ P Y))))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y))))))) :rule cong :premises (t20.t5))
% 0.22/0.54 (step t20.t7 (cl (= (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y))))))) :rule trans :premises (t20.t4 t20.t6))
% 0.22/0.54 (step t20 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y)))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y)))))))) :rule bind)
% 0.22/0.54 (step t21 (cl (= (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y))))))))) :rule cong :premises (t19 t20))
% 0.22/0.54 (step t22 (cl (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y)))))))) :rule resolution :premises (t18 t21 a8))
% 0.22/0.54 (step t23 (cl (not (= (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))) (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y))))))) (not (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y)))))) (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.22/0.54 (step t24 (cl (= tptp.mbox tptp.mbox)) :rule refl)
% 0.22/0.54 (anchor :step t25 :args ((R (-> $$unsorted $$unsorted Bool)) (:= R R) (P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.22/0.54 (step t25.t1 (cl (= R R)) :rule refl)
% 0.22/0.54 (step t25.t2 (cl (= P P)) :rule refl)
% 0.22/0.54 (step t25.t3 (cl (= X X)) :rule refl)
% 0.22/0.54 (step t25.t4 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y))))) :rule all_simplify)
% 0.22/0.54 (step t25 (cl (= (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y)))) (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))))) :rule bind)
% 0.22/0.54 (step t26 (cl (= (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))) (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y))))))) :rule cong :premises (t24 t25))
% 0.22/0.54 (step t27 (cl (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))))) :rule resolution :premises (t23 t26 a7))
% 0.22/0.54 (step t28 (cl (not (= (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))) (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))))) (not (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0)))) (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0)))))) :rule equiv_pos2)
% 0.22/0.54 (step t29 (cl (= tptp.miff tptp.miff)) :rule refl)
% 0.22/0.54 (anchor :step t30 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t30.t1 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t30.t2 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t30.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t30.t4 (cl (and (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) (not (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) (not (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) (not (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule and_neg)
% 0.22/0.54 (step t30.t5 (cl (not (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.22/0.54 (step t30.t6 (cl (= tptp.mimpl tptp.mimpl)) :rule refl)
% 0.22/0.54 (anchor :step t30.t7 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t30.t7.t1 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t30.t7.t2 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t30.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t30.t7.t4 (cl (and (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) (not (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) (not (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule and_neg)
% 0.22/0.54 (step t30.t7.t5 (cl (not (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) (not (= tptp.mtrue (lambda ((X $$unsorted)) true))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule equiv_pos2)
% 0.22/0.54 (step t30.t7.t6 (cl (= tptp.mtrue tptp.mtrue)) :rule refl)
% 0.22/0.54 (step t30.t7.t7 (cl (= (lambda ((X $$unsorted)) true) (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule all_simplify)
% 0.22/0.54 (step t30.t7.t8 (cl (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) :rule cong :premises (t30.t7.t6 t30.t7.t7))
% 0.22/0.54 (step t30.t7.t9 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule resolution :premises (t30.t7.t5 t30.t7.t8 a1))
% 0.22/0.54 (step t30.t7.t10 (cl (not (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) (not (= tptp.mfalse (lambda ((X $$unsorted)) false))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule equiv_pos2)
% 0.22/0.54 (step t30.t7.t11 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.22/0.54 (step t30.t7.t12 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule all_simplify)
% 0.22/0.54 (step t30.t7.t13 (cl (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule cong :premises (t30.t7.t11 t30.t7.t12))
% 0.22/0.54 (step t30.t7.t14 (cl (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule resolution :premises (t30.t7.t10 t30.t7.t13 a0))
% 0.22/0.54 (step t30.t7.t15 (cl (and (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule resolution :premises (t30.t7.t4 a4 a3 a2 t30.t7.t9 t30.t7.t14))
% 0.22/0.54 (step t30.t7.t16 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t30.t7.t15))
% 0.22/0.54 (step t30.t7.t17 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t30.t7.t15))
% 0.22/0.54 (step t30.t7.t18 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t30.t7.t19 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t30.t7.t17 t30.t7.t18))
% 0.22/0.54 (step t30.t7.t20 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t30.t7.t16 t30.t7.t19))
