%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SYN390^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n020.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 18:25:23 EDT 2024

% Result   : Theorem 0.65s 0.86s
% Output   : Proof 0.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SYN390^4 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue May 28 14:10:39 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TH0
% 0.65/0.86  --- Run --ho-elim --full-saturate-quant at 10...
% 0.65/0.86  % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.0LkT4eVYLE/cvc5---1.0.5_741.smt2
% 0.65/0.86  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.0LkT4eVYLE/cvc5---1.0.5_741.smt2
% 0.65/0.86  (assume a0 (forall ((X $$unsorted)) (@ (@ tptp.irel X) X)))
% 0.65/0.86  (assume a1 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ tptp.irel X) Y) (@ (@ tptp.irel Y) Z)) (@ (@ tptp.irel X) Z))))
% 0.65/0.86  (assume a2 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.65/0.86  (assume a3 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.65/0.86  (assume a4 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.65/0.86  (assume a5 (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.65/0.86  (assume a6 (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))
% 0.65/0.86  (assume a7 (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.65/0.86  (assume a8 (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))
% 0.65/0.86  (assume a9 (= tptp.itrue (lambda ((W $$unsorted)) true)))
% 0.65/0.86  (assume a10 (= tptp.ifalse (@ tptp.inot tptp.itrue)))
% 0.65/0.86  (assume a11 (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))
% 0.65/0.86  (assume a12 (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.65/0.86  (assume a13 (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.65/0.86  (assume a14 (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))
% 0.65/0.86  (assume a15 (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))
% 0.65/0.86  (assume a16 (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))
% 0.65/0.86  (assume a17 (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.65/0.86  (assume a18 (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.65/0.86  (assume a19 (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.65/0.86  (assume a20 (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.65/0.86  (assume a21 (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ tptp.iatom tptp.p)))))
% 0.65/0.86  (assume a22 true)
% 0.65/0.86  (step t1 (cl (not (= (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ tptp.iatom tptp.p)))) false)) (not (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ tptp.iatom tptp.p))))) false) :rule equiv_pos2)
% 0.65/0.86  (step t2 (cl (and (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))) (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))) (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))) (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))) (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W)))))) (not (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) (not (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) (not (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))))) (not (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))))) (not (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.86  (step t3 (cl (not (= (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))) (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))))) (not (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W)))))) (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) :rule equiv_pos2)
% 0.65/0.86  (step t4 (cl (= tptp.icountersatisfiable tptp.icountersatisfiable)) :rule refl)
% 0.65/0.86  (anchor :step t5 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi)))
% 0.65/0.86  (step t5.t1 (cl (= Phi Phi)) :rule refl)
% 0.65/0.86  (step t5.t2 (cl (= (exists ((W $$unsorted)) (not (@ Phi W))) (not (forall ((W $$unsorted)) (@ Phi W))))) :rule all_simplify)
% 0.65/0.86  (step t5 (cl (= (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W)))) (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) :rule bind)
% 0.65/0.86  (step t6 (cl (= (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))) (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))))) :rule cong :premises (t4 t5))
% 0.65/0.86  (step t7 (cl (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W)))))) :rule resolution :premises (t3 t6 a19))
% 0.65/0.86  (step t8 (cl (not (= (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))) (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))))) (not (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W))))) (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) :rule equiv_pos2)
% 0.65/0.86  (step t9 (cl (= tptp.isatisfiable tptp.isatisfiable)) :rule refl)
% 0.65/0.86  (anchor :step t10 :args ((Phi (-> $$unsorted Bool)) (:= Phi Phi)))
% 0.65/0.86  (step t10.t1 (cl (= Phi Phi)) :rule refl)
% 0.65/0.86  (step t10.t2 (cl (= (exists ((W $$unsorted)) (@ Phi W)) (not (forall ((W $$unsorted)) (not (@ Phi W)))))) :rule all_simplify)
% 0.65/0.86  (step t10 (cl (= (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) :rule bind)
% 0.65/0.86  (step t11 (cl (= (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))) (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))))) :rule cong :premises (t9 t10))
% 0.65/0.86  (step t12 (cl (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W))))))) :rule resolution :premises (t8 t11 a18))
% 0.65/0.86  (step t13 (cl (not (= (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))) (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))))) (not (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0)))) (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))))) :rule equiv_pos2)
% 0.65/0.86  (step t14 (cl (= tptp.ixor tptp.ixor)) :rule refl)
% 0.65/0.86  (anchor :step t15 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.86  (step t15.t1 (cl (= P P)) :rule refl)
% 0.65/0.86  (step t15.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.86  (step t15.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.86  (step t15.t4 (cl (and (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t5 (cl (not (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))))) (not (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0)))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t6 (cl (= tptp.iequiv tptp.iequiv)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t4 (cl (and (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t5 (cl (not (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t6 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t4 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t5 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t6 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t9 t15.t7.t7.t7.t7.t7.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t8 t15.t7.t7.t7.t7.t7.t11 a9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t5 t15.t7.t7.t7.t7.t7.t15.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t15.t4 t15.t7.t7.t7.t7.t7.t15.t7 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t15.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t15.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t11.t7 t15.t7.t7.t7.t7.t7.t15.t11.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t7.t15.t11.t6 t15.t7.t7.t7.t7.t7.t15.t11.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t11.t10 t15.t7.t7.t7.t7.t7.t15.t11.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t7.t15.t11.t12 t15.t7.t7.t7.t7.t7.t15.t11.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t7.t7.t7.t15.t10 t15.t7.t7.t7.t7.t7.t15.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t14.t4 t15.t7.t7.t7.t7.t7.t15.t14.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t14.t8.t3 t15.t7.t7.t7.t7.t7.t15.t14.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t15.t14.t7 t15.t7.t7.t7.t7.t7.t15.t14.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t7.t15.t14.t6 t15.t7.t7.t7.t7.t7.t15.t14.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t14.t10 t15.t7.t7.t7.t7.t7.t15.t14.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.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 (t15.t7.t7.t7.t7.t7.t15.t14.t12 t15.t7.t7.t7.t7.t7.t15.t14.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.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 (t15.t7.t7.t7.t7.t7.t15.t14.t14 t15.t7.t7.t7.t7.t7.t15.t14.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t7.t15.t14.t16 t15.t7.t7.t7.t7.t7.t15.t14.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t13 t15.t7.t7.t7.t7.t7.t15.t14))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t15.t12 t15.t7.t7.t7.t7.t7.t15.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t15.t9 t15.t7.t7.t7.t7.t7.t15.t16 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t15.t3 a7 t15.t7.t7.t7.t7.t7.t15.t8 t15.t7.t7.t7.t7.t7.t15.t17 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t15.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t15.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t20 t15.t7.t7.t7.t7.t7.t15.t21))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t19 t15.t7.t7.t7.t7.t7.t15.t22))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t15.t23 t15.t7.t7.t7.t7.t7.t15.t24))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t14 t15.t7.t7.t7.t7.t7.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t18.t3 t15.t7.t7.t7.t7.t7.t18.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t18.t7.t2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t18.t6 t15.t7.t7.t7.t7.t7.t18.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t18.t5 t15.t7.t7.t7.t7.t7.t18.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t18.t9 t15.t7.t7.t7.t7.t7.t18.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t18.t11 t15.t7.t7.t7.t7.t7.t18.t12))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t17 t15.t7.t7.t7.t7.t7.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t16 t15.t7.t7.t7.t7.t7.t19))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t13 t15.t7.t7.t7.t7.t7.t20 a8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t23 t15.t7.t7.t7.t7.t7.t24))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t22 t15.t7.t7.t7.t7.t7.t25 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t29.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t29.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t29.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t29.t7 t15.t7.t7.t7.t7.t7.t29.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t29.t6 t15.t7.t7.t7.t7.t7.t29.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t7.t29.t10 t15.t7.t7.t7.t7.t7.t29.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t29.t12 t15.t7.t7.t7.t7.t7.t29.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t28 t15.t7.t7.t7.t7.t7.t29))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t7.t32.t4 t15.t7.t7.t7.t7.t7.t32.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t32.t8.t3 t15.t7.t7.t7.t7.t7.t32.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.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 (t15.t7.t7.t7.t7.t7.t32.t7 t15.t7.t7.t7.t7.t7.t32.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t32.t6 t15.t7.t7.t7.t7.t7.t32.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t7.t32.t10 t15.t7.t7.t7.t7.t7.t32.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t32.t12 t15.t7.t7.t7.t7.t7.t32.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t32.t14 t15.t7.t7.t7.t7.t7.t32.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t32.t16 t15.t7.t7.t7.t7.t7.t32.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t31 t15.t7.t7.t7.t7.t7.t32))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t30 t15.t7.t7.t7.t7.t7.t33))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t27 t15.t7.t7.t7.t7.t7.t34 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t7 t15.t7.t7.t7.t7.t7.t12 t15.t7.t7.t7.t7.t7.t21 a7 t15.t7.t7.t7.t7.t7.t26 t15.t7.t7.t7.t7.t7.t35 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t36))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t7.t7.t7.t36))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t37 t15.t7.t7.t7.t7.t7.t38))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t6 t15.t7.t7.t7.t7.t7.t39))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t43.t2.t2 t15.t7.t7.t7.t7.t7.t43.t2.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t7.t7.t7.t43.t2.t4 t15.t7.t7.t7.t7.t7.t43.t2.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t7.t7.t7.t43.t2 t15.t7.t7.t7.t7.t7.t43.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t43.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t7.t7.t7.t43.t5 t15.t7.t7.t7.t7.t7.t43.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t43 t15.t7.t7.t7.t7.t7.t44))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t42 t15.t7.t7.t7.t7.t7.t45))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t41 t15.t7.t7.t7.t7.t7.t46))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t7.t7.t7.t40 t15.t7.t7.t7.t7.t7.t47))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t5 t15.t7.t7.t7.t7.t7.t48 a10))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t7.t4 t15.t7.t7.t7.t7.t7.t49 t15.t7.t7.t7.t7.t7.t12 t15.t7.t7.t7.t7.t7.t21 a7 t15.t7.t7.t7.t7.t7.t26 t15.t7.t7.t7.t7.t7.t35 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t7.t7.t50))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t51 t15.t7.t7.t7.t7.t7.t52))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t53 t15.t7.t7.t7.t7.t7.t54))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t7.t55 t15.t7.t7.t7.t7.t7.t56))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t7.t6 t15.t7.t7.t7.t7.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t7.t7.t7.t10.t4 t15.t7.t7.t7.t7.t10.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t7.t7.t7.t10.t6 t15.t7.t7.t7.t7.t10.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t10.t8 t15.t7.t7.t7.t7.t10.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t7.t7.t10.t10 t15.t7.t7.t7.t7.t10.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t7.t9 t15.t7.t7.t7.t7.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t7.t8 t15.t7.t7.t7.t7.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t7.t5 t15.t7.t7.t7.t7.t12 a11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t7.t18 t15.t7.t7.t7.t7.t19))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t7.t7.t17 t15.t7.t7.t7.t7.t20 a9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t5 t15.t7.t7.t7.t7.t24.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t24.t4 t15.t7.t7.t7.t7.t24.t7 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t24.t11.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t7.t24.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t7.t24.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t11.t7 t15.t7.t7.t7.t7.t24.t11.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t11.t6 t15.t7.t7.t7.t7.t24.t11.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t24.t11.t10 t15.t7.t7.t7.t7.t24.t11.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t11.t12 t15.t7.t7.t7.t7.t24.t11.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t10 t15.t7.t7.t7.t7.t24.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t24.t14.t4 t15.t7.t7.t7.t7.t24.t14.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t14.t8.t3 t15.t7.t7.t7.t7.t24.t14.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.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 (t15.t7.t7.t7.t7.t24.t14.t7 t15.t7.t7.t7.t7.t24.t14.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t7.t24.t14.t6 t15.t7.t7.t7.t7.t24.t14.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t24.t14.t10 t15.t7.t7.t7.t7.t24.t14.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t7.t7.t24.t14.t12 t15.t7.t7.t7.t7.t24.t14.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t14.t14 t15.t7.t7.t7.t7.t24.t14.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t7.t7.t24.t14.t16 t15.t7.t7.t7.t7.t24.t14.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t13 t15.t7.t7.t7.t7.t24.t14))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t7.t24.t12 t15.t7.t7.t7.t7.t24.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t7.t24.t9 t15.t7.t7.t7.t7.t24.t16 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t24.t3 a7 t15.t7.t7.t7.t7.t24.t8 t15.t7.t7.t7.t7.t24.t17 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t7.t24.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t7.t7.t24.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t20 t15.t7.t7.t7.t7.t24.t21))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t19 t15.t7.t7.t7.t7.t24.t22))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t24.t23 t15.t7.t7.t7.t7.t24.t24))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t7.t23 t15.t7.t7.t7.t7.t24))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t7.t27.t3 t15.t7.t7.t7.t7.t27.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t7.t7.t27.t7.t2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t7.t27.t6 t15.t7.t7.t7.t7.t27.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t7.t27.t5 t15.t7.t7.t7.t7.t27.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t27.t9 t15.t7.t7.t7.t7.t27.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t7.t7.t27.t11 t15.t7.t7.t7.t7.t27.t12))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t7.t7.t26 t15.t7.t7.t7.t7.t27))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t7.t7.t25 t15.t7.t7.t7.t7.t28))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t7.t7.t22 t15.t7.t7.t7.t7.t29 a8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t7.t32 t15.t7.t7.t7.t7.t33))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t31 t15.t7.t7.t7.t7.t34 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.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))))) (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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t38.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t7.t38.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t7.t38.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t7.t38.t7 t15.t7.t7.t7.t7.t38.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t38.t6 t15.t7.t7.t7.t7.t38.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t7.t7.t38.t10 t15.t7.t7.t7.t7.t38.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t38.t12 t15.t7.t7.t7.t7.t38.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t7.t7.t37 t15.t7.t7.t7.t7.t38))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t7.t7.t41.t4 t15.t7.t7.t7.t7.t41.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t7.t41.t8.t3 t15.t7.t7.t7.t7.t41.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t7.t41.t7 t15.t7.t7.t7.t7.t41.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t41.t6 t15.t7.t7.t7.t7.t41.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t7.t7.t41.t10 t15.t7.t7.t7.t7.t41.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.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 (t15.t7.t7.t7.t7.t41.t12 t15.t7.t7.t7.t7.t41.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.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 (t15.t7.t7.t7.t7.t41.t14 t15.t7.t7.t7.t7.t41.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t7.t41.t16 t15.t7.t7.t7.t7.t41.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t7.t40 t15.t7.t7.t7.t7.t41))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t7.t39 t15.t7.t7.t7.t7.t42))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t7.t36 t15.t7.t7.t7.t7.t43 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t16 t15.t7.t7.t7.t7.t21 t15.t7.t7.t7.t7.t30 a7 t15.t7.t7.t7.t7.t35 t15.t7.t7.t7.t7.t44 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t7.t7.t45))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t7.t7.t45))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t7.t46 t15.t7.t7.t7.t7.t47))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t7.t7.t15 t15.t7.t7.t7.t7.t48))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t7.t7.t52.t2.t2 t15.t7.t7.t7.t7.t52.t2.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t7.t7.t52.t2.t4 t15.t7.t7.t7.t7.t52.t2.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t7.t7.t52.t2 t15.t7.t7.t7.t7.t52.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t7.t7.t52.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t7.t7.t52.t5 t15.t7.t7.t7.t7.t52.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t7.t52 t15.t7.t7.t7.t7.t53))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t7.t51 t15.t7.t7.t7.t7.t54))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t7.t7.t50 t15.t7.t7.t7.t7.t55))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t7.t7.t49 t15.t7.t7.t7.t7.t56))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t7.t7.t14 t15.t7.t7.t7.t7.t57 a10))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t7.t4 t15.t7.t7.t7.t7.t13 t15.t7.t7.t7.t7.t58 t15.t7.t7.t7.t7.t21 t15.t7.t7.t7.t7.t30 a7 t15.t7.t7.t7.t7.t35 t15.t7.t7.t7.t7.t44 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t7.t59))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t7.t7.t59))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t62 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t7.t7.t61 t15.t7.t7.t7.t7.t62))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t7.t7.t60 t15.t7.t7.t7.t7.t63))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t65 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t7.t7.t7.t7.t61 t15.t7.t7.t7.t7.t65))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t7.t7.t7.t7.t64 t15.t7.t7.t7.t7.t66))
% 0.65/0.87  (step t15.t7.t7.t7.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t7.t67 t15.t7.t7.t7.t7.t68))
% 0.65/0.87  (step t15.t7.t7.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t6 t15.t7.t7.t7.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.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)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t10.t4 t15.t7.t7.t7.t10.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t10.t8.t3 t15.t7.t7.t7.t10.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t10.t7 t15.t7.t7.t7.t10.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t10.t6 t15.t7.t7.t7.t10.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t7.t7.t7.t10.t10 t15.t7.t7.t7.t10.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t7.t7.t7.t10.t14.t2 t15.t7.t7.t7.t10.t14.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t7.t7.t10.t13 t15.t7.t7.t7.t10.t14))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t7.t7.t10.t12 t15.t7.t7.t7.t10.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t10.t16 t15.t7.t7.t7.t10.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t7.t7.t7.t10.t18 t15.t7.t7.t7.t10.t19))
% 0.65/0.87  (step t15.t7.t7.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t7.t7.t7.t9 t15.t7.t7.t7.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t7.t7.t7.t8 t15.t7.t7.t7.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t7.t7.t7.t5 t15.t7.t7.t7.t12 a12))