% 0.22/0.54 (step t30.t7.t21 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t30.t7.t22 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t30.t7.t20 t30.t7.t21))
% 0.22/0.54 (step t30.t7.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t30.t7.t24 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t30.t7.t22 t30.t7.t23))
% 0.22/0.54 (step t30.t7 (cl (= (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)) (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.22/0.54 (step t30.t8 (cl (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t30.t6 t30.t7))
% 0.22/0.54 (step t30.t9 (cl (= tptp.mimpl tptp.mimpl)) :rule refl)
% 0.22/0.54 (anchor :step t30.t10 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t30.t10.t1 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t30.t10.t2 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t30.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t30.t10.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.22/0.54 (step t30.t10.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.22/0.54 (step t30.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))))) :rule cong :premises (t30.t10.t4 t30.t10.t5))
% 0.22/0.54 (step t30.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.22/0.54 (anchor :step t30.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.22/0.54 (step t30.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.22/0.54 (step t30.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t30.t10.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.22/0.54 (step t30.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.22/0.54 (step t30.t10.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t30.t10.t8.t3 t30.t10.t8.t4))
% 0.22/0.54 (step t30.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.22/0.54 (step t30.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t30.t10.t7 t30.t10.t8))
% 0.22/0.54 (step t30.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t30.t10.t6 t30.t10.t9))
% 0.22/0.54 (step t30.t10.t11 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t30.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t30.t10.t10 t30.t10.t11))
% 0.22/0.54 (step t30.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.22/0.54 (step t30.t10.t14 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t30.t10.t12 t30.t10.t13))
% 0.22/0.54 (step t30.t10.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t30.t10.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t30.t10.t14 t30.t10.t15))
% 0.22/0.54 (step t30.t10.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.22/0.54 (step t30.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t30.t10.t16 t30.t10.t17))
% 0.22/0.54 (step t30.t10 (cl (= (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)) (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.22/0.54 (step t30.t11 (cl (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t30.t9 t30.t10))
% 0.22/0.54 (step t30.t12 (cl (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t30.t8 t30.t11))
% 0.22/0.54 (step t30.t13 (cl (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t30.t5 t30.t12 a5))
% 0.22/0.54 (step t30.t14 (cl (not (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) (not (= tptp.mtrue (lambda ((X $$unsorted)) true))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule equiv_pos2)
% 0.22/0.54 (step t30.t15 (cl (= tptp.mtrue tptp.mtrue)) :rule refl)
% 0.22/0.54 (step t30.t16 (cl (= (lambda ((X $$unsorted)) true) (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule all_simplify)
% 0.22/0.54 (step t30.t17 (cl (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) :rule cong :premises (t30.t15 t30.t16))
% 0.22/0.54 (step t30.t18 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule resolution :premises (t30.t14 t30.t17 a1))
% 0.22/0.54 (step t30.t19 (cl (not (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) (not (= tptp.mfalse (lambda ((X $$unsorted)) false))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule equiv_pos2)
% 0.22/0.54 (step t30.t20 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.22/0.54 (step t30.t21 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule all_simplify)
% 0.22/0.54 (step t30.t22 (cl (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule cong :premises (t30.t20 t30.t21))
% 0.22/0.54 (step t30.t23 (cl (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule resolution :premises (t30.t19 t30.t22 a0))
% 0.22/0.54 (step t30.t24 (cl (and (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule resolution :premises (t30.t4 t30.t13 a4 a3 a2 t30.t18 t30.t23))
% 0.22/0.54 (step t30.t25 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t30.t24))
% 0.22/0.54 (step t30.t26 (cl (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t30.t24))
% 0.22/0.54 (step t30.t27 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t30.t28 (cl (= (@ tptp.mimpl U) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U))) :rule cong :premises (t30.t26 t30.t27))
% 0.22/0.54 (step t30.t29 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t30.t30 (cl (= (@ (@ tptp.mimpl U) V) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V))) :rule cong :premises (t30.t28 t30.t29))
% 0.22/0.54 (step t30.t31 (cl (= (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)))) :rule cong :premises (t30.t25 t30.t30))
% 0.22/0.54 (step t30.t32 (cl (= (@ tptp.mimpl V) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V))) :rule cong :premises (t30.t26 t30.t29))
% 0.22/0.54 (step t30.t33 (cl (= (@ (@ tptp.mimpl V) U) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U))) :rule cong :premises (t30.t32 t30.t27))
% 0.22/0.54 (step t30.t34 (cl (= (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)))) :rule cong :premises (t30.t31 t30.t33))
% 0.22/0.54 (step t30.t35 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t30.t36 (cl (= (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) __flatten_var_0))) :rule cong :premises (t30.t34 t30.t35))
% 0.22/0.54 (step t30 (cl (= (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0)) (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) __flatten_var_0)))) :rule bind)
% 0.22/0.54 (step t31 (cl (= (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))) (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) __flatten_var_0))))) :rule cong :premises (t29 t30))
% 0.22/0.54 (step t32 (cl (= tptp.miff tptp.miff)) :rule refl)
% 0.22/0.54 (anchor :step t33 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t33.t1 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t33.t2 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t33.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule refl)
% 0.22/0.54 (step t33.t5 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.22/0.54 (step t33.t6 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t33.t7 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V))) :rule cong :premises (t33.t5 t33.t6))
% 0.22/0.54 (step t33.t8 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.22/0.54 (step t33.t9 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule trans :premises (t33.t7 t33.t8))
% 0.22/0.54 (step t33.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t4 t33.t9))
% 0.22/0.54 (step t33.t11 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) (@ Y U))))) :rule all_simplify)
% 0.22/0.54 (anchor :step t33.t12 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.22/0.54 (step t33.t12.t1 (cl (= Y Y)) :rule refl)
% 0.22/0.54 (step t33.t12.t2 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t33.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) (or (not (@ U U)) (@ V U)))) :rule all_simplify)
% 0.22/0.54 (step t33.t12.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.22/0.54 (step t33.t12.t5 (cl (= (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) (@ Y U)) (and (or (not (@ U U)) (@ V U)) (@ Y U)))) :rule cong :premises (t33.t12.t3 t33.t12.t4))
% 0.22/0.54 (step t33.t12 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ Y U))))) :rule bind)
% 0.22/0.54 (step t33.t13 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ Y U))))) :rule trans :premises (t33.t11 t33.t12))
% 0.22/0.54 (step t33.t14 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ Y U))))) :rule trans :premises (t33.t10 t33.t13))
% 0.22/0.54 (step t33.t15 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.22/0.54 (step t33.t16 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t33.t17 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ V __flatten_var_0))) U))) :rule cong :premises (t33.t15 t33.t16))
% 0.22/0.54 (step t33.t18 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ V __flatten_var_0))) U) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))) :rule all_simplify)
% 0.22/0.54 (step t33.t19 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))) :rule trans :premises (t33.t17 t33.t18))
% 0.22/0.54 (step t33.t20 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ Y U))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0)))))) :rule cong :premises (t33.t14 t33.t19))
% 0.22/0.54 (step t33.t21 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ Y U))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0)))) (lambda ((U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))) U))))) :rule all_simplify)
% 0.22/0.54 (anchor :step t33.t22 :args ((U $$unsorted) (:= U U)))
% 0.22/0.54 (step t33.t22.t1 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t33.t22.t2 (cl (= (or (not (@ U U)) (@ V U)) (or (not (@ U U)) (@ V U)))) :rule refl)
% 0.22/0.54 (step t33.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))) U) (or (not (@ V U)) (@ U U)))) :rule all_simplify)
% 0.22/0.54 (step t33.t22.t4 (cl (= (and (or (not (@ U U)) (@ V U)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))) U)) (and (or (not (@ U U)) (@ V U)) (or (not (@ V U)) (@ U U))))) :rule cong :premises (t33.t22.t2 t33.t22.t3))
% 0.22/0.54 (step t33.t22 (cl (= (lambda ((U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))) U))) (lambda ((U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (or (not (@ V U)) (@ U U)))))) :rule bind)
% 0.22/0.54 (step t33.t23 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (@ Y U))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0)))) (lambda ((U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (or (not (@ V U)) (@ U U)))))) :rule trans :premises (t33.t21 t33.t22))
% 0.22/0.54 (step t33.t24 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) (lambda ((U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (or (not (@ V U)) (@ U U)))))) :rule trans :premises (t33.t20 t33.t23))
% 0.22/0.54 (step t33.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t33.t26 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (or (not (@ V U)) (@ U U)))) __flatten_var_0))) :rule cong :premises (t33.t24 t33.t25))