% 0.65/0.87  (step t15.t7.t7.t7.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t16.t9 t15.t7.t7.t7.t16.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t7.t16.t8 t15.t7.t7.t7.t16.t11 a9))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t5 t15.t7.t7.t7.t16.t15.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t16.t15.t4 t15.t7.t7.t7.t16.t15.t7 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t7.t16.t15.t11.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t16.t15.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t16.t15.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t11.t7 t15.t7.t7.t7.t16.t15.t11.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t16.t15.t11.t6 t15.t7.t7.t7.t16.t15.t11.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t11.t10 t15.t7.t7.t7.t16.t15.t11.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t16.t15.t11.t12 t15.t7.t7.t7.t16.t15.t11.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t7.t16.t15.t10 t15.t7.t7.t7.t16.t15.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t14.t4 t15.t7.t7.t7.t16.t15.t14.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t14.t8.t3 t15.t7.t7.t7.t16.t15.t14.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t16.t15.t14.t7 t15.t7.t7.t7.t16.t15.t14.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t16.t15.t14.t6 t15.t7.t7.t7.t16.t15.t14.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t14.t10 t15.t7.t7.t7.t16.t15.t14.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.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 (t15.t7.t7.t7.t16.t15.t14.t12 t15.t7.t7.t7.t16.t15.t14.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.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 (t15.t7.t7.t7.t16.t15.t14.t14 t15.t7.t7.t7.t16.t15.t14.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t16.t15.t14.t16 t15.t7.t7.t7.t16.t15.t14.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t13 t15.t7.t7.t7.t16.t15.t14))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t16.t15.t12 t15.t7.t7.t7.t16.t15.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t16.t15.t9 t15.t7.t7.t7.t16.t15.t16 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t16.t15.t3 a7 t15.t7.t7.t7.t16.t15.t8 t15.t7.t7.t7.t16.t15.t17 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t16.t15.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t7.t16.t15.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t20 t15.t7.t7.t7.t16.t15.t21))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t19 t15.t7.t7.t7.t16.t15.t22))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t16.t15.t23 t15.t7.t7.t7.t16.t15.t24))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t16.t14 t15.t7.t7.t7.t16.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t16.t18.t3 t15.t7.t7.t7.t16.t18.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t7.t16.t18.t7.t2))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t16.t18.t6 t15.t7.t7.t7.t16.t18.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t16.t18.t5 t15.t7.t7.t7.t16.t18.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t16.t18.t9 t15.t7.t7.t7.t16.t18.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t7.t16.t18.t11 t15.t7.t7.t7.t16.t18.t12))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t7.t16.t17 t15.t7.t7.t7.t16.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t7.t16.t16 t15.t7.t7.t7.t16.t19))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t7.t16.t13 t15.t7.t7.t7.t16.t20 a8))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t16.t23 t15.t7.t7.t7.t16.t24))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t16.t22 t15.t7.t7.t7.t16.t25 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t16.t29.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t16.t29.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t16.t29.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t16.t29.t7 t15.t7.t7.t7.t16.t29.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t7.t16.t29.t6 t15.t7.t7.t7.t16.t29.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t16.t29.t10 t15.t7.t7.t7.t16.t29.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t16.t29.t12 t15.t7.t7.t7.t16.t29.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t29 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t16.t28 t15.t7.t7.t7.t16.t29))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.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)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t16.t32.t4 t15.t7.t7.t7.t16.t32.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t16.t32.t8.t3 t15.t7.t7.t7.t16.t32.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.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 (t15.t7.t7.t7.t16.t32.t7 t15.t7.t7.t7.t16.t32.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t16.t32.t6 t15.t7.t7.t7.t16.t32.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t16.t32.t10 t15.t7.t7.t7.t16.t32.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t7.t16.t32.t12 t15.t7.t7.t7.t16.t32.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t16.t32.t14 t15.t7.t7.t7.t16.t32.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t7.t16.t32.t16 t15.t7.t7.t7.t16.t32.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t32 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t16.t31 t15.t7.t7.t7.t16.t32))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t16.t30 t15.t7.t7.t7.t16.t33))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t16.t27 t15.t7.t7.t7.t16.t34 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t7.t16.t7 t15.t7.t7.t7.t16.t12 t15.t7.t7.t7.t16.t21 a7 t15.t7.t7.t7.t16.t26 t15.t7.t7.t7.t16.t35 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t7.t16.t36))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t7.t16.t36))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t16.t37 t15.t7.t7.t7.t16.t38))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t7.t16.t6 t15.t7.t7.t7.t16.t39))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t7.t16.t43.t2.t2 t15.t7.t7.t7.t16.t43.t2.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t7.t16.t43.t2.t4 t15.t7.t7.t7.t16.t43.t2.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t7.t16.t43.t2 t15.t7.t7.t7.t16.t43.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t7.t16.t43.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t7.t16.t43.t5 t15.t7.t7.t7.t16.t43.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t16.t43 t15.t7.t7.t7.t16.t44))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t16.t42 t15.t7.t7.t7.t16.t45))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t7.t16.t41 t15.t7.t7.t7.t16.t46))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t7.t16.t40 t15.t7.t7.t7.t16.t47))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t7.t16.t5 t15.t7.t7.t7.t16.t48 a10))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t16.t4 t15.t7.t7.t7.t16.t49 t15.t7.t7.t7.t16.t12 t15.t7.t7.t7.t16.t21 a7 t15.t7.t7.t7.t16.t26 t15.t7.t7.t7.t16.t35 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t16.t50))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t52 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t7.t7.t16.t51 t15.t7.t7.t7.t16.t52))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t54 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t7.t7.t16.t53 t15.t7.t7.t7.t16.t54))
% 0.65/0.87  (step t15.t7.t7.t7.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t16.t55 t15.t7.t7.t7.t16.t56))
% 0.65/0.87  (step t15.t7.t7.t7.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t15 t15.t7.t7.t7.t16))
% 0.65/0.87  (step t15.t7.t7.t7.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t19.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t5 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t7.t7.t19.t4 t15.t7.t7.t7.t19.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t7.t7.t19.t6 t15.t7.t7.t7.t19.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t19.t8 t15.t7.t7.t7.t19.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t7.t19.t10 t15.t7.t7.t7.t19.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t18 t15.t7.t7.t7.t19))
% 0.65/0.87  (step t15.t7.t7.t7.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t17 t15.t7.t7.t7.t20))
% 0.65/0.87  (step t15.t7.t7.t7.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t14 t15.t7.t7.t7.t21 a11))
% 0.65/0.87  (step t15.t7.t7.t7.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t27 t15.t7.t7.t7.t28))
% 0.65/0.87  (step t15.t7.t7.t7.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t7.t26 t15.t7.t7.t7.t29 a9))
% 0.65/0.87  (step t15.t7.t7.t7.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t33.t5 t15.t7.t7.t7.t33.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t33.t4 t15.t7.t7.t7.t33.t7 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t33.t11.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t33.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t33.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t33.t11.t7 t15.t7.t7.t7.t33.t11.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t7.t33.t11.t6 t15.t7.t7.t7.t33.t11.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t33.t11.t10 t15.t7.t7.t7.t33.t11.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t33.t11.t12 t15.t7.t7.t7.t33.t11.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t11 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t33.t10 t15.t7.t7.t7.t33.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.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)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t33.t14.t4 t15.t7.t7.t7.t33.t14.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t33.t14.t8.t3 t15.t7.t7.t7.t33.t14.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.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 (t15.t7.t7.t7.t33.t14.t7 t15.t7.t7.t7.t33.t14.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t33.t14.t6 t15.t7.t7.t7.t33.t14.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t33.t14.t10 t15.t7.t7.t7.t33.t14.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t7.t33.t14.t12 t15.t7.t7.t7.t33.t14.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t33.t14.t14 t15.t7.t7.t7.t33.t14.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t7.t33.t14.t16 t15.t7.t7.t7.t33.t14.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t14 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t33.t13 t15.t7.t7.t7.t33.t14))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t33.t12 t15.t7.t7.t7.t33.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t33.t9 t15.t7.t7.t7.t33.t16 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t7.t33.t3 a7 t15.t7.t7.t7.t33.t8 t15.t7.t7.t7.t33.t17 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t33.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t7.t33.t18))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t21 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t7.t33.t20 t15.t7.t7.t7.t33.t21))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t7.t33.t19 t15.t7.t7.t7.t33.t22))
% 0.65/0.87  (step t15.t7.t7.t7.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t33.t23 t15.t7.t7.t7.t33.t24))
% 0.65/0.87  (step t15.t7.t7.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t7.t32 t15.t7.t7.t7.t33))
% 0.65/0.87  (step t15.t7.t7.t7.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t36.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t36.t3 t15.t7.t7.t7.t36.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t7.t36.t7.t2))
% 0.65/0.87  (step t15.t7.t7.t7.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t36.t6 t15.t7.t7.t7.t36.t7))
% 0.65/0.87  (step t15.t7.t7.t7.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t7.t36.t5 t15.t7.t7.t7.t36.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t36.t9 t15.t7.t7.t7.t36.t10))
% 0.65/0.87  (step t15.t7.t7.t7.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t7.t36.t11 t15.t7.t7.t7.t36.t12))
% 0.65/0.87  (step t15.t7.t7.t7.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t7.t35 t15.t7.t7.t7.t36))
% 0.65/0.87  (step t15.t7.t7.t7.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t7.t34 t15.t7.t7.t7.t37))
% 0.65/0.87  (step t15.t7.t7.t7.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t7.t31 t15.t7.t7.t7.t38 a8))
% 0.65/0.87  (step t15.t7.t7.t7.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t7.t42.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t42.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t7.t41 t15.t7.t7.t7.t42))
% 0.65/0.87  (step t15.t7.t7.t7.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t7.t40 t15.t7.t7.t7.t43 a6))
% 0.65/0.87  (step t15.t7.t7.t7.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t7.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t47.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t47.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t47.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))))) (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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t7.t47.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t7.t47.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t7.t47.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t7.t47.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t47.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t7.t47.t7 t15.t7.t7.t7.t47.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t47.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t47.t6 t15.t7.t7.t7.t47.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t47.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t47.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t7.t47.t10 t15.t7.t7.t7.t47.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t47.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t47.t12 t15.t7.t7.t7.t47.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t47 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t7.t46 t15.t7.t7.t7.t47))
% 0.65/0.87  (step t15.t7.t7.t7.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t50.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t7.t50.t4 t15.t7.t7.t7.t50.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t7.t50.t8.t3 t15.t7.t7.t7.t50.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t7.t50.t7 t15.t7.t7.t7.t50.t8))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t50.t6 t15.t7.t7.t7.t50.t9))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t7.t50.t10 t15.t7.t7.t7.t50.t11))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t50.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 (t15.t7.t7.t7.t50.t12 t15.t7.t7.t7.t50.t13))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t50.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 (t15.t7.t7.t7.t50.t14 t15.t7.t7.t7.t50.t15))
% 0.65/0.87  (step t15.t7.t7.t7.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t7.t50.t16 t15.t7.t7.t7.t50.t17))
% 0.65/0.87  (step t15.t7.t7.t7.t50 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t51 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t7.t49 t15.t7.t7.t7.t50))
% 0.65/0.87  (step t15.t7.t7.t7.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t7.t48 t15.t7.t7.t7.t51))
% 0.65/0.87  (step t15.t7.t7.t7.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t7.t45 t15.t7.t7.t7.t52 a5))
% 0.65/0.87  (step t15.t7.t7.t7.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t7.t25 t15.t7.t7.t7.t30 t15.t7.t7.t7.t39 a7 t15.t7.t7.t7.t44 t15.t7.t7.t7.t53 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t7.t54))
% 0.65/0.87  (step t15.t7.t7.t7.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t7.t54))
% 0.65/0.87  (step t15.t7.t7.t7.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t7.t55 t15.t7.t7.t7.t56))
% 0.65/0.87  (step t15.t7.t7.t7.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t7.t24 t15.t7.t7.t7.t57))
% 0.65/0.87  (step t15.t7.t7.t7.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t7.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t7.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.65/0.87  (step t15.t7.t7.t7.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t7.t61.t2.t2 t15.t7.t7.t7.t61.t2.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t7.t61.t2.t4 t15.t7.t7.t7.t61.t2.t5))
% 0.65/0.87  (step t15.t7.t7.t7.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t7.t61.t2 t15.t7.t7.t7.t61.t3))
% 0.65/0.87  (step t15.t7.t7.t7.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t7.t61.t4))
% 0.65/0.87  (step t15.t7.t7.t7.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t7.t61.t5 t15.t7.t7.t7.t61.t6))
% 0.65/0.87  (step t15.t7.t7.t7.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t7.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t7.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t61 t15.t7.t7.t7.t62))
% 0.65/0.87  (step t15.t7.t7.t7.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t7.t60 t15.t7.t7.t7.t63))
% 0.65/0.87  (step t15.t7.t7.t7.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t7.t59 t15.t7.t7.t7.t64))
% 0.65/0.87  (step t15.t7.t7.t7.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t7.t58 t15.t7.t7.t7.t65))
% 0.65/0.87  (step t15.t7.t7.t7.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t7.t23 t15.t7.t7.t7.t66 a10))
% 0.65/0.87  (step t15.t7.t7.t7.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t7.t4 t15.t7.t7.t7.t13 t15.t7.t7.t7.t22 t15.t7.t7.t7.t67 t15.t7.t7.t7.t30 t15.t7.t7.t7.t39 a7 t15.t7.t7.t7.t44 t15.t7.t7.t7.t53 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t7.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t15.t7.t7.t7.t68))
% 0.65/0.87  (step t15.t7.t7.t7.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t7.t68))
% 0.65/0.87  (step t15.t7.t7.t7.t71 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t7.t70 t15.t7.t7.t7.t71))
% 0.65/0.87  (step t15.t7.t7.t7.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t7.t69 t15.t7.t7.t7.t72))
% 0.65/0.87  (step t15.t7.t7.t7.t74 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t7.t7.t7.t70 t15.t7.t7.t7.t74))
% 0.65/0.87  (step t15.t7.t7.t7.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t7.t7.t7.t73 t15.t7.t7.t7.t75))
% 0.65/0.87  (step t15.t7.t7.t7.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t7.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t7.t76 t15.t7.t7.t7.t77))
% 0.65/0.87  (step t15.t7.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t8 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t6 t15.t7.t7.t7))
% 0.65/0.87  (step t15.t7.t7.t9 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t4 (cl (= (lambda ((U (-> $$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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t10.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t10.t4 t15.t7.t7.t10.t5))
% 0.65/0.87  (step t15.t7.t7.t10.t7 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t10.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t10.t8.t1 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t10.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t10.t8.t3))
% 0.65/0.87  (step t15.t7.t7.t10.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t15.t7.t7.t10.t8.t4 t15.t7.t7.t10.t8.t5))
% 0.65/0.87  (step t15.t7.t7.t10.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t10.t9 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t7.t7.t10.t7 t15.t7.t7.t10.t8))
% 0.65/0.87  (step t15.t7.t7.t10.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t7.t7.t10.t6 t15.t7.t7.t10.t9))
% 0.65/0.87  (step t15.t7.t7.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t7.t7.t10.t10 t15.t7.t7.t10.t11))
% 0.65/0.87  (step t15.t7.t7.t10.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t10.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t10.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t10.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t15.t7.t7.t10.t14.t2 t15.t7.t7.t10.t14.t3))
% 0.65/0.87  (step t15.t7.t7.t10.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t10.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t7.t10.t13 t15.t7.t7.t10.t14))
% 0.65/0.87  (step t15.t7.t7.t10.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t7.t10.t12 t15.t7.t7.t10.t15))
% 0.65/0.87  (step t15.t7.t7.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t10.t16 t15.t7.t7.t10.t17))
% 0.65/0.87  (step t15.t7.t7.t10.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t10.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t7.t7.t10.t18 t15.t7.t7.t10.t19))
% 0.65/0.87  (step t15.t7.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t11 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t7.t7.t9 t15.t7.t7.t10))
% 0.65/0.87  (step t15.t7.t7.t12 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t7.t7.t8 t15.t7.t7.t11))
% 0.65/0.87  (step t15.t7.t7.t13 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t7.t7.t5 t15.t7.t7.t12 a13))
% 0.65/0.87  (step t15.t7.t7.t14 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t15 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t16.t7.t9 t15.t7.t7.t16.t7.t10))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t16.t7.t8 t15.t7.t7.t16.t7.t11 a9))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t5 t15.t7.t7.t16.t7.t15.t6))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t16.t7.t15.t4 t15.t7.t7.t16.t7.t15.t7 a6))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t16.t7.t15.t11.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t16.t7.t15.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t16.t7.t15.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t11.t7 t15.t7.t7.t16.t7.t15.t11.t8))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t11.t6 t15.t7.t7.t16.t7.t15.t11.t9))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t7.t15.t11.t10 t15.t7.t7.t16.t7.t15.t11.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t11.t12 t15.t7.t7.t16.t7.t15.t11.t13))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t10 t15.t7.t7.t16.t7.t15.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.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)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t7.t15.t14.t4 t15.t7.t7.t16.t7.t15.t14.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t14.t8.t3 t15.t7.t7.t16.t7.t15.t14.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.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 (t15.t7.t7.t16.t7.t15.t14.t7 t15.t7.t7.t16.t7.t15.t14.t8))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t16.t7.t15.t14.t6 t15.t7.t7.t16.t7.t15.t14.t9))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t7.t15.t14.t10 t15.t7.t7.t16.t7.t15.t14.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t16.t7.t15.t14.t12 t15.t7.t7.t16.t7.t15.t14.t13))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t14.t14 t15.t7.t7.t16.t7.t15.t14.t15))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t16.t7.t15.t14.t16 t15.t7.t7.t16.t7.t15.t14.t17))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t13 t15.t7.t7.t16.t7.t15.t14))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t16.t7.t15.t12 t15.t7.t7.t16.t7.t15.t15))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t16.t7.t15.t9 t15.t7.t7.t16.t7.t15.t16 a5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t16.t7.t15.t3 a7 t15.t7.t7.t16.t7.t15.t8 t15.t7.t7.t16.t7.t15.t17 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t16.t7.t15.t18))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t16.t7.t15.t18))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t20 t15.t7.t7.t16.t7.t15.t21))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t19 t15.t7.t7.t16.t7.t15.t22))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t7.t15.t23 t15.t7.t7.t16.t7.t15.t24))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t16.t7.t14 t15.t7.t7.t16.t7.t15))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t16.t7.t18.t3 t15.t7.t7.t16.t7.t18.t4))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t16.t7.t18.t7.t2))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t16.t7.t18.t6 t15.t7.t7.t16.t7.t18.t7))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t16.t7.t18.t5 t15.t7.t7.t16.t7.t18.t8))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t7.t18.t9 t15.t7.t7.t16.t7.t18.t10))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t16.t7.t18.t11 t15.t7.t7.t16.t7.t18.t12))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t16.t7.t17 t15.t7.t7.t16.t7.t18))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t16.t7.t16 t15.t7.t7.t16.t7.t19))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t16.t7.t13 t15.t7.t7.t16.t7.t20 a8))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t16.t7.t23 t15.t7.t7.t16.t7.t24))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t16.t7.t22 t15.t7.t7.t16.t7.t25 a6))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t16.t7.t29.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t16.t7.t29.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t16.t7.t29.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t16.t7.t29.t7 t15.t7.t7.t16.t7.t29.t8))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t7.t29.t6 t15.t7.t7.t16.t7.t29.t9))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t16.t7.t29.t10 t15.t7.t7.t16.t7.t29.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t7.t29.t12 t15.t7.t7.t16.t7.t29.t13))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t16.t7.t28 t15.t7.t7.t16.t7.t29))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t16.t7.t32.t4 t15.t7.t7.t16.t7.t32.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t16.t7.t32.t8.t3 t15.t7.t7.t16.t7.t32.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t16.t7.t32.t7 t15.t7.t7.t16.t7.t32.t8))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t7.t32.t6 t15.t7.t7.t16.t7.t32.t9))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t16.t7.t32.t10 t15.t7.t7.t16.t7.t32.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.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 (t15.t7.t7.t16.t7.t32.t12 t15.t7.t7.t16.t7.t32.t13))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.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 (t15.t7.t7.t16.t7.t32.t14 t15.t7.t7.t16.t7.t32.t15))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t7.t32.t16 t15.t7.t7.t16.t7.t32.t17))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t16.t7.t31 t15.t7.t7.t16.t7.t32))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t16.t7.t30 t15.t7.t7.t16.t7.t33))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t16.t7.t27 t15.t7.t7.t16.t7.t34 a5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t16.t7.t7 t15.t7.t7.t16.t7.t12 t15.t7.t7.t16.t7.t21 a7 t15.t7.t7.t16.t7.t26 t15.t7.t7.t16.t7.t35 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t16.t7.t36))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t16.t7.t36))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t16.t7.t37 t15.t7.t7.t16.t7.t38))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t16.t7.t6 t15.t7.t7.t16.t7.t39))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t16.t7.t43.t2.t2 t15.t7.t7.t16.t7.t43.t2.t3))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t16.t7.t43.t2.t4 t15.t7.t7.t16.t7.t43.t2.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t16.t7.t43.t2 t15.t7.t7.t16.t7.t43.t3))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t16.t7.t43.t4))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t16.t7.t43.t5 t15.t7.t7.t16.t7.t43.t6))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t16.t7.t43 t15.t7.t7.t16.t7.t44))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t16.t7.t42 t15.t7.t7.t16.t7.t45))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t16.t7.t41 t15.t7.t7.t16.t7.t46))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t16.t7.t40 t15.t7.t7.t16.t7.t47))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t16.t7.t5 t15.t7.t7.t16.t7.t48 a10))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t16.t7.t4 t15.t7.t7.t16.t7.t49 t15.t7.t7.t16.t7.t12 t15.t7.t7.t16.t7.t21 a7 t15.t7.t7.t16.t7.t26 t15.t7.t7.t16.t7.t35 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t16.t7.t50))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t52 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t7.t16.t7.t51 t15.t7.t7.t16.t7.t52))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t54 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t7.t16.t7.t53 t15.t7.t7.t16.t7.t54))
% 0.65/0.87  (step t15.t7.t7.t16.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t7.t55 t15.t7.t7.t16.t7.t56))
% 0.65/0.87  (step t15.t7.t7.t16.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t16.t6 t15.t7.t7.t16.t7))
% 0.65/0.87  (step t15.t7.t7.t16.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t10.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t2 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t5 (cl (= Q Q)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t7.t16.t10.t4 t15.t7.t7.t16.t10.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t7.t16.t10.t6 t15.t7.t7.t16.t10.t7))
% 0.65/0.87  (step t15.t7.t7.t16.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t10.t8 t15.t7.t7.t16.t10.t9))
% 0.65/0.87  (step t15.t7.t7.t16.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t16.t10.t10 t15.t7.t7.t16.t10.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t16.t9 t15.t7.t7.t16.t10))
% 0.65/0.87  (step t15.t7.t7.t16.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t16.t8 t15.t7.t7.t16.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t16.t5 t15.t7.t7.t16.t12 a11))
% 0.65/0.87  (step t15.t7.t7.t16.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t16.t18 t15.t7.t7.t16.t19))
% 0.65/0.87  (step t15.t7.t7.t16.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t16.t17 t15.t7.t7.t16.t20 a9))
% 0.65/0.87  (step t15.t7.t7.t16.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t16.t24.t5 t15.t7.t7.t16.t24.t6))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t16.t24.t4 t15.t7.t7.t16.t24.t7 a6))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t16.t24.t11.t4 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t16.t24.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t16.t24.t11.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t16.t24.t11.t7 t15.t7.t7.t16.t24.t11.t8))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t24.t11.t6 t15.t7.t7.t16.t24.t11.t9))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t16.t24.t11.t10 t15.t7.t7.t16.t24.t11.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t24.t11.t12 t15.t7.t7.t16.t24.t11.t13))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t16.t24.t10 t15.t7.t7.t16.t24.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t16.t24.t14.t4 t15.t7.t7.t16.t24.t14.t5))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t16.t24.t14.t8.t3 t15.t7.t7.t16.t24.t14.t8.t4))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t16.t24.t14.t7 t15.t7.t7.t16.t24.t14.t8))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t24.t14.t6 t15.t7.t7.t16.t24.t14.t9))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t16.t24.t14.t10 t15.t7.t7.t16.t24.t14.t11))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.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 (t15.t7.t7.t16.t24.t14.t12 t15.t7.t7.t16.t24.t14.t13))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.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 (t15.t7.t7.t16.t24.t14.t14 t15.t7.t7.t16.t24.t14.t15))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t24.t14.t16 t15.t7.t7.t16.t24.t14.t17))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t16.t24.t13 t15.t7.t7.t16.t24.t14))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t16.t24.t12 t15.t7.t7.t16.t24.t15))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t16.t24.t9 t15.t7.t7.t16.t24.t16 a5))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t16.t24.t3 a7 t15.t7.t7.t16.t24.t8 t15.t7.t7.t16.t24.t17 a4 a3 a2))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t16.t24.t18))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t16.t24.t18))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t21 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t16.t24.t20 t15.t7.t7.t16.t24.t21))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t16.t24.t19 t15.t7.t7.t16.t24.t22))
% 0.65/0.87  (step t15.t7.t7.t16.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t24.t23 t15.t7.t7.t16.t24.t24))
% 0.65/0.87  (step t15.t7.t7.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.65/0.87  (step t15.t7.t7.t16.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t16.t23 t15.t7.t7.t16.t24))
% 0.65/0.87  (step t15.t7.t7.t16.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.65/0.87  (anchor :step t15.t7.t7.t16.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.65/0.87  (step t15.t7.t7.t16.t27.t1 (cl (= P P)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.65/0.87  (step t15.t7.t7.t16.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t16.t27.t3 t15.t7.t7.t16.t27.t4))
% 0.68/0.87  (step t15.t7.t7.t16.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t16.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t16.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t16.t27.t7.t2))
% 0.68/0.87  (step t15.t7.t7.t16.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t16.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t16.t27.t6 t15.t7.t7.t16.t27.t7))
% 0.68/0.87  (step t15.t7.t7.t16.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t16.t27.t5 t15.t7.t7.t16.t27.t8))
% 0.68/0.87  (step t15.t7.t7.t16.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t27.t9 t15.t7.t7.t16.t27.t10))
% 0.68/0.87  (step t15.t7.t7.t16.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t16.t27.t11 t15.t7.t7.t16.t27.t12))
% 0.68/0.87  (step t15.t7.t7.t16.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t16.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t16.t26 t15.t7.t7.t16.t27))
% 0.68/0.87  (step t15.t7.t7.t16.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t16.t25 t15.t7.t7.t16.t28))
% 0.68/0.87  (step t15.t7.t7.t16.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t16.t22 t15.t7.t7.t16.t29 a8))
% 0.68/0.87  (step t15.t7.t7.t16.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t16.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t16.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.87  (step t15.t7.t7.t16.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t16.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t16.t32 t15.t7.t7.t16.t33))
% 0.68/0.87  (step t15.t7.t7.t16.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t16.t31 t15.t7.t7.t16.t34 a6))
% 0.68/0.87  (step t15.t7.t7.t16.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t16.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t16.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t16.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t16.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t16.t38.t4 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t16.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t16.t38.t5))
% 0.68/0.87  (step t15.t7.t7.t16.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t16.t38.t5))
% 0.68/0.87  (step t15.t7.t7.t16.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t16.t38.t7 t15.t7.t7.t16.t38.t8))
% 0.68/0.87  (step t15.t7.t7.t16.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t16.t38.t6 t15.t7.t7.t16.t38.t9))
% 0.68/0.87  (step t15.t7.t7.t16.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t38.t10 t15.t7.t7.t16.t38.t11))
% 0.68/0.87  (step t15.t7.t7.t16.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t38.t12 t15.t7.t7.t16.t38.t13))
% 0.68/0.87  (step t15.t7.t7.t16.t38 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t16.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t16.t37 t15.t7.t7.t16.t38))
% 0.68/0.87  (step t15.t7.t7.t16.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t16.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t16.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.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)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t41.t4 t15.t7.t7.t16.t41.t5))
% 0.68/0.87  (step t15.t7.t7.t16.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t16.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t16.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t16.t41.t8.t3 t15.t7.t7.t16.t41.t8.t4))
% 0.68/0.87  (step t15.t7.t7.t16.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t16.t41.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 (t15.t7.t7.t16.t41.t7 t15.t7.t7.t16.t41.t8))
% 0.68/0.87  (step t15.t7.t7.t16.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t16.t41.t6 t15.t7.t7.t16.t41.t9))
% 0.68/0.87  (step t15.t7.t7.t16.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t16.t41.t10 t15.t7.t7.t16.t41.t11))
% 0.68/0.87  (step t15.t7.t7.t16.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t16.t41.t12 t15.t7.t7.t16.t41.t13))
% 0.68/0.87  (step t15.t7.t7.t16.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t41.t14 t15.t7.t7.t16.t41.t15))
% 0.68/0.87  (step t15.t7.t7.t16.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t16.t41.t16 t15.t7.t7.t16.t41.t17))
% 0.68/0.87  (step t15.t7.t7.t16.t41 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t16.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t16.t40 t15.t7.t7.t16.t41))
% 0.68/0.87  (step t15.t7.t7.t16.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t16.t39 t15.t7.t7.t16.t42))
% 0.68/0.87  (step t15.t7.t7.t16.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t16.t36 t15.t7.t7.t16.t43 a5))
% 0.68/0.87  (step t15.t7.t7.t16.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t16.t16 t15.t7.t7.t16.t21 t15.t7.t7.t16.t30 a7 t15.t7.t7.t16.t35 t15.t7.t7.t16.t44 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t16.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t16.t45))
% 0.68/0.87  (step t15.t7.t7.t16.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t16.t45))
% 0.68/0.87  (step t15.t7.t7.t16.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t16.t46 t15.t7.t7.t16.t47))
% 0.68/0.87  (step t15.t7.t7.t16.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t16.t15 t15.t7.t7.t16.t48))
% 0.68/0.87  (step t15.t7.t7.t16.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t16.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t16.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t16.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.87  (step t15.t7.t7.t16.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t16.t52.t2.t2 t15.t7.t7.t16.t52.t2.t3))
% 0.68/0.87  (step t15.t7.t7.t16.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t16.t52.t2.t4 t15.t7.t7.t16.t52.t2.t5))
% 0.68/0.87  (step t15.t7.t7.t16.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t16.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t16.t52.t2 t15.t7.t7.t16.t52.t3))
% 0.68/0.87  (step t15.t7.t7.t16.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t16.t52.t4))
% 0.68/0.87  (step t15.t7.t7.t16.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t16.t52.t5 t15.t7.t7.t16.t52.t6))
% 0.68/0.87  (step t15.t7.t7.t16.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t16.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t16.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t16.t52 t15.t7.t7.t16.t53))
% 0.68/0.87  (step t15.t7.t7.t16.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t16.t51 t15.t7.t7.t16.t54))
% 0.68/0.87  (step t15.t7.t7.t16.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t16.t50 t15.t7.t7.t16.t55))
% 0.68/0.87  (step t15.t7.t7.t16.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t16.t49 t15.t7.t7.t16.t56))
% 0.68/0.87  (step t15.t7.t7.t16.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t16.t14 t15.t7.t7.t16.t57 a10))
% 0.68/0.87  (step t15.t7.t7.t16.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t16.t4 t15.t7.t7.t16.t13 t15.t7.t7.t16.t58 t15.t7.t7.t16.t21 t15.t7.t7.t16.t30 a7 t15.t7.t7.t16.t35 t15.t7.t7.t16.t44 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t16.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t16.t59))
% 0.68/0.87  (step t15.t7.t7.t16.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t16.t59))
% 0.68/0.87  (step t15.t7.t7.t16.t62 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t16.t61 t15.t7.t7.t16.t62))
% 0.68/0.87  (step t15.t7.t7.t16.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t16.t60 t15.t7.t7.t16.t63))
% 0.68/0.87  (step t15.t7.t7.t16.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t7.t7.t16.t61 t15.t7.t7.t16.t65))
% 0.68/0.87  (step t15.t7.t7.t16.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t7.t7.t16.t64 t15.t7.t7.t16.t66))
% 0.68/0.87  (step t15.t7.t7.t16.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t16.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t16.t67 t15.t7.t7.t16.t68))
% 0.68/0.87  (step t15.t7.t7.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t17 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t15 t15.t7.t7.t16))
% 0.68/0.87  (step t15.t7.t7.t18 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t19.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t19.t4 t15.t7.t7.t19.t5))
% 0.68/0.87  (step t15.t7.t7.t19.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t19.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t19.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t19.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t7.t7.t19.t8.t3 t15.t7.t7.t19.t8.t4))
% 0.68/0.87  (step t15.t7.t7.t19.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t19.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t7.t19.t7 t15.t7.t7.t19.t8))
% 0.68/0.87  (step t15.t7.t7.t19.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t7.t19.t6 t15.t7.t7.t19.t9))
% 0.68/0.87  (step t15.t7.t7.t19.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t19.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t7.t7.t19.t10 t15.t7.t7.t19.t11))
% 0.68/0.87  (step t15.t7.t7.t19.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t19.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t19.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t19.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t7.t7.t19.t14.t2 t15.t7.t7.t19.t14.t3))
% 0.68/0.87  (step t15.t7.t7.t19.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t19.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t7.t19.t13 t15.t7.t7.t19.t14))
% 0.68/0.87  (step t15.t7.t7.t19.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t7.t19.t12 t15.t7.t7.t19.t15))
% 0.68/0.87  (step t15.t7.t7.t19.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t19.t16 t15.t7.t7.t19.t17))
% 0.68/0.87  (step t15.t7.t7.t19.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t19.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t7.t7.t19.t18 t15.t7.t7.t19.t19))
% 0.68/0.87  (step t15.t7.t7.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t20 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t7.t7.t18 t15.t7.t7.t19))
% 0.68/0.87  (step t15.t7.t7.t21 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t7.t7.t17 t15.t7.t7.t20))
% 0.68/0.87  (step t15.t7.t7.t22 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t7.t7.t14 t15.t7.t7.t21 a12))
% 0.68/0.87  (step t15.t7.t7.t23 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t24 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t25.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t25.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t25.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t25.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t25.t9 t15.t7.t7.t25.t10))
% 0.68/0.87  (step t15.t7.t7.t25.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t25.t8 t15.t7.t7.t25.t11 a9))
% 0.68/0.87  (step t15.t7.t7.t25.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t25.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t25.t15.t5 t15.t7.t7.t25.t15.t6))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t25.t15.t4 t15.t7.t7.t25.t15.t7 a6))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t25.t15.t11.t4 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t25.t15.t11.t5))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t25.t15.t11.t5))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t25.t15.t11.t7 t15.t7.t7.t25.t15.t11.t8))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t25.t15.t11.t6 t15.t7.t7.t25.t15.t11.t9))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t25.t15.t11.t10 t15.t7.t7.t25.t15.t11.t11))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t25.t15.t11.t12 t15.t7.t7.t25.t15.t11.t13))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t25.t15.t10 t15.t7.t7.t25.t15.t11))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.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)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t25.t15.t14.t4 t15.t7.t7.t25.t15.t14.t5))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t25.t15.t14.t8.t3 t15.t7.t7.t25.t15.t14.t8.t4))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.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 (t15.t7.t7.t25.t15.t14.t7 t15.t7.t7.t25.t15.t14.t8))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t25.t15.t14.t6 t15.t7.t7.t25.t15.t14.t9))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t25.t15.t14.t10 t15.t7.t7.t25.t15.t14.t11))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t25.t15.t14.t12 t15.t7.t7.t25.t15.t14.t13))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t25.t15.t14.t14 t15.t7.t7.t25.t15.t14.t15))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t25.t15.t14.t16 t15.t7.t7.t25.t15.t14.t17))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t25.t15.t13 t15.t7.t7.t25.t15.t14))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t25.t15.t12 t15.t7.t7.t25.t15.t15))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t25.t15.t9 t15.t7.t7.t25.t15.t16 a5))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t25.t15.t3 a7 t15.t7.t7.t25.t15.t8 t15.t7.t7.t25.t15.t17 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t25.t15.t18))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t25.t15.t18))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t25.t15.t20 t15.t7.t7.t25.t15.t21))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t25.t15.t19 t15.t7.t7.t25.t15.t22))
% 0.68/0.87  (step t15.t7.t7.t25.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t25.t15.t23 t15.t7.t7.t25.t15.t24))
% 0.68/0.87  (step t15.t7.t7.t25.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t25.t14 t15.t7.t7.t25.t15))
% 0.68/0.87  (step t15.t7.t7.t25.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t25.t18.t3 t15.t7.t7.t25.t18.t4))
% 0.68/0.87  (step t15.t7.t7.t25.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t25.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t25.t18.t7.t2))
% 0.68/0.87  (step t15.t7.t7.t25.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t25.t18.t6 t15.t7.t7.t25.t18.t7))
% 0.68/0.87  (step t15.t7.t7.t25.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t25.t18.t5 t15.t7.t7.t25.t18.t8))
% 0.68/0.87  (step t15.t7.t7.t25.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t25.t18.t9 t15.t7.t7.t25.t18.t10))
% 0.68/0.87  (step t15.t7.t7.t25.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t25.t18.t11 t15.t7.t7.t25.t18.t12))
% 0.68/0.87  (step t15.t7.t7.t25.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t25.t17 t15.t7.t7.t25.t18))
% 0.68/0.87  (step t15.t7.t7.t25.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t25.t16 t15.t7.t7.t25.t19))
% 0.68/0.87  (step t15.t7.t7.t25.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t25.t13 t15.t7.t7.t25.t20 a8))
% 0.68/0.87  (step t15.t7.t7.t25.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t25.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.87  (step t15.t7.t7.t25.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t25.t23 t15.t7.t7.t25.t24))
% 0.68/0.87  (step t15.t7.t7.t25.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t25.t22 t15.t7.t7.t25.t25 a6))
% 0.68/0.87  (step t15.t7.t7.t25.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t25.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t25.t29.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t25.t29.t4 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t25.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t25.t29.t5))
% 0.68/0.87  (step t15.t7.t7.t25.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t25.t29.t5))
% 0.68/0.87  (step t15.t7.t7.t25.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t25.t29.t7 t15.t7.t7.t25.t29.t8))
% 0.68/0.87  (step t15.t7.t7.t25.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t25.t29.t6 t15.t7.t7.t25.t29.t9))
% 0.68/0.87  (step t15.t7.t7.t25.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t25.t29.t10 t15.t7.t7.t25.t29.t11))
% 0.68/0.87  (step t15.t7.t7.t25.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t25.t29.t12 t15.t7.t7.t25.t29.t13))
% 0.68/0.87  (step t15.t7.t7.t25.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t25.t28 t15.t7.t7.t25.t29))
% 0.68/0.87  (step t15.t7.t7.t25.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t25.t32.t4 t15.t7.t7.t25.t32.t5))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t25.t32.t8.t3 t15.t7.t7.t25.t32.t8.t4))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t25.t32.t7 t15.t7.t7.t25.t32.t8))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t25.t32.t6 t15.t7.t7.t25.t32.t9))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t25.t32.t10 t15.t7.t7.t25.t32.t11))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t32.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 (t15.t7.t7.t25.t32.t12 t15.t7.t7.t25.t32.t13))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t32.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 (t15.t7.t7.t25.t32.t14 t15.t7.t7.t25.t32.t15))
% 0.68/0.87  (step t15.t7.t7.t25.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t25.t32.t16 t15.t7.t7.t25.t32.t17))
% 0.68/0.87  (step t15.t7.t7.t25.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t25.t31 t15.t7.t7.t25.t32))
% 0.68/0.87  (step t15.t7.t7.t25.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t25.t30 t15.t7.t7.t25.t33))
% 0.68/0.87  (step t15.t7.t7.t25.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t25.t27 t15.t7.t7.t25.t34 a5))
% 0.68/0.87  (step t15.t7.t7.t25.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t25.t7 t15.t7.t7.t25.t12 t15.t7.t7.t25.t21 a7 t15.t7.t7.t25.t26 t15.t7.t7.t25.t35 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t25.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t25.t36))
% 0.68/0.87  (step t15.t7.t7.t25.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t25.t36))
% 0.68/0.87  (step t15.t7.t7.t25.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t25.t37 t15.t7.t7.t25.t38))
% 0.68/0.87  (step t15.t7.t7.t25.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t25.t6 t15.t7.t7.t25.t39))
% 0.68/0.87  (step t15.t7.t7.t25.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t25.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t25.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.87  (step t15.t7.t7.t25.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t25.t43.t2.t2 t15.t7.t7.t25.t43.t2.t3))
% 0.68/0.87  (step t15.t7.t7.t25.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t25.t43.t2.t4 t15.t7.t7.t25.t43.t2.t5))
% 0.68/0.87  (step t15.t7.t7.t25.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t25.t43.t2 t15.t7.t7.t25.t43.t3))
% 0.68/0.87  (step t15.t7.t7.t25.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t25.t43.t4))
% 0.68/0.87  (step t15.t7.t7.t25.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t25.t43.t5 t15.t7.t7.t25.t43.t6))