% 0.22/0.54 (step t33.t27 (cl (= (@ (lambda ((U $$unsorted)) (and (or (not (@ U U)) (@ V U)) (or (not (@ V U)) (@ U U)))) __flatten_var_0) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))) :rule all_simplify)
% 0.22/0.54 (step t33.t28 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) __flatten_var_0) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))) :rule trans :premises (t33.t26 t33.t27))
% 0.22/0.54 (step t33 (cl (= (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) __flatten_var_0)) (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0)))))) :rule bind)
% 0.22/0.54 (step t34 (cl (= (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) U) V)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) V) U)) __flatten_var_0))) (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))))) :rule cong :premises (t32 t33))
% 0.22/0.54 (step t35 (cl (= (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))) (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))))) :rule trans :premises (t31 t34))
% 0.22/0.54 (step t36 (cl (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0)))))) :rule resolution :premises (t28 t35 a6))
% 0.22/0.54 (step t37 (cl (not (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.22/0.54 (step t38 (cl (= tptp.mimpl tptp.mimpl)) :rule refl)
% 0.22/0.54 (anchor :step t39 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t39.t1 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t39.t2 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t39.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t39.t4 (cl (and (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) (not (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) (not (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) (not (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) (not (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) (not (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule and_neg)
% 0.22/0.54 (step t39.t5 (cl (not (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) (not (= tptp.mtrue (lambda ((X $$unsorted)) true))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule equiv_pos2)
% 0.22/0.54 (step t39.t6 (cl (= tptp.mtrue tptp.mtrue)) :rule refl)
% 0.22/0.54 (step t39.t7 (cl (= (lambda ((X $$unsorted)) true) (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule all_simplify)
% 0.22/0.54 (step t39.t8 (cl (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) :rule cong :premises (t39.t6 t39.t7))
% 0.22/0.54 (step t39.t9 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule resolution :premises (t39.t5 t39.t8 a1))
% 0.22/0.54 (step t39.t10 (cl (not (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) (not (= tptp.mfalse (lambda ((X $$unsorted)) false))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule equiv_pos2)
% 0.22/0.54 (step t39.t11 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.22/0.54 (step t39.t12 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule all_simplify)
% 0.22/0.54 (step t39.t13 (cl (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule cong :premises (t39.t11 t39.t12))
% 0.22/0.54 (step t39.t14 (cl (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule resolution :premises (t39.t10 t39.t13 a0))
% 0.22/0.54 (step t39.t15 (cl (and (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule resolution :premises (t39.t4 a4 a3 a2 t39.t9 t39.t14))
% 0.22/0.54 (step t39.t16 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t39.t15))
% 0.22/0.54 (step t39.t17 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t39.t15))
% 0.22/0.54 (step t39.t18 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t39.t19 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t39.t17 t39.t18))
% 0.22/0.54 (step t39.t20 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t39.t16 t39.t19))
% 0.22/0.54 (step t39.t21 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t39.t22 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t39.t20 t39.t21))
% 0.22/0.54 (step t39.t23 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t39.t24 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t39.t22 t39.t23))
% 0.22/0.54 (step t39 (cl (= (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)) (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.22/0.54 (step t40 (cl (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t38 t39))
% 0.22/0.54 (step t41 (cl (= tptp.mimpl tptp.mimpl)) :rule refl)
% 0.22/0.54 (anchor :step t42 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t42.t1 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t42.t2 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t42.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.22/0.54 (step t42.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.22/0.54 (step t42.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))))) :rule cong :premises (t42.t4 t42.t5))
% 0.22/0.54 (step t42.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.22/0.54 (anchor :step t42.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.22/0.54 (step t42.t8.t1 (cl (= Y Y)) :rule refl)
% 0.22/0.54 (step t42.t8.t2 (cl (= U U)) :rule refl)
% 0.22/0.54 (step t42.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.22/0.54 (step t42.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.22/0.54 (step t42.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t8.t3 t42.t8.t4))