% 0.68/0.87  (step t15.t7.t7.t25.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t25.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t25.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t25.t43 t15.t7.t7.t25.t44))
% 0.68/0.87  (step t15.t7.t7.t25.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t25.t42 t15.t7.t7.t25.t45))
% 0.68/0.87  (step t15.t7.t7.t25.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t25.t41 t15.t7.t7.t25.t46))
% 0.68/0.87  (step t15.t7.t7.t25.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t25.t40 t15.t7.t7.t25.t47))
% 0.68/0.87  (step t15.t7.t7.t25.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t25.t5 t15.t7.t7.t25.t48 a10))
% 0.68/0.87  (step t15.t7.t7.t25.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t25.t4 t15.t7.t7.t25.t49 t15.t7.t7.t25.t12 t15.t7.t7.t25.t21 a7 t15.t7.t7.t25.t26 t15.t7.t7.t25.t35 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t25.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t25.t50))
% 0.68/0.87  (step t15.t7.t7.t25.t52 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t7.t25.t51 t15.t7.t7.t25.t52))
% 0.68/0.87  (step t15.t7.t7.t25.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t7.t25.t53 t15.t7.t7.t25.t54))
% 0.68/0.87  (step t15.t7.t7.t25.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t25.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t25.t55 t15.t7.t7.t25.t56))
% 0.68/0.87  (step t15.t7.t7.t25 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t26 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t24 t15.t7.t7.t25))
% 0.68/0.87  (step t15.t7.t7.t27 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t28 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t28.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t28.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t28.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t28.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t28.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t7.t28.t4 t15.t7.t7.t28.t5))
% 0.68/0.87  (step t15.t7.t7.t28.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t28.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t7.t28.t6 t15.t7.t7.t28.t7))
% 0.68/0.87  (step t15.t7.t7.t28.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t28.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t28.t8 t15.t7.t7.t28.t9))
% 0.68/0.87  (step t15.t7.t7.t28.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t28.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t28.t10 t15.t7.t7.t28.t11))
% 0.68/0.87  (step t15.t7.t7.t28 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t29 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t27 t15.t7.t7.t28))
% 0.68/0.87  (step t15.t7.t7.t30 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t26 t15.t7.t7.t29))
% 0.68/0.87  (step t15.t7.t7.t31 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t23 t15.t7.t7.t30 a11))
% 0.68/0.87  (step t15.t7.t7.t32 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t33 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t34 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t35 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t36 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t37 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t38 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t36 t15.t7.t7.t37))
% 0.68/0.87  (step t15.t7.t7.t39 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t7.t35 t15.t7.t7.t38 a9))
% 0.68/0.87  (step t15.t7.t7.t40 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t41 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t42.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t42.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t42.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.87  (step t15.t7.t7.t42.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t42.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t42.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t42.t5 t15.t7.t7.t42.t6))
% 0.68/0.87  (step t15.t7.t7.t42.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t42.t4 t15.t7.t7.t42.t7 a6))
% 0.68/0.87  (step t15.t7.t7.t42.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t42.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t42.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t42.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t42.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t7.t42.t11.t4 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t42.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t42.t11.t5))
% 0.68/0.87  (step t15.t7.t7.t42.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t42.t11.t5))
% 0.68/0.87  (step t15.t7.t7.t42.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t42.t11.t7 t15.t7.t7.t42.t11.t8))
% 0.68/0.87  (step t15.t7.t7.t42.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t7.t42.t11.t6 t15.t7.t7.t42.t11.t9))
% 0.68/0.87  (step t15.t7.t7.t42.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t7.t42.t11.t10 t15.t7.t7.t42.t11.t11))
% 0.68/0.87  (step t15.t7.t7.t42.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t42.t11.t12 t15.t7.t7.t42.t11.t13))
% 0.68/0.87  (step t15.t7.t7.t42.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t42.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t7.t42.t10 t15.t7.t7.t42.t11))
% 0.68/0.87  (step t15.t7.t7.t42.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t42.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t42.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t7.t42.t14.t4 t15.t7.t7.t42.t14.t5))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.87  (anchor :step t15.t7.t7.t42.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t42.t14.t8.t3 t15.t7.t7.t42.t14.t8.t4))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t42.t14.t7 t15.t7.t7.t42.t14.t8))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t42.t14.t6 t15.t7.t7.t42.t14.t9))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t7.t42.t14.t10 t15.t7.t7.t42.t14.t11))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t42.t14.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 (t15.t7.t7.t42.t14.t12 t15.t7.t7.t42.t14.t13))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t14.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 (t15.t7.t7.t42.t14.t14 t15.t7.t7.t42.t14.t15))
% 0.68/0.87  (step t15.t7.t7.t42.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t42.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t42.t14.t16 t15.t7.t7.t42.t14.t17))
% 0.68/0.87  (step t15.t7.t7.t42.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t42.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t42.t13 t15.t7.t7.t42.t14))
% 0.68/0.87  (step t15.t7.t7.t42.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t42.t12 t15.t7.t7.t42.t15))
% 0.68/0.87  (step t15.t7.t7.t42.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t42.t9 t15.t7.t7.t42.t16 a5))
% 0.68/0.87  (step t15.t7.t7.t42.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t42.t3 a7 t15.t7.t7.t42.t8 t15.t7.t7.t42.t17 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t42.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t42.t18))
% 0.68/0.87  (step t15.t7.t7.t42.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t7.t42.t18))
% 0.68/0.87  (step t15.t7.t7.t42.t21 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t7.t42.t20 t15.t7.t7.t42.t21))
% 0.68/0.87  (step t15.t7.t7.t42.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t7.t42.t19 t15.t7.t7.t42.t22))
% 0.68/0.87  (step t15.t7.t7.t42.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t42.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t42.t23 t15.t7.t7.t42.t24))
% 0.68/0.87  (step t15.t7.t7.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t43 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t41 t15.t7.t7.t42))
% 0.68/0.87  (step t15.t7.t7.t44 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t45 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t45.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t45.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t45.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t45.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t45.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t45.t3 t15.t7.t7.t45.t4))
% 0.68/0.87  (step t15.t7.t7.t45.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t45.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t45.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t45.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t45.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t7.t45.t7.t2))
% 0.68/0.87  (step t15.t7.t7.t45.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t45.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t45.t6 t15.t7.t7.t45.t7))
% 0.68/0.87  (step t15.t7.t7.t45.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t7.t45.t5 t15.t7.t7.t45.t8))
% 0.68/0.87  (step t15.t7.t7.t45.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t45.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t45.t9 t15.t7.t7.t45.t10))
% 0.68/0.87  (step t15.t7.t7.t45.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t45.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t7.t45.t11 t15.t7.t7.t45.t12))
% 0.68/0.87  (step t15.t7.t7.t45 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t46 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t7.t44 t15.t7.t7.t45))
% 0.68/0.87  (step t15.t7.t7.t47 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t7.t43 t15.t7.t7.t46))
% 0.68/0.87  (step t15.t7.t7.t48 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t7.t40 t15.t7.t7.t47 a8))
% 0.68/0.87  (step t15.t7.t7.t49 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t50 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t51 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.87  (step t15.t7.t7.t51.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t51.t2 (cl (= X X)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t51.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t51 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t52 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t7.t50 t15.t7.t7.t51))
% 0.68/0.87  (step t15.t7.t7.t53 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t7.t49 t15.t7.t7.t52 a6))
% 0.68/0.87  (step t15.t7.t7.t54 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t7.t55 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t56 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t56.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t56.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t56.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t56.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t7.t56.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t7.t56.t4 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t56.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t7.t56.t5))
% 0.68/0.87  (step t15.t7.t7.t56.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t7.t56.t5))
% 0.68/0.87  (step t15.t7.t7.t56.t8 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t56.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t7.t56.t7 t15.t7.t7.t56.t8))
% 0.68/0.87  (step t15.t7.t7.t56.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t7.t56.t6 t15.t7.t7.t56.t9))
% 0.68/0.87  (step t15.t7.t7.t56.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t56.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t56.t10 t15.t7.t7.t56.t11))
% 0.68/0.87  (step t15.t7.t7.t56.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t56.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t56.t12 t15.t7.t7.t56.t13))
% 0.68/0.87  (step t15.t7.t7.t56 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t57 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t7.t55 t15.t7.t7.t56))
% 0.68/0.87  (step t15.t7.t7.t58 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t59 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t59.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.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)
% 0.68/0.87  (step t15.t7.t7.t59.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t59.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t7.t59.t4 t15.t7.t7.t59.t5))
% 0.68/0.87  (step t15.t7.t7.t59.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t59.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t7.t59.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t59.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t7.t59.t8.t3 t15.t7.t7.t59.t8.t4))
% 0.68/0.87  (step t15.t7.t7.t59.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t59.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 (t15.t7.t7.t59.t7 t15.t7.t7.t59.t8))
% 0.68/0.87  (step t15.t7.t7.t59.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t7.t59.t6 t15.t7.t7.t59.t9))
% 0.68/0.87  (step t15.t7.t7.t59.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t7.t59.t10 t15.t7.t7.t59.t11))
% 0.68/0.87  (step t15.t7.t7.t59.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t59.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t7.t59.t12 t15.t7.t7.t59.t13))
% 0.68/0.87  (step t15.t7.t7.t59.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t59.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t59.t14 t15.t7.t7.t59.t15))
% 0.68/0.87  (step t15.t7.t7.t59.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t59.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t7.t59.t16 t15.t7.t7.t59.t17))
% 0.68/0.87  (step t15.t7.t7.t59 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t7.t60 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t7.t58 t15.t7.t7.t59))
% 0.68/0.87  (step t15.t7.t7.t61 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t7.t57 t15.t7.t7.t60))
% 0.68/0.87  (step t15.t7.t7.t62 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t7.t54 t15.t7.t7.t61 a5))
% 0.68/0.87  (step t15.t7.t7.t63 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t34 t15.t7.t7.t39 t15.t7.t7.t48 a7 t15.t7.t7.t53 t15.t7.t7.t62 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t64 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t7.t63))
% 0.68/0.87  (step t15.t7.t7.t65 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t7.t63))
% 0.68/0.87  (step t15.t7.t7.t66 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t7.t64 t15.t7.t7.t65))
% 0.68/0.87  (step t15.t7.t7.t67 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t7.t33 t15.t7.t7.t66))
% 0.68/0.87  (step t15.t7.t7.t68 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t69 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t7.t70 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t7.t70.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t7.t70.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.87  (step t15.t7.t7.t70.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t70.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t70.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t70.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t7.t70.t2.t2 t15.t7.t7.t70.t2.t3))
% 0.68/0.87  (step t15.t7.t7.t70.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t70.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t7.t70.t2.t4 t15.t7.t7.t70.t2.t5))
% 0.68/0.87  (step t15.t7.t7.t70.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t70.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t70.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t7.t70.t2 t15.t7.t7.t70.t3))
% 0.68/0.87  (step t15.t7.t7.t70.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t7.t70.t4))
% 0.68/0.87  (step t15.t7.t7.t70.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t70.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t7.t70.t5 t15.t7.t7.t70.t6))
% 0.68/0.87  (step t15.t7.t7.t70 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.87  (step t15.t7.t7.t71 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t7.t72 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t70 t15.t7.t7.t71))
% 0.68/0.87  (step t15.t7.t7.t73 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t7.t69 t15.t7.t7.t72))
% 0.68/0.87  (step t15.t7.t7.t74 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t7.t68 t15.t7.t7.t73))
% 0.68/0.87  (step t15.t7.t7.t75 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t7.t67 t15.t7.t7.t74))
% 0.68/0.87  (step t15.t7.t7.t76 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t7.t32 t15.t7.t7.t75 a10))
% 0.68/0.87  (step t15.t7.t7.t77 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t7.t4 t15.t7.t7.t13 t15.t7.t7.t22 t15.t7.t7.t31 t15.t7.t7.t76 t15.t7.t7.t39 t15.t7.t7.t48 a7 t15.t7.t7.t53 t15.t7.t7.t62 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t7.t78 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule and :premises (t15.t7.t7.t77))
% 0.68/0.87  (step t15.t7.t7.t79 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t80 (cl (= (@ tptp.iimplies Q) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t15.t7.t7.t78 t15.t7.t7.t79))
% 0.68/0.87  (step t15.t7.t7.t81 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t82 (cl (= (@ (@ tptp.iimplies Q) P) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P))) :rule cong :premises (t15.t7.t7.t80 t15.t7.t7.t81))
% 0.68/0.87  (step t15.t7.t7.t83 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t7.t84 (cl (= (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) :rule cong :premises (t15.t7.t7.t82 t15.t7.t7.t83))
% 0.68/0.87  (step t15.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t8 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))))) :rule cong :premises (t15.t7.t6 t15.t7.t7))
% 0.68/0.87  (step t15.t7.t9 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t10.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t10.t5 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t10.t6 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t15.t7.t10.t4 t15.t7.t10.t5))
% 0.68/0.87  (step t15.t7.t10.t7 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t10.t8 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t10.t6 t15.t7.t10.t7))
% 0.68/0.87  (step t15.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t10.t8 t15.t7.t10.t9))
% 0.68/0.87  (step t15.t7.t10.t11 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t10.t10 t15.t7.t10.t11))
% 0.68/0.87  (step t15.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t11 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t9 t15.t7.t10))
% 0.68/0.87  (step t15.t7.t12 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t8 t15.t7.t11))
% 0.68/0.87  (step t15.t7.t13 (cl (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t5 t15.t7.t12 a14))
% 0.68/0.87  (step t15.t7.t14 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t15 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t16.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t16.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t7.t7.t9 t15.t7.t16.t7.t7.t10))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t16.t7.t7.t8 t15.t7.t16.t7.t7.t11 a9))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t5 t15.t7.t16.t7.t7.t15.t6))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t7.t7.t15.t4 t15.t7.t16.t7.t7.t15.t7 a6))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t7.t7.t15.t11.t5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t7.t7.t15.t11.t5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t11.t7 t15.t7.t16.t7.t7.t15.t11.t8))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t11.t6 t15.t7.t16.t7.t7.t15.t11.t9))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t7.t15.t11.t10 t15.t7.t16.t7.t7.t15.t11.t11))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t11.t12 t15.t7.t16.t7.t7.t15.t11.t13))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t10 t15.t7.t16.t7.t7.t15.t11))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.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)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t7.t15.t14.t4 t15.t7.t16.t7.t7.t15.t14.t5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t14.t8.t3 t15.t7.t16.t7.t7.t15.t14.t8.t4))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.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 (t15.t7.t16.t7.t7.t15.t14.t7 t15.t7.t16.t7.t7.t15.t14.t8))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t7.t7.t15.t14.t6 t15.t7.t16.t7.t7.t15.t14.t9))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t7.t15.t14.t10 t15.t7.t16.t7.t7.t15.t14.t11))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t16.t7.t7.t15.t14.t12 t15.t7.t16.t7.t7.t15.t14.t13))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t14.t14 t15.t7.t16.t7.t7.t15.t14.t15))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t16.t7.t7.t15.t14.t16 t15.t7.t16.t7.t7.t15.t14.t17))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t13 t15.t7.t16.t7.t7.t15.t14))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t7.t7.t15.t12 t15.t7.t16.t7.t7.t15.t15))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t7.t7.t15.t9 t15.t7.t16.t7.t7.t15.t16 a5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t16.t7.t7.t15.t3 a7 t15.t7.t16.t7.t7.t15.t8 t15.t7.t16.t7.t7.t15.t17 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t7.t7.t15.t18))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t16.t7.t7.t15.t18))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t20 t15.t7.t16.t7.t7.t15.t21))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t19 t15.t7.t16.t7.t7.t15.t22))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t7.t15.t23 t15.t7.t16.t7.t7.t15.t24))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t7.t7.t14 t15.t7.t16.t7.t7.t15))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t7.t7.t18.t3 t15.t7.t16.t7.t7.t18.t4))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t16.t7.t7.t18.t7.t2))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t7.t7.t18.t6 t15.t7.t16.t7.t7.t18.t7))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t7.t7.t18.t5 t15.t7.t16.t7.t7.t18.t8))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t7.t18.t9 t15.t7.t16.t7.t7.t18.t10))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t16.t7.t7.t18.t11 t15.t7.t16.t7.t7.t18.t12))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t16.t7.t7.t17 t15.t7.t16.t7.t7.t18))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t16.t7.t7.t16 t15.t7.t16.t7.t7.t19))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t16.t7.t7.t13 t15.t7.t16.t7.t7.t20 a8))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t7.t7.t23 t15.t7.t16.t7.t7.t24))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t7.t7.t22 t15.t7.t16.t7.t7.t25 a6))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t5 (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)))))) :rule resolution :premises (t15.t7.t16.t7.t7.t29.t4 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t7.t7.t29.t5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t7.t7.t29.t5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t7.t7.t29.t7 t15.t7.t16.t7.t7.t29.t8))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t7.t29.t6 t15.t7.t16.t7.t7.t29.t9))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t16.t7.t7.t29.t10 t15.t7.t16.t7.t7.t29.t11))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t7.t29.t12 t15.t7.t16.t7.t7.t29.t13))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t16.t7.t7.t28 t15.t7.t16.t7.t7.t29))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t16.t7.t7.t32.t4 t15.t7.t16.t7.t7.t32.t5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t7.t7.t32.t8.t3 t15.t7.t16.t7.t7.t32.t8.t4))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t7.t7.t32.t7 t15.t7.t16.t7.t7.t32.t8))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t7.t32.t6 t15.t7.t16.t7.t7.t32.t9))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t16.t7.t7.t32.t10 t15.t7.t16.t7.t7.t32.t11))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.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 (t15.t7.t16.t7.t7.t32.t12 t15.t7.t16.t7.t7.t32.t13))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.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 (t15.t7.t16.t7.t7.t32.t14 t15.t7.t16.t7.t7.t32.t15))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t7.t32.t16 t15.t7.t16.t7.t7.t32.t17))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t7.t7.t31 t15.t7.t16.t7.t7.t32))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t7.t7.t30 t15.t7.t16.t7.t7.t33))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t7.t7.t27 t15.t7.t16.t7.t7.t34 a5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t7.t7.t7 t15.t7.t16.t7.t7.t12 t15.t7.t16.t7.t7.t21 a7 t15.t7.t16.t7.t7.t26 t15.t7.t16.t7.t7.t35 a4 a3 a2))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t16.t7.t7.t36))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t16.t7.t7.t36))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t7.t7.t37 t15.t7.t16.t7.t7.t38))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t16.t7.t7.t6 t15.t7.t16.t7.t7.t39))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.87  (anchor :step t15.t7.t16.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t16.t7.t7.t43.t2.t2 t15.t7.t16.t7.t7.t43.t2.t3))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t16.t7.t7.t43.t2.t4 t15.t7.t16.t7.t7.t43.t2.t5))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t16.t7.t7.t43.t2 t15.t7.t16.t7.t7.t43.t3))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t16.t7.t7.t43.t4))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t16.t7.t7.t43.t5 t15.t7.t16.t7.t7.t43.t6))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.87  (step t15.t7.t16.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t7.t7.t43 t15.t7.t16.t7.t7.t44))
% 0.68/0.87  (step t15.t7.t16.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t7.t7.t42 t15.t7.t16.t7.t7.t45))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t16.t7.t7.t41 t15.t7.t16.t7.t7.t46))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t16.t7.t7.t40 t15.t7.t16.t7.t7.t47))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t16.t7.t7.t5 t15.t7.t16.t7.t7.t48 a10))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t16.t7.t7.t4 t15.t7.t16.t7.t7.t49 t15.t7.t16.t7.t7.t12 t15.t7.t16.t7.t7.t21 a7 t15.t7.t16.t7.t7.t26 t15.t7.t16.t7.t7.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t7.t7.t50))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t16.t7.t7.t51 t15.t7.t16.t7.t7.t52))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t16.t7.t7.t53 t15.t7.t16.t7.t7.t54))
% 0.68/0.88  (step t15.t7.t16.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t7.t55 t15.t7.t16.t7.t7.t56))
% 0.68/0.88  (step t15.t7.t16.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t7.t6 t15.t7.t16.t7.t7))
% 0.68/0.88  (step t15.t7.t16.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t16.t7.t10.t4 t15.t7.t16.t7.t10.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t16.t7.t10.t6 t15.t7.t16.t7.t10.t7))
% 0.68/0.88  (step t15.t7.t16.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t10.t8 t15.t7.t16.t7.t10.t9))
% 0.68/0.88  (step t15.t7.t16.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t16.t7.t10.t10 t15.t7.t16.t7.t10.t11))
% 0.68/0.88  (step t15.t7.t16.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t7.t9 t15.t7.t16.t7.t10))
% 0.68/0.88  (step t15.t7.t16.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t7.t8 t15.t7.t16.t7.t11))
% 0.68/0.88  (step t15.t7.t16.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t7.t5 t15.t7.t16.t7.t12 a11))
% 0.68/0.88  (step t15.t7.t16.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t7.t18 t15.t7.t16.t7.t19))
% 0.68/0.88  (step t15.t7.t16.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t16.t7.t17 t15.t7.t16.t7.t20 a9))
% 0.68/0.88  (step t15.t7.t16.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t7.t24.t5 t15.t7.t16.t7.t24.t6))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t7.t24.t4 t15.t7.t16.t7.t24.t7 a6))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t16.t7.t24.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t7.t24.t11.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t7.t24.t11.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t7.t24.t11.t7 t15.t7.t16.t7.t24.t11.t8))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t24.t11.t6 t15.t7.t16.t7.t24.t11.t9))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t16.t7.t24.t11.t10 t15.t7.t16.t7.t24.t11.t11))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t24.t11.t12 t15.t7.t16.t7.t24.t11.t13))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t16.t7.t24.t10 t15.t7.t16.t7.t24.t11))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t16.t7.t24.t14.t4 t15.t7.t16.t7.t24.t14.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t7.t24.t14.t8.t3 t15.t7.t16.t7.t24.t14.t8.t4))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t7.t24.t14.t7 t15.t7.t16.t7.t24.t14.t8))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t24.t14.t6 t15.t7.t16.t7.t24.t14.t9))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t16.t7.t24.t14.t10 t15.t7.t16.t7.t24.t14.t11))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.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 (t15.t7.t16.t7.t24.t14.t12 t15.t7.t16.t7.t24.t14.t13))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.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 (t15.t7.t16.t7.t24.t14.t14 t15.t7.t16.t7.t24.t14.t15))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t24.t14.t16 t15.t7.t16.t7.t24.t14.t17))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t7.t24.t13 t15.t7.t16.t7.t24.t14))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t7.t24.t12 t15.t7.t16.t7.t24.t15))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t7.t24.t9 t15.t7.t16.t7.t24.t16 a5))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t7.t24.t3 a7 t15.t7.t16.t7.t24.t8 t15.t7.t16.t7.t24.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t7.t24.t18))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t16.t7.t24.t18))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t16.t7.t24.t20 t15.t7.t16.t7.t24.t21))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t16.t7.t24.t19 t15.t7.t16.t7.t24.t22))
% 0.68/0.88  (step t15.t7.t16.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t24.t23 t15.t7.t16.t7.t24.t24))
% 0.68/0.88  (step t15.t7.t16.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t7.t23 t15.t7.t16.t7.t24))
% 0.68/0.88  (step t15.t7.t16.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t7.t27.t3 t15.t7.t16.t7.t27.t4))
% 0.68/0.88  (step t15.t7.t16.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t16.t7.t27.t7.t2))
% 0.68/0.88  (step t15.t7.t16.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t7.t27.t6 t15.t7.t16.t7.t27.t7))
% 0.68/0.88  (step t15.t7.t16.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t7.t27.t5 t15.t7.t16.t7.t27.t8))
% 0.68/0.88  (step t15.t7.t16.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t27.t9 t15.t7.t16.t7.t27.t10))
% 0.68/0.88  (step t15.t7.t16.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t16.t7.t27.t11 t15.t7.t16.t7.t27.t12))
% 0.68/0.88  (step t15.t7.t16.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t16.t7.t26 t15.t7.t16.t7.t27))
% 0.68/0.88  (step t15.t7.t16.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t16.t7.t25 t15.t7.t16.t7.t28))
% 0.68/0.88  (step t15.t7.t16.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t16.t7.t22 t15.t7.t16.t7.t29 a8))
% 0.68/0.88  (step t15.t7.t16.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t16.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t7.t32 t15.t7.t16.t7.t33))
% 0.68/0.88  (step t15.t7.t16.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t7.t31 t15.t7.t16.t7.t34 a6))
% 0.68/0.88  (step t15.t7.t16.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t7.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t7.t38.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t7.t38.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t7.t38.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t7.t38.t7 t15.t7.t16.t7.t38.t8))
% 0.68/0.88  (step t15.t7.t16.t7.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t16.t7.t38.t6 t15.t7.t16.t7.t38.t9))
% 0.68/0.88  (step t15.t7.t16.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t38.t10 t15.t7.t16.t7.t38.t11))
% 0.68/0.88  (step t15.t7.t16.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t38.t12 t15.t7.t16.t7.t38.t13))
% 0.68/0.88  (step t15.t7.t16.t7.t38 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t7.t37 t15.t7.t16.t7.t38))
% 0.68/0.88  (step t15.t7.t16.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.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)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t41.t4 t15.t7.t16.t7.t41.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t7.t41.t8.t3 t15.t7.t16.t7.t41.t8.t4))
% 0.68/0.88  (step t15.t7.t16.t7.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t7.t41.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 (t15.t7.t16.t7.t41.t7 t15.t7.t16.t7.t41.t8))
% 0.68/0.88  (step t15.t7.t16.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t7.t41.t6 t15.t7.t16.t7.t41.t9))
% 0.68/0.88  (step t15.t7.t16.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t7.t41.t10 t15.t7.t16.t7.t41.t11))
% 0.68/0.88  (step t15.t7.t16.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t16.t7.t41.t12 t15.t7.t16.t7.t41.t13))
% 0.68/0.88  (step t15.t7.t16.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t41.t14 t15.t7.t16.t7.t41.t15))
% 0.68/0.88  (step t15.t7.t16.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t16.t7.t41.t16 t15.t7.t16.t7.t41.t17))
% 0.68/0.88  (step t15.t7.t16.t7.t41 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t7.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t7.t40 t15.t7.t16.t7.t41))
% 0.68/0.88  (step t15.t7.t16.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t7.t39 t15.t7.t16.t7.t42))
% 0.68/0.88  (step t15.t7.t16.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t7.t36 t15.t7.t16.t7.t43 a5))
% 0.68/0.88  (step t15.t7.t16.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t16.t7.t16 t15.t7.t16.t7.t21 t15.t7.t16.t7.t30 a7 t15.t7.t16.t7.t35 t15.t7.t16.t7.t44 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t16.t7.t45))
% 0.68/0.88  (step t15.t7.t16.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t16.t7.t45))
% 0.68/0.88  (step t15.t7.t16.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t7.t46 t15.t7.t16.t7.t47))
% 0.68/0.88  (step t15.t7.t16.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t16.t7.t15 t15.t7.t16.t7.t48))
% 0.68/0.88  (step t15.t7.t16.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t7.t16.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t16.t7.t52.t2.t2 t15.t7.t16.t7.t52.t2.t3))
% 0.68/0.88  (step t15.t7.t16.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t16.t7.t52.t2.t4 t15.t7.t16.t7.t52.t2.t5))
% 0.68/0.88  (step t15.t7.t16.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t16.t7.t52.t2 t15.t7.t16.t7.t52.t3))
% 0.68/0.88  (step t15.t7.t16.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t16.t7.t52.t4))
% 0.68/0.88  (step t15.t7.t16.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t16.t7.t52.t5 t15.t7.t16.t7.t52.t6))
% 0.68/0.88  (step t15.t7.t16.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t7.t52 t15.t7.t16.t7.t53))
% 0.68/0.88  (step t15.t7.t16.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t7.t51 t15.t7.t16.t7.t54))
% 0.68/0.88  (step t15.t7.t16.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t16.t7.t50 t15.t7.t16.t7.t55))
% 0.68/0.88  (step t15.t7.t16.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t16.t7.t49 t15.t7.t16.t7.t56))
% 0.68/0.88  (step t15.t7.t16.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t16.t7.t14 t15.t7.t16.t7.t57 a10))
% 0.68/0.88  (step t15.t7.t16.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t16.t7.t4 t15.t7.t16.t7.t13 t15.t7.t16.t7.t58 t15.t7.t16.t7.t21 t15.t7.t16.t7.t30 a7 t15.t7.t16.t7.t35 t15.t7.t16.t7.t44 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t7.t59))
% 0.68/0.88  (step t15.t7.t16.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t16.t7.t59))
% 0.68/0.88  (step t15.t7.t16.t7.t62 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t16.t7.t61 t15.t7.t16.t7.t62))
% 0.68/0.88  (step t15.t7.t16.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t16.t7.t60 t15.t7.t16.t7.t63))
% 0.68/0.88  (step t15.t7.t16.t7.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t7.t16.t7.t61 t15.t7.t16.t7.t65))
% 0.68/0.88  (step t15.t7.t16.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t7.t16.t7.t64 t15.t7.t16.t7.t66))
% 0.68/0.88  (step t15.t7.t16.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t7.t67 t15.t7.t16.t7.t68))
% 0.68/0.88  (step t15.t7.t16.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t6 t15.t7.t16.t7))
% 0.68/0.88  (step t15.t7.t16.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t10.t4 t15.t7.t16.t10.t5))
% 0.68/0.88  (step t15.t7.t16.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t7.t16.t10.t8.t3 t15.t7.t16.t10.t8.t4))
% 0.68/0.88  (step t15.t7.t16.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t16.t10.t7 t15.t7.t16.t10.t8))
% 0.68/0.88  (step t15.t7.t16.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t16.t10.t6 t15.t7.t16.t10.t9))
% 0.68/0.88  (step t15.t7.t16.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t7.t16.t10.t10 t15.t7.t16.t10.t11))
% 0.68/0.88  (step t15.t7.t16.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t7.t16.t10.t14.t2 t15.t7.t16.t10.t14.t3))
% 0.68/0.88  (step t15.t7.t16.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t16.t10.t13 t15.t7.t16.t10.t14))
% 0.68/0.88  (step t15.t7.t16.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t16.t10.t12 t15.t7.t16.t10.t15))
% 0.68/0.88  (step t15.t7.t16.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t10.t16 t15.t7.t16.t10.t17))
% 0.68/0.88  (step t15.t7.t16.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t7.t16.t10.t18 t15.t7.t16.t10.t19))
% 0.68/0.88  (step t15.t7.t16.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t7.t16.t9 t15.t7.t16.t10))
% 0.68/0.88  (step t15.t7.t16.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t7.t16.t8 t15.t7.t16.t11))
% 0.68/0.88  (step t15.t7.t16.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t7.t16.t5 t15.t7.t16.t12 a12))
% 0.68/0.88  (step t15.t7.t16.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t16.t9 t15.t7.t16.t16.t10))
% 0.68/0.88  (step t15.t7.t16.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t16.t16.t8 t15.t7.t16.t16.t11 a9))
% 0.68/0.88  (step t15.t7.t16.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t16.t15.t5 t15.t7.t16.t16.t15.t6))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t16.t15.t4 t15.t7.t16.t16.t15.t7 a6))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t16.t15.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t16.t15.t11.t5))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t16.t15.t11.t5))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t16.t15.t11.t7 t15.t7.t16.t16.t15.t11.t8))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t16.t16.t15.t11.t6 t15.t7.t16.t16.t15.t11.t9))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t16.t15.t11.t10 t15.t7.t16.t16.t15.t11.t11))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t16.t15.t11.t12 t15.t7.t16.t16.t15.t11.t13))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t16.t15.t10 t15.t7.t16.t16.t15.t11))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.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)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t16.t15.t14.t4 t15.t7.t16.t16.t15.t14.t5))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t16.t15.t14.t8.t3 t15.t7.t16.t16.t15.t14.t8.t4))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.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 (t15.t7.t16.t16.t15.t14.t7 t15.t7.t16.t16.t15.t14.t8))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t16.t15.t14.t6 t15.t7.t16.t16.t15.t14.t9))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t16.t15.t14.t10 t15.t7.t16.t16.t15.t14.t11))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t16.t16.t15.t14.t12 t15.t7.t16.t16.t15.t14.t13))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t16.t15.t14.t14 t15.t7.t16.t16.t15.t14.t15))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t16.t16.t15.t14.t16 t15.t7.t16.t16.t15.t14.t17))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t16.t15.t13 t15.t7.t16.t16.t15.t14))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t16.t15.t12 t15.t7.t16.t16.t15.t15))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t16.t15.t9 t15.t7.t16.t16.t15.t16 a5))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t16.t16.t15.t3 a7 t15.t7.t16.t16.t15.t8 t15.t7.t16.t16.t15.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t16.t15.t18))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t16.t16.t15.t18))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t16.t16.t15.t20 t15.t7.t16.t16.t15.t21))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t16.t16.t15.t19 t15.t7.t16.t16.t15.t22))
% 0.68/0.88  (step t15.t7.t16.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t16.t15.t23 t15.t7.t16.t16.t15.t24))
% 0.68/0.88  (step t15.t7.t16.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t16.t14 t15.t7.t16.t16.t15))
% 0.68/0.88  (step t15.t7.t16.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t16.t18.t3 t15.t7.t16.t16.t18.t4))
% 0.68/0.88  (step t15.t7.t16.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t16.t16.t18.t7.t2))
% 0.68/0.88  (step t15.t7.t16.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t16.t18.t6 t15.t7.t16.t16.t18.t7))
% 0.68/0.88  (step t15.t7.t16.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t16.t18.t5 t15.t7.t16.t16.t18.t8))
% 0.68/0.88  (step t15.t7.t16.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t16.t18.t9 t15.t7.t16.t16.t18.t10))
% 0.68/0.88  (step t15.t7.t16.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t16.t16.t18.t11 t15.t7.t16.t16.t18.t12))
% 0.68/0.88  (step t15.t7.t16.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t16.t16.t17 t15.t7.t16.t16.t18))
% 0.68/0.88  (step t15.t7.t16.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t16.t16.t16 t15.t7.t16.t16.t19))
% 0.68/0.88  (step t15.t7.t16.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t16.t16.t13 t15.t7.t16.t16.t20 a8))
% 0.68/0.88  (step t15.t7.t16.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t16.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t16.t23 t15.t7.t16.t16.t24))
% 0.68/0.88  (step t15.t7.t16.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t16.t22 t15.t7.t16.t16.t25 a6))
% 0.68/0.88  (step t15.t7.t16.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t16.t29.t5 (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)))))) :rule resolution :premises (t15.t7.t16.t16.t29.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t16.t29.t5))
% 0.68/0.88  (step t15.t7.t16.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t16.t29.t5))
% 0.68/0.88  (step t15.t7.t16.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t16.t29.t7 t15.t7.t16.t16.t29.t8))
% 0.68/0.88  (step t15.t7.t16.t16.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t16.t16.t29.t6 t15.t7.t16.t16.t29.t9))
% 0.68/0.88  (step t15.t7.t16.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t16.t16.t29.t10 t15.t7.t16.t16.t29.t11))
% 0.68/0.88  (step t15.t7.t16.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t16.t29.t12 t15.t7.t16.t16.t29.t13))
% 0.68/0.88  (step t15.t7.t16.t16.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t16.t16.t28 t15.t7.t16.t16.t29))
% 0.68/0.88  (step t15.t7.t16.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t16.t16.t32.t4 t15.t7.t16.t16.t32.t5))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t16.t32.t8.t3 t15.t7.t16.t16.t32.t8.t4))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t16.t32.t7 t15.t7.t16.t16.t32.t8))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t16.t32.t6 t15.t7.t16.t16.t32.t9))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t16.t16.t32.t10 t15.t7.t16.t16.t32.t11))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t32.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 (t15.t7.t16.t16.t32.t12 t15.t7.t16.t16.t32.t13))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t32.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 (t15.t7.t16.t16.t32.t14 t15.t7.t16.t16.t32.t15))
% 0.68/0.88  (step t15.t7.t16.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t16.t32.t16 t15.t7.t16.t16.t32.t17))
% 0.68/0.88  (step t15.t7.t16.t16.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t16.t31 t15.t7.t16.t16.t32))
% 0.68/0.88  (step t15.t7.t16.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t16.t30 t15.t7.t16.t16.t33))
% 0.68/0.88  (step t15.t7.t16.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t16.t27 t15.t7.t16.t16.t34 a5))
% 0.68/0.88  (step t15.t7.t16.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t16.t7 t15.t7.t16.t16.t12 t15.t7.t16.t16.t21 a7 t15.t7.t16.t16.t26 t15.t7.t16.t16.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t16.t16.t36))
% 0.68/0.88  (step t15.t7.t16.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t16.t16.t36))
% 0.68/0.88  (step t15.t7.t16.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t16.t37 t15.t7.t16.t16.t38))
% 0.68/0.88  (step t15.t7.t16.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t16.t16.t6 t15.t7.t16.t16.t39))
% 0.68/0.88  (step t15.t7.t16.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t7.t16.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t16.t16.t43.t2.t2 t15.t7.t16.t16.t43.t2.t3))
% 0.68/0.88  (step t15.t7.t16.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t16.t16.t43.t2.t4 t15.t7.t16.t16.t43.t2.t5))
% 0.68/0.88  (step t15.t7.t16.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t16.t16.t43.t2 t15.t7.t16.t16.t43.t3))
% 0.68/0.88  (step t15.t7.t16.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t16.t16.t43.t4))
% 0.68/0.88  (step t15.t7.t16.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t16.t16.t43.t5 t15.t7.t16.t16.t43.t6))
% 0.68/0.88  (step t15.t7.t16.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t16.t43 t15.t7.t16.t16.t44))
% 0.68/0.88  (step t15.t7.t16.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t16.t42 t15.t7.t16.t16.t45))
% 0.68/0.88  (step t15.t7.t16.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t16.t16.t41 t15.t7.t16.t16.t46))
% 0.68/0.88  (step t15.t7.t16.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t16.t16.t40 t15.t7.t16.t16.t47))
% 0.68/0.88  (step t15.t7.t16.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t16.t16.t5 t15.t7.t16.t16.t48 a10))
% 0.68/0.88  (step t15.t7.t16.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t16.t16.t4 t15.t7.t16.t16.t49 t15.t7.t16.t16.t12 t15.t7.t16.t16.t21 a7 t15.t7.t16.t16.t26 t15.t7.t16.t16.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t16.t50))
% 0.68/0.88  (step t15.t7.t16.t16.t52 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t16.t16.t51 t15.t7.t16.t16.t52))
% 0.68/0.88  (step t15.t7.t16.t16.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t16.t16.t53 t15.t7.t16.t16.t54))
% 0.68/0.88  (step t15.t7.t16.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t16.t55 t15.t7.t16.t16.t56))
% 0.68/0.88  (step t15.t7.t16.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t15 t15.t7.t16.t16))
% 0.68/0.88  (step t15.t7.t16.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t19.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t16.t19.t4 t15.t7.t16.t19.t5))
% 0.68/0.88  (step t15.t7.t16.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t16.t19.t6 t15.t7.t16.t19.t7))
% 0.68/0.88  (step t15.t7.t16.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t19.t8 t15.t7.t16.t19.t9))
% 0.68/0.88  (step t15.t7.t16.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t16.t19.t10 t15.t7.t16.t19.t11))
% 0.68/0.88  (step t15.t7.t16.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t18 t15.t7.t16.t19))
% 0.68/0.88  (step t15.t7.t16.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t17 t15.t7.t16.t20))
% 0.68/0.88  (step t15.t7.t16.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t14 t15.t7.t16.t21 a11))
% 0.68/0.88  (step t15.t7.t16.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t27 t15.t7.t16.t28))
% 0.68/0.88  (step t15.t7.t16.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t16.t26 t15.t7.t16.t29 a9))
% 0.68/0.88  (step t15.t7.t16.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t16.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t33.t5 t15.t7.t16.t33.t6))
% 0.68/0.88  (step t15.t7.t16.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t33.t4 t15.t7.t16.t33.t7 a6))
% 0.68/0.88  (step t15.t7.t16.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t33.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t16.t33.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t33.t11.t5))
% 0.68/0.88  (step t15.t7.t16.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t33.t11.t5))
% 0.68/0.88  (step t15.t7.t16.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t33.t11.t7 t15.t7.t16.t33.t11.t8))
% 0.68/0.88  (step t15.t7.t16.t33.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t16.t33.t11.t6 t15.t7.t16.t33.t11.t9))
% 0.68/0.88  (step t15.t7.t16.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t16.t33.t11.t10 t15.t7.t16.t33.t11.t11))
% 0.68/0.88  (step t15.t7.t16.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t33.t11.t12 t15.t7.t16.t33.t11.t13))
% 0.68/0.88  (step t15.t7.t16.t33.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t16.t33.t10 t15.t7.t16.t33.t11))