% 0.22/0.54 (step t42.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.22/0.54 (step t42.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t7 t42.t8))
% 0.22/0.54 (step t42.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t6 t42.t9))
% 0.22/0.54 (step t42.t11 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t42.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t42.t10 t42.t11))
% 0.22/0.54 (step t42.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.22/0.54 (step t42.t14 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t42.t12 t42.t13))
% 0.22/0.54 (step t42.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t42.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t42.t14 t42.t15))
% 0.22/0.54 (step t42.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.22/0.54 (step t42.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t42.t16 t42.t17))
% 0.22/0.54 (step t42 (cl (= (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)) (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.22/0.54 (step t43 (cl (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t41 t42))
% 0.22/0.54 (step t44 (cl (= (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t40 t43))
% 0.22/0.54 (step t45 (cl (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t37 t44 a5))
% 0.22/0.54 (step t46 (cl (not (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) (not (= tptp.mtrue (lambda ((X $$unsorted)) true))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule equiv_pos2)
% 0.22/0.54 (step t47 (cl (= tptp.mtrue tptp.mtrue)) :rule refl)
% 0.22/0.54 (step t48 (cl (= (lambda ((X $$unsorted)) true) (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule all_simplify)
% 0.22/0.54 (step t49 (cl (= (= tptp.mtrue (lambda ((X $$unsorted)) true)) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)))) :rule cong :premises (t47 t48))
% 0.22/0.54 (step t50 (cl (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true))) :rule resolution :premises (t46 t49 a1))
% 0.22/0.54 (step t51 (cl (not (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) (not (= tptp.mfalse (lambda ((X $$unsorted)) false))) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule equiv_pos2)
% 0.22/0.54 (step t52 (cl (= tptp.mfalse tptp.mfalse)) :rule refl)
% 0.22/0.54 (step t53 (cl (= (lambda ((X $$unsorted)) false) (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule all_simplify)
% 0.22/0.54 (step t54 (cl (= (= tptp.mfalse (lambda ((X $$unsorted)) false)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule cong :premises (t52 t53))
% 0.22/0.54 (step t55 (cl (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false))) :rule resolution :premises (t51 t54 a0))
% 0.22/0.54 (step t56 (cl (and (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))) (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ P W))))) (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ P W)))))) (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))) (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (not (forall ((X tptp.individuals)) (not (@ (@ P X) W)))))) (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))) (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (not (@ P Y))))))) (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y))))) (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)) (or (not (@ V __flatten_var_0)) (@ U __flatten_var_0))))) (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))) (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))) (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))) (= tptp.mtrue (lambda ((BOUND_VARIABLE_1729 $$unsorted)) true)) (= tptp.mfalse (lambda ((BOUND_VARIABLE_1733 $$unsorted)) false)))) :rule resolution :premises (t2 a14 t7 t12 a11 t17 a9 t22 t27 t36 t45 a4 a3 a2 t50 t55))
% 0.22/0.54 (step t57 (cl (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))))) :rule and :premises (t56))
% 0.22/0.54 (step t58 (cl (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t56))
% 0.22/0.54 (step t59 (cl (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))))) :rule and :premises (t56))
% 0.22/0.54 (step t60 (cl (= tptp.r tptp.r)) :rule refl)
% 0.22/0.54 (step t61 (cl (= (@ tptp.mbox tptp.r) (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r))) :rule cong :premises (t59 t60))
% 0.22/0.54 (step t62 (cl (= tptp.a tptp.a)) :rule refl)
% 0.22/0.54 (step t63 (cl (= (@ (@ tptp.mbox tptp.r) tptp.a) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a))) :rule cong :premises (t61 t62))
% 0.22/0.54 (step t64 (cl (= (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)))) :rule cong :premises (t58 t63))
% 0.22/0.54 (step t65 (cl (= (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)))) :rule cong :premises (t64 t63))
% 0.22/0.54 (step t66 (cl (= (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ tptp.mbox tptp.r) tptp.a))) (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a))))) :rule cong :premises (t57 t65))
% 0.22/0.54 (step t67 (cl (= (not (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ tptp.mbox tptp.r) tptp.a)))) (not (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)))))) :rule cong :premises (t66))
% 0.22/0.54 (step t68 (cl (= (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))))) :rule refl)
% 0.22/0.54 (step t69 (cl (= (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule refl)