% 0.68/0.88  (step t15.t7.t16.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t33.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t16.t33.t14.t4 t15.t7.t16.t33.t14.t5))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t7.t16.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t33.t14.t8.t3 t15.t7.t16.t33.t14.t8.t4))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t33.t14.t7 t15.t7.t16.t33.t14.t8))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t33.t14.t6 t15.t7.t16.t33.t14.t9))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t16.t33.t14.t10 t15.t7.t16.t33.t14.t11))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t33.t14.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 (t15.t7.t16.t33.t14.t12 t15.t7.t16.t33.t14.t13))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t14.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 (t15.t7.t16.t33.t14.t14 t15.t7.t16.t33.t14.t15))
% 0.68/0.88  (step t15.t7.t16.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t33.t14.t16 t15.t7.t16.t33.t14.t17))
% 0.68/0.88  (step t15.t7.t16.t33.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t33.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t33.t13 t15.t7.t16.t33.t14))
% 0.68/0.88  (step t15.t7.t16.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t33.t12 t15.t7.t16.t33.t15))
% 0.68/0.88  (step t15.t7.t16.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t33.t9 t15.t7.t16.t33.t16 a5))
% 0.68/0.88  (step t15.t7.t16.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t33.t3 a7 t15.t7.t16.t33.t8 t15.t7.t16.t33.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t33.t18))
% 0.68/0.88  (step t15.t7.t16.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t16.t33.t18))
% 0.68/0.88  (step t15.t7.t16.t33.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t16.t33.t20 t15.t7.t16.t33.t21))
% 0.68/0.88  (step t15.t7.t16.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t16.t33.t19 t15.t7.t16.t33.t22))
% 0.68/0.88  (step t15.t7.t16.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t33.t23 t15.t7.t16.t33.t24))
% 0.68/0.88  (step t15.t7.t16.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t32 t15.t7.t16.t33))
% 0.68/0.88  (step t15.t7.t16.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t36.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t36.t3 t15.t7.t16.t36.t4))
% 0.68/0.88  (step t15.t7.t16.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t16.t36.t7.t2))
% 0.68/0.88  (step t15.t7.t16.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t36.t6 t15.t7.t16.t36.t7))
% 0.68/0.88  (step t15.t7.t16.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t16.t36.t5 t15.t7.t16.t36.t8))
% 0.68/0.88  (step t15.t7.t16.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t36.t9 t15.t7.t16.t36.t10))
% 0.68/0.88  (step t15.t7.t16.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t16.t36.t11 t15.t7.t16.t36.t12))
% 0.68/0.88  (step t15.t7.t16.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t16.t35 t15.t7.t16.t36))
% 0.68/0.88  (step t15.t7.t16.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t16.t34 t15.t7.t16.t37))
% 0.68/0.88  (step t15.t7.t16.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t16.t31 t15.t7.t16.t38 a8))
% 0.68/0.88  (step t15.t7.t16.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t16.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t42.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t16.t41 t15.t7.t16.t42))
% 0.68/0.88  (step t15.t7.t16.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t16.t40 t15.t7.t16.t43 a6))
% 0.68/0.88  (step t15.t7.t16.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t16.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t47.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t47.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t47.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t16.t47.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t47.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t16.t47.t5))
% 0.68/0.88  (step t15.t7.t16.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t16.t47.t5))
% 0.68/0.88  (step t15.t7.t16.t47.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t16.t47.t7 t15.t7.t16.t47.t8))
% 0.68/0.88  (step t15.t7.t16.t47.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t16.t47.t6 t15.t7.t16.t47.t9))
% 0.68/0.88  (step t15.t7.t16.t47.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t47.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t47.t10 t15.t7.t16.t47.t11))
% 0.68/0.88  (step t15.t7.t16.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t47.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t47.t12 t15.t7.t16.t47.t13))
% 0.68/0.88  (step t15.t7.t16.t47 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t16.t46 t15.t7.t16.t47))
% 0.68/0.88  (step t15.t7.t16.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t50.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.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)
% 0.68/0.88  (step t15.t7.t16.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t50.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t16.t50.t4 t15.t7.t16.t50.t5))
% 0.68/0.88  (step t15.t7.t16.t50.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t16.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t16.t50.t8.t3 t15.t7.t16.t50.t8.t4))
% 0.68/0.88  (step t15.t7.t16.t50.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t50.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 (t15.t7.t16.t50.t7 t15.t7.t16.t50.t8))
% 0.68/0.88  (step t15.t7.t16.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t16.t50.t6 t15.t7.t16.t50.t9))
% 0.68/0.88  (step t15.t7.t16.t50.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t16.t50.t10 t15.t7.t16.t50.t11))
% 0.68/0.88  (step t15.t7.t16.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t50.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t16.t50.t12 t15.t7.t16.t50.t13))
% 0.68/0.88  (step t15.t7.t16.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t50.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t50.t14 t15.t7.t16.t50.t15))
% 0.68/0.88  (step t15.t7.t16.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t16.t50.t16 t15.t7.t16.t50.t17))
% 0.68/0.88  (step t15.t7.t16.t50 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t16.t51 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t16.t49 t15.t7.t16.t50))
% 0.68/0.88  (step t15.t7.t16.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t16.t48 t15.t7.t16.t51))
% 0.68/0.88  (step t15.t7.t16.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t16.t45 t15.t7.t16.t52 a5))
% 0.68/0.88  (step t15.t7.t16.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t16.t25 t15.t7.t16.t30 t15.t7.t16.t39 a7 t15.t7.t16.t44 t15.t7.t16.t53 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t16.t54))
% 0.68/0.88  (step t15.t7.t16.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t16.t54))
% 0.68/0.88  (step t15.t7.t16.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t16.t55 t15.t7.t16.t56))
% 0.68/0.88  (step t15.t7.t16.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t16.t24 t15.t7.t16.t57))
% 0.68/0.88  (step t15.t7.t16.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t16.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t16.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t16.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t7.t16.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t16.t61.t2.t2 t15.t7.t16.t61.t2.t3))
% 0.68/0.88  (step t15.t7.t16.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t16.t61.t2.t4 t15.t7.t16.t61.t2.t5))
% 0.68/0.88  (step t15.t7.t16.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t16.t61.t2 t15.t7.t16.t61.t3))
% 0.68/0.88  (step t15.t7.t16.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t16.t61.t4))
% 0.68/0.88  (step t15.t7.t16.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t16.t61.t5 t15.t7.t16.t61.t6))
% 0.68/0.88  (step t15.t7.t16.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t7.t16.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t16.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t61 t15.t7.t16.t62))
% 0.68/0.88  (step t15.t7.t16.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t16.t60 t15.t7.t16.t63))
% 0.68/0.88  (step t15.t7.t16.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t16.t59 t15.t7.t16.t64))
% 0.68/0.88  (step t15.t7.t16.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t16.t58 t15.t7.t16.t65))
% 0.68/0.88  (step t15.t7.t16.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t16.t23 t15.t7.t16.t66 a10))
% 0.68/0.88  (step t15.t7.t16.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t16.t4 t15.t7.t16.t13 t15.t7.t16.t22 t15.t7.t16.t67 t15.t7.t16.t30 t15.t7.t16.t39 a7 t15.t7.t16.t44 t15.t7.t16.t53 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t16.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t15.t7.t16.t68))
% 0.68/0.88  (step t15.t7.t16.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t16.t68))
% 0.68/0.88  (step t15.t7.t16.t71 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t16.t70 t15.t7.t16.t71))
% 0.68/0.88  (step t15.t7.t16.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t16.t69 t15.t7.t16.t72))
% 0.68/0.88  (step t15.t7.t16.t74 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t7.t16.t70 t15.t7.t16.t74))
% 0.68/0.88  (step t15.t7.t16.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t7.t16.t73 t15.t7.t16.t75))
% 0.68/0.88  (step t15.t7.t16.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t16.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t7.t16.t76 t15.t7.t16.t77))
% 0.68/0.88  (step t15.t7.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t17 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t7.t15 t15.t7.t16))
% 0.68/0.88  (step t15.t7.t18 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t4 (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)
% 0.68/0.88  (step t15.t7.t19.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t19.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t19.t4 t15.t7.t19.t5))
% 0.68/0.88  (step t15.t7.t19.t7 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t19.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t19.t8.t1 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t19.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t19.t8.t3))
% 0.68/0.88  (step t15.t7.t19.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t15.t7.t19.t8.t4 t15.t7.t19.t8.t5))
% 0.68/0.88  (step t15.t7.t19.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t19.t9 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t7.t19.t7 t15.t7.t19.t8))
% 0.68/0.88  (step t15.t7.t19.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t7.t19.t6 t15.t7.t19.t9))
% 0.68/0.88  (step t15.t7.t19.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t19.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t7.t19.t10 t15.t7.t19.t11))
% 0.68/0.88  (step t15.t7.t19.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t19.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t19.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t19.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t15.t7.t19.t14.t2 t15.t7.t19.t14.t3))
% 0.68/0.88  (step t15.t7.t19.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t19.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t19.t13 t15.t7.t19.t14))
% 0.68/0.88  (step t15.t7.t19.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t19.t12 t15.t7.t19.t15))
% 0.68/0.88  (step t15.t7.t19.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t19.t16 t15.t7.t19.t17))
% 0.68/0.88  (step t15.t7.t19.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t19.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t7.t19.t18 t15.t7.t19.t19))
% 0.68/0.88  (step t15.t7.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t20 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t7.t18 t15.t7.t19))
% 0.68/0.88  (step t15.t7.t21 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t7.t17 t15.t7.t20))
% 0.68/0.88  (step t15.t7.t22 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t7.t14 t15.t7.t21 a13))
% 0.68/0.88  (step t15.t7.t23 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t24 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t25.t7.t9 t15.t7.t25.t7.t10))
% 0.68/0.88  (step t15.t7.t25.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t25.t7.t8 t15.t7.t25.t7.t11 a9))
% 0.68/0.88  (step t15.t7.t25.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t25.t7.t15.t5 t15.t7.t25.t7.t15.t6))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t25.t7.t15.t4 t15.t7.t25.t7.t15.t7 a6))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t25.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t25.t7.t15.t11.t5))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t25.t7.t15.t11.t5))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t25.t7.t15.t11.t7 t15.t7.t25.t7.t15.t11.t8))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t25.t7.t15.t11.t6 t15.t7.t25.t7.t15.t11.t9))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t25.t7.t15.t11.t10 t15.t7.t25.t7.t15.t11.t11))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t7.t15.t11.t12 t15.t7.t25.t7.t15.t11.t13))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t25.t7.t15.t10 t15.t7.t25.t7.t15.t11))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t25.t7.t15.t14.t4 t15.t7.t25.t7.t15.t14.t5))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t25.t7.t15.t14.t8.t3 t15.t7.t25.t7.t15.t14.t8.t4))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t25.t7.t15.t14.t7 t15.t7.t25.t7.t15.t14.t8))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t25.t7.t15.t14.t6 t15.t7.t25.t7.t15.t14.t9))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t25.t7.t15.t14.t10 t15.t7.t25.t7.t15.t14.t11))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.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 (t15.t7.t25.t7.t15.t14.t12 t15.t7.t25.t7.t15.t14.t13))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.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 (t15.t7.t25.t7.t15.t14.t14 t15.t7.t25.t7.t15.t14.t15))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t7.t15.t14.t16 t15.t7.t25.t7.t15.t14.t17))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t25.t7.t15.t13 t15.t7.t25.t7.t15.t14))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t25.t7.t15.t12 t15.t7.t25.t7.t15.t15))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t25.t7.t15.t9 t15.t7.t25.t7.t15.t16 a5))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t25.t7.t15.t3 a7 t15.t7.t25.t7.t15.t8 t15.t7.t25.t7.t15.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t25.t7.t15.t18))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t25.t7.t15.t18))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t25.t7.t15.t20 t15.t7.t25.t7.t15.t21))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t25.t7.t15.t19 t15.t7.t25.t7.t15.t22))
% 0.68/0.88  (step t15.t7.t25.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t7.t15.t23 t15.t7.t25.t7.t15.t24))
% 0.68/0.88  (step t15.t7.t25.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t25.t7.t14 t15.t7.t25.t7.t15))
% 0.68/0.88  (step t15.t7.t25.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t25.t7.t18.t3 t15.t7.t25.t7.t18.t4))
% 0.68/0.88  (step t15.t7.t25.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t25.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t25.t7.t18.t7.t2))
% 0.68/0.88  (step t15.t7.t25.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t25.t7.t18.t6 t15.t7.t25.t7.t18.t7))
% 0.68/0.88  (step t15.t7.t25.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t25.t7.t18.t5 t15.t7.t25.t7.t18.t8))
% 0.68/0.88  (step t15.t7.t25.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t7.t18.t9 t15.t7.t25.t7.t18.t10))
% 0.68/0.88  (step t15.t7.t25.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t25.t7.t18.t11 t15.t7.t25.t7.t18.t12))
% 0.68/0.88  (step t15.t7.t25.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t25.t7.t17 t15.t7.t25.t7.t18))
% 0.68/0.88  (step t15.t7.t25.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t25.t7.t16 t15.t7.t25.t7.t19))
% 0.68/0.88  (step t15.t7.t25.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t25.t7.t13 t15.t7.t25.t7.t20 a8))
% 0.68/0.88  (step t15.t7.t25.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t25.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t25.t7.t23 t15.t7.t25.t7.t24))
% 0.68/0.88  (step t15.t7.t25.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t25.t7.t22 t15.t7.t25.t7.t25 a6))
% 0.68/0.88  (step t15.t7.t25.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t25.t7.t29.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t25.t7.t29.t5))
% 0.68/0.88  (step t15.t7.t25.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t25.t7.t29.t5))
% 0.68/0.88  (step t15.t7.t25.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t25.t7.t29.t7 t15.t7.t25.t7.t29.t8))
% 0.68/0.88  (step t15.t7.t25.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t25.t7.t29.t6 t15.t7.t25.t7.t29.t9))
% 0.68/0.88  (step t15.t7.t25.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t7.t29.t10 t15.t7.t25.t7.t29.t11))
% 0.68/0.88  (step t15.t7.t25.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t7.t29.t12 t15.t7.t25.t7.t29.t13))
% 0.68/0.88  (step t15.t7.t25.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t25.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t25.t7.t28 t15.t7.t25.t7.t29))
% 0.68/0.88  (step t15.t7.t25.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.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)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t25.t7.t32.t4 t15.t7.t25.t7.t32.t5))
% 0.68/0.88  (step t15.t7.t25.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t25.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t25.t7.t32.t8.t3 t15.t7.t25.t7.t32.t8.t4))
% 0.68/0.88  (step t15.t7.t25.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t7.t25.t7.t32.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 (t15.t7.t25.t7.t32.t7 t15.t7.t25.t7.t32.t8))
% 0.68/0.88  (step t15.t7.t25.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t25.t7.t32.t6 t15.t7.t25.t7.t32.t9))
% 0.68/0.88  (step t15.t7.t25.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t7.t32.t10 t15.t7.t25.t7.t32.t11))
% 0.68/0.88  (step t15.t7.t25.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t25.t7.t32.t12 t15.t7.t25.t7.t32.t13))
% 0.68/0.88  (step t15.t7.t25.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t7.t32.t14 t15.t7.t25.t7.t32.t15))
% 0.68/0.88  (step t15.t7.t25.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t25.t7.t32.t16 t15.t7.t25.t7.t32.t17))
% 0.68/0.88  (step t15.t7.t25.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t25.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t25.t7.t31 t15.t7.t25.t7.t32))
% 0.68/0.88  (step t15.t7.t25.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t25.t7.t30 t15.t7.t25.t7.t33))
% 0.68/0.88  (step t15.t7.t25.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t25.t7.t27 t15.t7.t25.t7.t34 a5))
% 0.68/0.88  (step t15.t7.t25.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t25.t7.t7 t15.t7.t25.t7.t12 t15.t7.t25.t7.t21 a7 t15.t7.t25.t7.t26 t15.t7.t25.t7.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t25.t7.t36))
% 0.68/0.88  (step t15.t7.t25.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t25.t7.t36))
% 0.68/0.88  (step t15.t7.t25.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t25.t7.t37 t15.t7.t25.t7.t38))
% 0.68/0.88  (step t15.t7.t25.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t25.t7.t6 t15.t7.t25.t7.t39))
% 0.68/0.88  (step t15.t7.t25.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t7.t25.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t25.t7.t43.t2.t2 t15.t7.t25.t7.t43.t2.t3))
% 0.68/0.88  (step t15.t7.t25.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t25.t7.t43.t2.t4 t15.t7.t25.t7.t43.t2.t5))
% 0.68/0.88  (step t15.t7.t25.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t25.t7.t43.t2 t15.t7.t25.t7.t43.t3))
% 0.68/0.88  (step t15.t7.t25.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t25.t7.t43.t4))
% 0.68/0.88  (step t15.t7.t25.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t25.t7.t43.t5 t15.t7.t25.t7.t43.t6))
% 0.68/0.88  (step t15.t7.t25.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t25.t7.t43 t15.t7.t25.t7.t44))
% 0.68/0.88  (step t15.t7.t25.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t25.t7.t42 t15.t7.t25.t7.t45))
% 0.68/0.88  (step t15.t7.t25.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t25.t7.t41 t15.t7.t25.t7.t46))
% 0.68/0.88  (step t15.t7.t25.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t25.t7.t40 t15.t7.t25.t7.t47))
% 0.68/0.88  (step t15.t7.t25.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t25.t7.t5 t15.t7.t25.t7.t48 a10))
% 0.68/0.88  (step t15.t7.t25.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t25.t7.t4 t15.t7.t25.t7.t49 t15.t7.t25.t7.t12 t15.t7.t25.t7.t21 a7 t15.t7.t25.t7.t26 t15.t7.t25.t7.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t25.t7.t50))
% 0.68/0.88  (step t15.t7.t25.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t25.t7.t51 t15.t7.t25.t7.t52))
% 0.68/0.88  (step t15.t7.t25.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t25.t7.t53 t15.t7.t25.t7.t54))
% 0.68/0.88  (step t15.t7.t25.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t7.t55 t15.t7.t25.t7.t56))
% 0.68/0.88  (step t15.t7.t25.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t25.t6 t15.t7.t25.t7))
% 0.68/0.88  (step t15.t7.t25.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t25.t10.t4 t15.t7.t25.t10.t5))
% 0.68/0.88  (step t15.t7.t25.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t25.t10.t6 t15.t7.t25.t10.t7))
% 0.68/0.88  (step t15.t7.t25.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t10.t8 t15.t7.t25.t10.t9))
% 0.68/0.88  (step t15.t7.t25.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t25.t10.t10 t15.t7.t25.t10.t11))
% 0.68/0.88  (step t15.t7.t25.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t25.t9 t15.t7.t25.t10))
% 0.68/0.88  (step t15.t7.t25.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t25.t8 t15.t7.t25.t11))
% 0.68/0.88  (step t15.t7.t25.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t25.t5 t15.t7.t25.t12 a11))
% 0.68/0.88  (step t15.t7.t25.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t25.t18 t15.t7.t25.t19))
% 0.68/0.88  (step t15.t7.t25.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t25.t17 t15.t7.t25.t20 a9))
% 0.68/0.88  (step t15.t7.t25.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t25.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t25.t24.t5 t15.t7.t25.t24.t6))
% 0.68/0.88  (step t15.t7.t25.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t25.t24.t4 t15.t7.t25.t24.t7 a6))
% 0.68/0.88  (step t15.t7.t25.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t25.t24.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t25.t24.t11.t5))
% 0.68/0.88  (step t15.t7.t25.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t25.t24.t11.t5))
% 0.68/0.88  (step t15.t7.t25.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t25.t24.t11.t7 t15.t7.t25.t24.t11.t8))
% 0.68/0.88  (step t15.t7.t25.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t25.t24.t11.t6 t15.t7.t25.t24.t11.t9))
% 0.68/0.88  (step t15.t7.t25.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t24.t11.t10 t15.t7.t25.t24.t11.t11))
% 0.68/0.88  (step t15.t7.t25.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t24.t11.t12 t15.t7.t25.t24.t11.t13))
% 0.68/0.88  (step t15.t7.t25.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t25.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t25.t24.t10 t15.t7.t25.t24.t11))
% 0.68/0.88  (step t15.t7.t25.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.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)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t25.t24.t14.t4 t15.t7.t25.t24.t14.t5))
% 0.68/0.88  (step t15.t7.t25.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t25.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t25.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t25.t24.t14.t8.t3 t15.t7.t25.t24.t14.t8.t4))
% 0.68/0.88  (step t15.t7.t25.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t7.t25.t24.t14.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 (t15.t7.t25.t24.t14.t7 t15.t7.t25.t24.t14.t8))
% 0.68/0.88  (step t15.t7.t25.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t25.t24.t14.t6 t15.t7.t25.t24.t14.t9))
% 0.68/0.88  (step t15.t7.t25.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t24.t14.t10 t15.t7.t25.t24.t14.t11))
% 0.68/0.88  (step t15.t7.t25.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t25.t24.t14.t12 t15.t7.t25.t24.t14.t13))
% 0.68/0.88  (step t15.t7.t25.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t24.t14.t14 t15.t7.t25.t24.t14.t15))
% 0.68/0.88  (step t15.t7.t25.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t25.t24.t14.t16 t15.t7.t25.t24.t14.t17))
% 0.68/0.88  (step t15.t7.t25.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t25.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t25.t24.t13 t15.t7.t25.t24.t14))
% 0.68/0.88  (step t15.t7.t25.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t25.t24.t12 t15.t7.t25.t24.t15))
% 0.68/0.88  (step t15.t7.t25.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t25.t24.t9 t15.t7.t25.t24.t16 a5))
% 0.68/0.88  (step t15.t7.t25.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t25.t24.t3 a7 t15.t7.t25.t24.t8 t15.t7.t25.t24.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t25.t24.t18))
% 0.68/0.88  (step t15.t7.t25.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t25.t24.t18))
% 0.68/0.88  (step t15.t7.t25.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t25.t24.t20 t15.t7.t25.t24.t21))
% 0.68/0.88  (step t15.t7.t25.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t25.t24.t19 t15.t7.t25.t24.t22))
% 0.68/0.88  (step t15.t7.t25.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t24.t23 t15.t7.t25.t24.t24))
% 0.68/0.88  (step t15.t7.t25.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t25.t23 t15.t7.t25.t24))
% 0.68/0.88  (step t15.t7.t25.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t25.t27.t3 t15.t7.t25.t27.t4))
% 0.68/0.88  (step t15.t7.t25.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t25.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t25.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t25.t27.t7.t2))
% 0.68/0.88  (step t15.t7.t25.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t25.t27.t6 t15.t7.t25.t27.t7))
% 0.68/0.88  (step t15.t7.t25.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t25.t27.t5 t15.t7.t25.t27.t8))
% 0.68/0.88  (step t15.t7.t25.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t27.t9 t15.t7.t25.t27.t10))
% 0.68/0.88  (step t15.t7.t25.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t25.t27.t11 t15.t7.t25.t27.t12))
% 0.68/0.88  (step t15.t7.t25.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t25.t26 t15.t7.t25.t27))
% 0.68/0.88  (step t15.t7.t25.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t25.t25 t15.t7.t25.t28))
% 0.68/0.88  (step t15.t7.t25.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t25.t22 t15.t7.t25.t29 a8))
% 0.68/0.88  (step t15.t7.t25.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t25.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t25.t32 t15.t7.t25.t33))
% 0.68/0.88  (step t15.t7.t25.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t25.t31 t15.t7.t25.t34 a6))
% 0.68/0.88  (step t15.t7.t25.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t25.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t38.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t25.t38.t5 (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)))))) :rule resolution :premises (t15.t7.t25.t38.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t25.t38.t5))
% 0.68/0.88  (step t15.t7.t25.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t25.t38.t5))
% 0.68/0.88  (step t15.t7.t25.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t25.t38.t7 t15.t7.t25.t38.t8))
% 0.68/0.88  (step t15.t7.t25.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t25.t38.t6 t15.t7.t25.t38.t9))
% 0.68/0.88  (step t15.t7.t25.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t25.t38.t10 t15.t7.t25.t38.t11))
% 0.68/0.88  (step t15.t7.t25.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t38.t12 t15.t7.t25.t38.t13))
% 0.68/0.88  (step t15.t7.t25.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t25.t37 t15.t7.t25.t38))
% 0.68/0.88  (step t15.t7.t25.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t25.t41.t4 t15.t7.t25.t41.t5))
% 0.68/0.88  (step t15.t7.t25.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t7.t25.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t25.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t25.t41.t8.t3 t15.t7.t25.t41.t8.t4))
% 0.68/0.88  (step t15.t7.t25.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t25.t41.t7 t15.t7.t25.t41.t8))
% 0.68/0.88  (step t15.t7.t25.t41.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t25.t41.t6 t15.t7.t25.t41.t9))
% 0.68/0.88  (step t15.t7.t25.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t25.t41.t10 t15.t7.t25.t41.t11))
% 0.68/0.88  (step t15.t7.t25.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t41.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 (t15.t7.t25.t41.t12 t15.t7.t25.t41.t13))
% 0.68/0.88  (step t15.t7.t25.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t41.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 (t15.t7.t25.t41.t14 t15.t7.t25.t41.t15))
% 0.68/0.88  (step t15.t7.t25.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t25.t41.t16 t15.t7.t25.t41.t17))
% 0.68/0.88  (step t15.t7.t25.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t25.t40 t15.t7.t25.t41))
% 0.68/0.88  (step t15.t7.t25.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t25.t39 t15.t7.t25.t42))
% 0.68/0.88  (step t15.t7.t25.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t25.t36 t15.t7.t25.t43 a5))
% 0.68/0.88  (step t15.t7.t25.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t25.t16 t15.t7.t25.t21 t15.t7.t25.t30 a7 t15.t7.t25.t35 t15.t7.t25.t44 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t25.t45))
% 0.68/0.88  (step t15.t7.t25.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t25.t45))
% 0.68/0.88  (step t15.t7.t25.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t25.t46 t15.t7.t25.t47))
% 0.68/0.88  (step t15.t7.t25.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t25.t15 t15.t7.t25.t48))
% 0.68/0.88  (step t15.t7.t25.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t25.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t25.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t25.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t7.t25.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t25.t52.t2.t2 t15.t7.t25.t52.t2.t3))
% 0.68/0.88  (step t15.t7.t25.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t25.t52.t2.t4 t15.t7.t25.t52.t2.t5))
% 0.68/0.88  (step t15.t7.t25.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t25.t52.t2 t15.t7.t25.t52.t3))
% 0.68/0.88  (step t15.t7.t25.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t25.t52.t4))
% 0.68/0.88  (step t15.t7.t25.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t25.t52.t5 t15.t7.t25.t52.t6))
% 0.68/0.88  (step t15.t7.t25.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t7.t25.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t25.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t25.t52 t15.t7.t25.t53))
% 0.68/0.88  (step t15.t7.t25.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t25.t51 t15.t7.t25.t54))
% 0.68/0.88  (step t15.t7.t25.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t25.t50 t15.t7.t25.t55))
% 0.68/0.88  (step t15.t7.t25.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t25.t49 t15.t7.t25.t56))
% 0.68/0.88  (step t15.t7.t25.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t25.t14 t15.t7.t25.t57 a10))
% 0.68/0.88  (step t15.t7.t25.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t25.t4 t15.t7.t25.t13 t15.t7.t25.t58 t15.t7.t25.t21 t15.t7.t25.t30 a7 t15.t7.t25.t35 t15.t7.t25.t44 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t25.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t25.t59))
% 0.68/0.88  (step t15.t7.t25.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t25.t59))
% 0.68/0.88  (step t15.t7.t25.t62 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t25.t61 t15.t7.t25.t62))
% 0.68/0.88  (step t15.t7.t25.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t25.t60 t15.t7.t25.t63))
% 0.68/0.88  (step t15.t7.t25.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t7.t25.t61 t15.t7.t25.t65))
% 0.68/0.88  (step t15.t7.t25.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t7.t25.t64 t15.t7.t25.t66))
% 0.68/0.88  (step t15.t7.t25.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t25.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t7.t25.t67 t15.t7.t25.t68))
% 0.68/0.88  (step t15.t7.t25 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t26 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t7.t24 t15.t7.t25))
% 0.68/0.88  (step t15.t7.t27 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t28 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t28.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t28.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)
% 0.68/0.88  (step t15.t7.t28.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t28.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t28.t4 t15.t7.t28.t5))
% 0.68/0.88  (step t15.t7.t28.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t28.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t28.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t28.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t7.t28.t8.t3 t15.t7.t28.t8.t4))
% 0.68/0.88  (step t15.t7.t28.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t28.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t28.t7 t15.t7.t28.t8))
% 0.68/0.88  (step t15.t7.t28.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t7.t28.t6 t15.t7.t28.t9))
% 0.68/0.88  (step t15.t7.t28.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t28.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t7.t28.t10 t15.t7.t28.t11))
% 0.68/0.88  (step t15.t7.t28.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t28.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t28.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t28.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t7.t28.t14.t2 t15.t7.t28.t14.t3))
% 0.68/0.88  (step t15.t7.t28.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t28.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t28.t13 t15.t7.t28.t14))
% 0.68/0.88  (step t15.t7.t28.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t7.t28.t12 t15.t7.t28.t15))
% 0.68/0.88  (step t15.t7.t28.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t28.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t28.t16 t15.t7.t28.t17))
% 0.68/0.88  (step t15.t7.t28.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t28.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t7.t28.t18 t15.t7.t28.t19))
% 0.68/0.88  (step t15.t7.t28 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t29 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t7.t27 t15.t7.t28))
% 0.68/0.88  (step t15.t7.t30 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t7.t26 t15.t7.t29))
% 0.68/0.88  (step t15.t7.t31 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t7.t23 t15.t7.t30 a12))
% 0.68/0.88  (step t15.t7.t32 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t33 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t34.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t34.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t34.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t34.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t34.t9 t15.t7.t34.t10))
% 0.68/0.88  (step t15.t7.t34.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t34.t8 t15.t7.t34.t11 a9))
% 0.68/0.88  (step t15.t7.t34.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t34.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t34.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t34.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t34.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t34.t15.t5 t15.t7.t34.t15.t6))
% 0.68/0.88  (step t15.t7.t34.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t34.t15.t4 t15.t7.t34.t15.t7 a6))
% 0.68/0.88  (step t15.t7.t34.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t34.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t34.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t7.t34.t15.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t34.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t34.t15.t11.t5))
% 0.68/0.88  (step t15.t7.t34.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t34.t15.t11.t5))
% 0.68/0.88  (step t15.t7.t34.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t34.t15.t11.t7 t15.t7.t34.t15.t11.t8))
% 0.68/0.88  (step t15.t7.t34.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t34.t15.t11.t6 t15.t7.t34.t15.t11.t9))
% 0.68/0.88  (step t15.t7.t34.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t34.t15.t11.t10 t15.t7.t34.t15.t11.t11))
% 0.68/0.88  (step t15.t7.t34.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t34.t15.t11.t12 t15.t7.t34.t15.t11.t13))
% 0.68/0.88  (step t15.t7.t34.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t34.t15.t10 t15.t7.t34.t15.t11))
% 0.68/0.88  (step t15.t7.t34.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t34.t15.t14.t4 t15.t7.t34.t15.t14.t5))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t7.t34.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t34.t15.t14.t8.t3 t15.t7.t34.t15.t14.t8.t4))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t34.t15.t14.t7 t15.t7.t34.t15.t14.t8))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t34.t15.t14.t6 t15.t7.t34.t15.t14.t9))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t34.t15.t14.t10 t15.t7.t34.t15.t14.t11))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t15.t14.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 (t15.t7.t34.t15.t14.t12 t15.t7.t34.t15.t14.t13))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t14.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 (t15.t7.t34.t15.t14.t14 t15.t7.t34.t15.t14.t15))
% 0.68/0.88  (step t15.t7.t34.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t34.t15.t14.t16 t15.t7.t34.t15.t14.t17))
% 0.68/0.88  (step t15.t7.t34.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t34.t15.t13 t15.t7.t34.t15.t14))
% 0.68/0.88  (step t15.t7.t34.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t34.t15.t12 t15.t7.t34.t15.t15))
% 0.68/0.88  (step t15.t7.t34.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t34.t15.t9 t15.t7.t34.t15.t16 a5))
% 0.68/0.88  (step t15.t7.t34.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t34.t15.t3 a7 t15.t7.t34.t15.t8 t15.t7.t34.t15.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t34.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t34.t15.t18))
% 0.68/0.88  (step t15.t7.t34.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t34.t15.t18))
% 0.68/0.88  (step t15.t7.t34.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t34.t15.t20 t15.t7.t34.t15.t21))
% 0.68/0.88  (step t15.t7.t34.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t34.t15.t19 t15.t7.t34.t15.t22))
% 0.68/0.88  (step t15.t7.t34.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t34.t15.t23 t15.t7.t34.t15.t24))
% 0.68/0.88  (step t15.t7.t34.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t34.t14 t15.t7.t34.t15))
% 0.68/0.88  (step t15.t7.t34.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t34.t18.t3 t15.t7.t34.t18.t4))
% 0.68/0.88  (step t15.t7.t34.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t34.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t34.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t34.t18.t7.t2))
% 0.68/0.88  (step t15.t7.t34.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t34.t18.t6 t15.t7.t34.t18.t7))
% 0.68/0.88  (step t15.t7.t34.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t34.t18.t5 t15.t7.t34.t18.t8))
% 0.68/0.88  (step t15.t7.t34.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t34.t18.t9 t15.t7.t34.t18.t10))
% 0.68/0.88  (step t15.t7.t34.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t34.t18.t11 t15.t7.t34.t18.t12))
% 0.68/0.88  (step t15.t7.t34.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t34.t17 t15.t7.t34.t18))
% 0.68/0.88  (step t15.t7.t34.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t34.t16 t15.t7.t34.t19))
% 0.68/0.88  (step t15.t7.t34.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t34.t13 t15.t7.t34.t20 a8))
% 0.68/0.88  (step t15.t7.t34.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t34.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t34.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t34.t23 t15.t7.t34.t24))
% 0.68/0.88  (step t15.t7.t34.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t34.t22 t15.t7.t34.t25 a6))
% 0.68/0.88  (step t15.t7.t34.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t34.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t34.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t34.t29.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t34.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t34.t29.t5))
% 0.68/0.88  (step t15.t7.t34.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t34.t29.t5))
% 0.68/0.88  (step t15.t7.t34.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t34.t29.t7 t15.t7.t34.t29.t8))
% 0.68/0.88  (step t15.t7.t34.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t34.t29.t6 t15.t7.t34.t29.t9))
% 0.68/0.88  (step t15.t7.t34.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t34.t29.t10 t15.t7.t34.t29.t11))
% 0.68/0.88  (step t15.t7.t34.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t34.t29.t12 t15.t7.t34.t29.t13))
% 0.68/0.88  (step t15.t7.t34.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t34.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t34.t28 t15.t7.t34.t29))
% 0.68/0.88  (step t15.t7.t34.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.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)
% 0.68/0.88  (step t15.t7.t34.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t34.t32.t4 t15.t7.t34.t32.t5))
% 0.68/0.88  (step t15.t7.t34.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t34.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t34.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t34.t32.t8.t3 t15.t7.t34.t32.t8.t4))
% 0.68/0.88  (step t15.t7.t34.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t7.t34.t32.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 (t15.t7.t34.t32.t7 t15.t7.t34.t32.t8))
% 0.68/0.88  (step t15.t7.t34.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t34.t32.t6 t15.t7.t34.t32.t9))
% 0.68/0.88  (step t15.t7.t34.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t34.t32.t10 t15.t7.t34.t32.t11))
% 0.68/0.88  (step t15.t7.t34.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t34.t32.t12 t15.t7.t34.t32.t13))
% 0.68/0.88  (step t15.t7.t34.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t34.t32.t14 t15.t7.t34.t32.t15))
% 0.68/0.88  (step t15.t7.t34.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t34.t32.t16 t15.t7.t34.t32.t17))
% 0.68/0.88  (step t15.t7.t34.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t34.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t34.t31 t15.t7.t34.t32))
% 0.68/0.88  (step t15.t7.t34.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t34.t30 t15.t7.t34.t33))
% 0.68/0.88  (step t15.t7.t34.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t34.t27 t15.t7.t34.t34 a5))
% 0.68/0.88  (step t15.t7.t34.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t34.t7 t15.t7.t34.t12 t15.t7.t34.t21 a7 t15.t7.t34.t26 t15.t7.t34.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t34.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t34.t36))
% 0.68/0.88  (step t15.t7.t34.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t34.t36))
% 0.68/0.88  (step t15.t7.t34.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t34.t37 t15.t7.t34.t38))
% 0.68/0.88  (step t15.t7.t34.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t34.t6 t15.t7.t34.t39))
% 0.68/0.88  (step t15.t7.t34.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t34.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t34.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t34.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t7.t34.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t34.t43.t2.t2 t15.t7.t34.t43.t2.t3))
% 0.68/0.88  (step t15.t7.t34.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t34.t43.t2.t4 t15.t7.t34.t43.t2.t5))
% 0.68/0.88  (step t15.t7.t34.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t34.t43.t2 t15.t7.t34.t43.t3))
% 0.68/0.88  (step t15.t7.t34.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t34.t43.t4))
% 0.68/0.88  (step t15.t7.t34.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t34.t43.t5 t15.t7.t34.t43.t6))
% 0.68/0.88  (step t15.t7.t34.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t7.t34.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t34.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t34.t43 t15.t7.t34.t44))
% 0.68/0.88  (step t15.t7.t34.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t34.t42 t15.t7.t34.t45))
% 0.68/0.88  (step t15.t7.t34.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t34.t41 t15.t7.t34.t46))
% 0.68/0.88  (step t15.t7.t34.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t34.t40 t15.t7.t34.t47))
% 0.68/0.88  (step t15.t7.t34.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t34.t5 t15.t7.t34.t48 a10))
% 0.68/0.88  (step t15.t7.t34.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t34.t4 t15.t7.t34.t49 t15.t7.t34.t12 t15.t7.t34.t21 a7 t15.t7.t34.t26 t15.t7.t34.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t34.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t34.t50))
% 0.68/0.88  (step t15.t7.t34.t52 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t7.t34.t51 t15.t7.t34.t52))
% 0.68/0.88  (step t15.t7.t34.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t7.t34.t53 t15.t7.t34.t54))
% 0.68/0.88  (step t15.t7.t34.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t34.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t7.t34.t55 t15.t7.t34.t56))
% 0.68/0.88  (step t15.t7.t34 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t35 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t7.t33 t15.t7.t34))
% 0.68/0.88  (step t15.t7.t36 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t37 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t37.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t37.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t37.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t37.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t37.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t7.t37.t4 t15.t7.t37.t5))
% 0.68/0.88  (step t15.t7.t37.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t37.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t7.t37.t6 t15.t7.t37.t7))
% 0.68/0.88  (step t15.t7.t37.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t37.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t7.t37.t8 t15.t7.t37.t9))
% 0.68/0.88  (step t15.t7.t37.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t37.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t7.t37.t10 t15.t7.t37.t11))
% 0.68/0.88  (step t15.t7.t37 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t38 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t7.t36 t15.t7.t37))
% 0.68/0.88  (step t15.t7.t39 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t7.t35 t15.t7.t38))
% 0.68/0.88  (step t15.t7.t40 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t7.t32 t15.t7.t39 a11))
% 0.68/0.88  (step t15.t7.t41 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t42 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t43 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t44 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t45 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t7.t46 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t47 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t45 t15.t7.t46))
% 0.68/0.88  (step t15.t7.t48 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t7.t44 t15.t7.t47 a9))
% 0.68/0.88  (step t15.t7.t49 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t50 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t51 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t51.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t51.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t51.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t51.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t51.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t51.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t51.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t51.t5 t15.t7.t51.t6))
% 0.68/0.88  (step t15.t7.t51.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t51.t4 t15.t7.t51.t7 a6))
% 0.68/0.88  (step t15.t7.t51.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t51.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t51.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t51.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t51.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t51.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t51.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t51.t11.t5))