% 0.22/0.54 (step t70 (cl (= (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.22/0.54 (step t71 (cl (= tptp.a tptp.a)) :rule refl)
% 0.22/0.54 (step t72 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ P Y)))) tptp.a))) :rule cong :premises (t70 t71))
% 0.22/0.54 (step t73 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ P Y)))) tptp.a) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))))) :rule all_simplify)
% 0.22/0.54 (step t74 (cl (= (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))))) :rule trans :premises (t72 t73))
% 0.22/0.54 (step t75 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y))))))) :rule cong :premises (t69 t74))
% 0.22/0.54 (step t76 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.22/0.54 (anchor :step t77 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t77.t1 (cl (= V V)) :rule refl)
% 0.22/0.54 (step t77.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t77.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))) :rule all_simplify)
% 0.22/0.54 (step t77.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))))) :rule cong :premises (t77.t3))
% 0.22/0.54 (step t77.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.22/0.54 (step t77.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t77.t4 t77.t5))
% 0.22/0.54 (step t77 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.22/0.54 (step t78 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t76 t77))
% 0.22/0.54 (step t79 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t75 t78))
% 0.22/0.54 (step t80 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y))))))) :rule cong :premises (t79 t74))
% 0.22/0.54 (step t81 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.22/0.54 (anchor :step t82 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.22/0.54 (step t82.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.22/0.54 (step t82.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))))) :rule refl)
% 0.22/0.54 (step t82.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))) :rule all_simplify)
% 0.22/0.54 (step t82.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))))) :rule cong :premises (t82.t2 t82.t3))
% 0.22/0.54 (step t82 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))))) :rule bind)
% 0.22/0.54 (step t83 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r X) Y)) (@ tptp.a Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))))) :rule trans :premises (t81 t82))
% 0.22/0.54 (step t84 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))))) :rule trans :premises (t80 t83))
% 0.22/0.54 (step t85 (cl (= (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a))) (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))))))) :rule cong :premises (t68 t84))
% 0.22/0.54 (step t86 (cl (= (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))))) (forall ((W $$unsorted)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))) W)))) :rule all_simplify)
% 0.22/0.54 (anchor :step t87 :args ((W $$unsorted) (:= W W)))
% 0.22/0.54 (step t87.t1 (cl (= W W)) :rule refl)
% 0.22/0.54 (step t87.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))) W) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y)))))) :rule all_simplify)
% 0.22/0.54 (step t87 (cl (= (forall ((W $$unsorted)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))) W)) (forall ((W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y))))))) :rule bind)
% 0.22/0.54 (step t88 (cl (= (forall ((W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y))))) (forall ((W $$unsorted)) true))) :rule all_simplify)
% 0.22/0.54 (step t89 (cl (= (forall ((W $$unsorted)) true) true)) :rule all_simplify)
% 0.22/0.54 (step t90 (cl (= (forall ((W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r W) Y)) (@ tptp.a Y))))) true)) :rule trans :premises (t88 t89))
% 0.22/0.55 (step t91 (cl (= (forall ((W $$unsorted)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y))))) W)) true)) :rule trans :premises (t87 t90))
% 0.22/0.55 (step t92 (cl (= (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.r __flatten_var_0) Y)) (@ tptp.a Y)))))) true)) :rule trans :premises (t86 t91))
% 0.22/0.55 (step t93 (cl (= (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a))) true)) :rule trans :premises (t85 t92))
% 0.22/0.55 (step t94 (cl (= (not (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)))) (not true))) :rule cong :premises (t93))
% 0.22/0.55 (step t95 (cl (= (not true) false)) :rule all_simplify)
% 0.22/0.55 (step t96 (cl (= (not (@ (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W))) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)) (@ (@ (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ R X) Y)) (@ P Y)))) tptp.r) tptp.a)))) false)) :rule trans :premises (t94 t95))
% 0.22/0.55 (step t97 (cl (= (not (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.r) tptp.a)) (@ (@ tptp.mbox tptp.r) tptp.a)))) false)) :rule trans :premises (t67 t96))
% 0.22/0.55 (step t98 (cl false) :rule resolution :premises (t1 t97 a15))
% 0.22/0.55 (step t99 (cl (not false)) :rule false)
% 0.22/0.55 (step t100 (cl) :rule resolution :premises (t98 t99))
% 0.22/0.55
% 0.22/0.55 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.hoNr71nlbK/cvc5---1.0.5_4028.smt2
% 0.22/0.55 % cvc5---1.0.5 exiting
% 0.22/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------