% 0.68/0.88  (step t15.t7.t51.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t51.t11.t5))
% 0.68/0.88  (step t15.t7.t51.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t51.t11.t7 t15.t7.t51.t11.t8))
% 0.68/0.88  (step t15.t7.t51.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t7.t51.t11.t6 t15.t7.t51.t11.t9))
% 0.68/0.88  (step t15.t7.t51.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t7.t51.t11.t10 t15.t7.t51.t11.t11))
% 0.68/0.88  (step t15.t7.t51.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t7.t51.t11.t12 t15.t7.t51.t11.t13))
% 0.68/0.88  (step t15.t7.t51.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t51.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t7.t51.t10 t15.t7.t51.t11))
% 0.68/0.88  (step t15.t7.t51.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t51.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t51.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.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)
% 0.68/0.88  (step t15.t7.t51.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t51.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t51.t14.t4 t15.t7.t51.t14.t5))
% 0.68/0.88  (step t15.t7.t51.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t51.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t51.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t51.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t51.t14.t8.t3 t15.t7.t51.t14.t8.t4))
% 0.68/0.88  (step t15.t7.t51.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t7.t51.t14.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 (t15.t7.t51.t14.t7 t15.t7.t51.t14.t8))
% 0.68/0.88  (step t15.t7.t51.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t51.t14.t6 t15.t7.t51.t14.t9))
% 0.68/0.88  (step t15.t7.t51.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t7.t51.t14.t10 t15.t7.t51.t14.t11))
% 0.68/0.88  (step t15.t7.t51.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t51.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t7.t51.t14.t12 t15.t7.t51.t14.t13))
% 0.68/0.88  (step t15.t7.t51.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t7.t51.t14.t14 t15.t7.t51.t14.t15))
% 0.68/0.88  (step t15.t7.t51.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t51.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t7.t51.t14.t16 t15.t7.t51.t14.t17))
% 0.68/0.88  (step t15.t7.t51.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t7.t51.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t51.t13 t15.t7.t51.t14))
% 0.68/0.88  (step t15.t7.t51.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t51.t12 t15.t7.t51.t15))
% 0.68/0.88  (step t15.t7.t51.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t51.t9 t15.t7.t51.t16 a5))
% 0.68/0.88  (step t15.t7.t51.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t51.t3 a7 t15.t7.t51.t8 t15.t7.t51.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t51.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t51.t18))
% 0.68/0.88  (step t15.t7.t51.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t7.t51.t18))
% 0.68/0.88  (step t15.t7.t51.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t7.t51.t20 t15.t7.t51.t21))
% 0.68/0.88  (step t15.t7.t51.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t7.t51.t19 t15.t7.t51.t22))
% 0.68/0.88  (step t15.t7.t51.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t51.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t51.t23 t15.t7.t51.t24))
% 0.68/0.88  (step t15.t7.t51 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t52 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t7.t50 t15.t7.t51))
% 0.68/0.88  (step t15.t7.t53 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t54 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t54.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t54.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t54.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t54.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t54.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t54.t3 t15.t7.t54.t4))
% 0.68/0.88  (step t15.t7.t54.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t54.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t54.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t54.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t54.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t7.t54.t7.t2))
% 0.68/0.88  (step t15.t7.t54.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t54.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t54.t6 t15.t7.t54.t7))
% 0.68/0.88  (step t15.t7.t54.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t7.t54.t5 t15.t7.t54.t8))
% 0.68/0.88  (step t15.t7.t54.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t54.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t7.t54.t9 t15.t7.t54.t10))
% 0.68/0.88  (step t15.t7.t54.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t54.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t7.t54.t11 t15.t7.t54.t12))
% 0.68/0.88  (step t15.t7.t54 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t7.t55 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t7.t53 t15.t7.t54))
% 0.68/0.88  (step t15.t7.t56 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t7.t52 t15.t7.t55))
% 0.68/0.88  (step t15.t7.t57 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t7.t49 t15.t7.t56 a8))
% 0.68/0.88  (step t15.t7.t58 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t59 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t60 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t7.t60.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t60.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t7.t60.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t60 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t7.t61 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t7.t59 t15.t7.t60))
% 0.68/0.88  (step t15.t7.t62 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t7.t58 t15.t7.t61 a6))
% 0.68/0.88  (step t15.t7.t63 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t7.t64 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t65 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t65.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t65.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t65.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t65.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t7.t65.t5 (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)))))) :rule resolution :premises (t15.t7.t65.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t65.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t7.t65.t5))
% 0.68/0.88  (step t15.t7.t65.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t7.t65.t5))
% 0.68/0.88  (step t15.t7.t65.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t65.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t7.t65.t7 t15.t7.t65.t8))
% 0.68/0.88  (step t15.t7.t65.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t7.t65.t6 t15.t7.t65.t9))
% 0.68/0.88  (step t15.t7.t65.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t65.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t7.t65.t10 t15.t7.t65.t11))
% 0.68/0.88  (step t15.t7.t65.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t65.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t65.t12 t15.t7.t65.t13))
% 0.68/0.88  (step t15.t7.t65 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t7.t66 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t7.t64 t15.t7.t65))
% 0.68/0.88  (step t15.t7.t67 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t68 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t68.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t68.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t68.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t68.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t7.t68.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t68.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t7.t68.t4 t15.t7.t68.t5))
% 0.68/0.88  (step t15.t7.t68.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t7.t68.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t7.t68.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t68.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t7.t68.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t68.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t7.t68.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t7.t68.t8.t3 t15.t7.t68.t8.t4))
% 0.68/0.88  (step t15.t7.t68.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t7.t68.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t7.t68.t7 t15.t7.t68.t8))
% 0.68/0.88  (step t15.t7.t68.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t7.t68.t6 t15.t7.t68.t9))
% 0.68/0.88  (step t15.t7.t68.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t7.t68.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t7.t68.t10 t15.t7.t68.t11))
% 0.68/0.88  (step t15.t7.t68.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t68.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 (t15.t7.t68.t12 t15.t7.t68.t13))
% 0.68/0.88  (step t15.t7.t68.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t68.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 (t15.t7.t68.t14 t15.t7.t68.t15))
% 0.68/0.88  (step t15.t7.t68.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t68.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t7.t68.t16 t15.t7.t68.t17))
% 0.68/0.88  (step t15.t7.t68 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t7.t69 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t7.t67 t15.t7.t68))
% 0.68/0.88  (step t15.t7.t70 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t7.t66 t15.t7.t69))
% 0.68/0.88  (step t15.t7.t71 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t7.t63 t15.t7.t70 a5))
% 0.68/0.88  (step t15.t7.t72 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t7.t43 t15.t7.t48 t15.t7.t57 a7 t15.t7.t62 t15.t7.t71 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t73 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t7.t72))
% 0.68/0.88  (step t15.t7.t74 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t7.t72))
% 0.68/0.88  (step t15.t7.t75 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t7.t73 t15.t7.t74))
% 0.68/0.88  (step t15.t7.t76 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t7.t42 t15.t7.t75))
% 0.68/0.88  (step t15.t7.t77 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t7.t78 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t7.t79 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t7.t79.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t7.t79.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t7.t79.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t7.t79.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t7.t79.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t79.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t7.t79.t2.t2 t15.t7.t79.t2.t3))
% 0.68/0.88  (step t15.t7.t79.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t79.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t7.t79.t2.t4 t15.t7.t79.t2.t5))
% 0.68/0.88  (step t15.t7.t79.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t7.t79.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t79.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t7.t79.t2 t15.t7.t79.t3))
% 0.68/0.88  (step t15.t7.t79.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t7.t79.t4))
% 0.68/0.88  (step t15.t7.t79.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t79.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t7.t79.t5 t15.t7.t79.t6))
% 0.68/0.88  (step t15.t7.t79 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t7.t80 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t7.t81 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t79 t15.t7.t80))
% 0.68/0.88  (step t15.t7.t82 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t7.t78 t15.t7.t81))
% 0.68/0.88  (step t15.t7.t83 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t7.t77 t15.t7.t82))
% 0.68/0.88  (step t15.t7.t84 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t7.t76 t15.t7.t83))
% 0.68/0.88  (step t15.t7.t85 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t7.t41 t15.t7.t84 a10))
% 0.68/0.88  (step t15.t7.t86 (cl (and (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t7.t4 t15.t7.t13 t15.t7.t22 t15.t7.t31 t15.t7.t40 t15.t7.t85 t15.t7.t48 t15.t7.t57 a7 t15.t7.t62 t15.t7.t71 a4 a3 a2))
% 0.68/0.88  (step t15.t7.t87 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule and :premises (t15.t7.t86))
% 0.68/0.88  (step t15.t7.t88 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule and :premises (t15.t7.t86))
% 0.68/0.88  (step t15.t7.t89 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t7.t90 (cl (= (@ tptp.iimplies P) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t15.t7.t88 t15.t7.t89))
% 0.68/0.88  (step t15.t7.t91 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t7.t92 (cl (= (@ (@ tptp.iimplies P) Q) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q))) :rule cong :premises (t15.t7.t90 t15.t7.t91))
% 0.68/0.88  (step t15.t7.t93 (cl (= (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)))) :rule cong :premises (t15.t7.t87 t15.t7.t92))
% 0.68/0.88  (step t15.t7.t94 (cl (= (@ tptp.iimplies Q) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t15.t7.t88 t15.t7.t91))
% 0.68/0.88  (step t15.t7.t95 (cl (= (@ (@ tptp.iimplies Q) P) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P))) :rule cong :premises (t15.t7.t94 t15.t7.t89))
% 0.68/0.88  (step t15.t7.t96 (cl (= (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)))) :rule cong :premises (t15.t7.t93 t15.t7.t95))
% 0.68/0.88  (step t15.t7.t97 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t7.t98 (cl (= (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0))) :rule cong :premises (t15.t7.t96 t15.t7.t97))
% 0.68/0.88  (step t15.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t8 (cl (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0))))) :rule cong :premises (t15.t6 t15.t7))
% 0.68/0.88  (step t15.t9 (cl (= tptp.iequiv tptp.iequiv)) :rule refl)
% 0.68/0.88  (anchor :step t15.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t10.t4 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule refl)
% 0.68/0.88  (step t15.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.88  (step t15.t10.t6 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t10.t7 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t15.t10.t5 t15.t10.t6))
% 0.68/0.88  (step t15.t10.t8 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.88  (step t15.t10.t9 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t10.t7 t15.t10.t8))
% 0.68/0.88  (step t15.t10.t10 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t10.t4 t15.t10.t9))
% 0.68/0.88  (step t15.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (@ Q __flatten_var_0))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t10.t12 :args ((Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t10.t12.t1 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t10.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t10.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t10.t12.t4 (cl (= (@ Q __flatten_var_0) (@ Q __flatten_var_0))) :rule refl)
% 0.68/0.88  (step t15.t10.t12.t5 (cl (= (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (@ Q __flatten_var_0)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0)))) :rule cong :premises (t15.t10.t12.t3 t15.t10.t12.t4))
% 0.68/0.88  (step t15.t10.t12 (cl (= (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t10.t13 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))))) :rule trans :premises (t15.t10.t11 t15.t10.t12))
% 0.68/0.88  (step t15.t10.t14 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))))) :rule trans :premises (t15.t10.t10 t15.t10.t13))
% 0.68/0.88  (step t15.t10.t15 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.88  (step t15.t10.t16 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t10.t17 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t15.t10.t15 t15.t10.t16))
% 0.68/0.88  (step t15.t10.t18 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.88  (step t15.t10.t19 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t15.t10.t17 t15.t10.t18))
% 0.68/0.88  (step t15.t10.t20 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t10.t14 t15.t10.t19))
% 0.68/0.88  (step t15.t10.t21 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t10.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t10.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t10.t22.t2 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule refl)
% 0.68/0.88  (step t15.t10.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t10.t22.t4 (cl (= (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule cong :premises (t15.t10.t22.t2 t15.t10.t22.t3))
% 0.68/0.88  (step t15.t10.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule bind)
% 0.68/0.88  (step t15.t10.t23 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t10.t21 t15.t10.t22))
% 0.68/0.88  (step t15.t10.t24 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t10.t20 t15.t10.t23))
% 0.68/0.88  (step t15.t10.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t10.t26 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) __flatten_var_0))) :rule cong :premises (t15.t10.t24 t15.t10.t25))
% 0.68/0.88  (step t15.t10.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) __flatten_var_0) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.88  (step t15.t10.t28 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t15.t10.t26 t15.t10.t27))
% 0.68/0.88  (step t15.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule bind)
% 0.68/0.88  (step t15.t11 (cl (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))))) :rule cong :premises (t15.t9 t15.t10))
% 0.68/0.88  (step t15.t12 (cl (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))))) :rule trans :premises (t15.t8 t15.t11))
% 0.68/0.88  (step t15.t13 (cl (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule resolution :premises (t15.t5 t15.t12 a15))
% 0.68/0.88  (step t15.t14 (cl (not (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t15 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t4 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t5 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t6 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t7.t7.t9 t15.t16.t7.t7.t7.t10))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t7.t7.t7.t8 t15.t16.t7.t7.t7.t11 a9))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t5 t15.t16.t7.t7.t7.t15.t6))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t7.t7.t15.t4 t15.t16.t7.t7.t7.t15.t7 a6))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t16.t7.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t7.t7.t15.t11.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t7.t7.t15.t11.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t11.t7 t15.t16.t7.t7.t7.t15.t11.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t7.t15.t11.t6 t15.t16.t7.t7.t7.t15.t11.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t11.t10 t15.t16.t7.t7.t7.t15.t11.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t7.t15.t11.t12 t15.t16.t7.t7.t7.t15.t11.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t7.t7.t7.t15.t10 t15.t16.t7.t7.t7.t15.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t14.t4 t15.t16.t7.t7.t7.t15.t14.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t14.t8.t3 t15.t16.t7.t7.t7.t15.t14.t8.t4))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t7.t7.t15.t14.t7 t15.t16.t7.t7.t7.t15.t14.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t7.t15.t14.t6 t15.t16.t7.t7.t7.t15.t14.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t14.t10 t15.t16.t7.t7.t7.t15.t14.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.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 (t15.t16.t7.t7.t7.t15.t14.t12 t15.t16.t7.t7.t7.t15.t14.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.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 (t15.t16.t7.t7.t7.t15.t14.t14 t15.t16.t7.t7.t7.t15.t14.t15))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t7.t15.t14.t16 t15.t16.t7.t7.t7.t15.t14.t17))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t13 t15.t16.t7.t7.t7.t15.t14))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t7.t7.t15.t12 t15.t16.t7.t7.t7.t15.t15))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t7.t7.t15.t9 t15.t16.t7.t7.t7.t15.t16 a5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t7.t7.t15.t3 a7 t15.t16.t7.t7.t7.t15.t8 t15.t16.t7.t7.t7.t15.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t7.t7.t15.t18))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t7.t7.t7.t15.t18))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t20 t15.t16.t7.t7.t7.t15.t21))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t19 t15.t16.t7.t7.t7.t15.t22))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t7.t15.t23 t15.t16.t7.t7.t7.t15.t24))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t7.t7.t14 t15.t16.t7.t7.t7.t15))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t7.t7.t18.t3 t15.t16.t7.t7.t7.t18.t4))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t7.t7.t7.t18.t7.t2))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t7.t7.t18.t6 t15.t16.t7.t7.t7.t18.t7))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t7.t7.t18.t5 t15.t16.t7.t7.t7.t18.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t7.t18.t9 t15.t16.t7.t7.t7.t18.t10))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t7.t7.t7.t18.t11 t15.t16.t7.t7.t7.t18.t12))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t7.t7.t7.t17 t15.t16.t7.t7.t7.t18))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t7.t7.t7.t16 t15.t16.t7.t7.t7.t19))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t7.t7.t7.t13 t15.t16.t7.t7.t7.t20 a8))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t7.t7.t23 t15.t16.t7.t7.t7.t24))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t7.t7.t22 t15.t16.t7.t7.t7.t25 a6))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t7.t7.t29.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t7.t7.t29.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t7.t7.t29.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t7.t7.t29.t7 t15.t16.t7.t7.t7.t29.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t7.t7.t7.t29.t6 t15.t16.t7.t7.t7.t29.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t7.t29.t10 t15.t16.t7.t7.t7.t29.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t7.t29.t12 t15.t16.t7.t7.t7.t29.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t7.t7.t28 t15.t16.t7.t7.t7.t29))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.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)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t7.t32.t4 t15.t16.t7.t7.t7.t32.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t7.t7.t32.t8.t3 t15.t16.t7.t7.t7.t32.t8.t4))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.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 (t15.t16.t7.t7.t7.t32.t7 t15.t16.t7.t7.t7.t32.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t7.t7.t32.t6 t15.t16.t7.t7.t7.t32.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t7.t32.t10 t15.t16.t7.t7.t7.t32.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t7.t7.t7.t32.t12 t15.t16.t7.t7.t7.t32.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t7.t32.t14 t15.t16.t7.t7.t7.t32.t15))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t7.t7.t7.t32.t16 t15.t16.t7.t7.t7.t32.t17))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t7.t7.t31 t15.t16.t7.t7.t7.t32))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t7.t7.t30 t15.t16.t7.t7.t7.t33))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t7.t7.t27 t15.t16.t7.t7.t7.t34 a5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t7.t7.t7.t7 t15.t16.t7.t7.t7.t12 t15.t16.t7.t7.t7.t21 a7 t15.t16.t7.t7.t7.t26 t15.t16.t7.t7.t7.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t7.t7.t7.t36))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t7.t7.t7.t36))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t7.t7.t37 t15.t16.t7.t7.t7.t38))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t7.t7.t7.t6 t15.t16.t7.t7.t7.t39))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t7.t7.t7.t43.t2.t2 t15.t16.t7.t7.t7.t43.t2.t3))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t7.t7.t7.t43.t2.t4 t15.t16.t7.t7.t7.t43.t2.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t7.t7.t7.t43.t2 t15.t16.t7.t7.t7.t43.t3))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t7.t7.t7.t43.t4))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t7.t7.t7.t43.t5 t15.t16.t7.t7.t7.t43.t6))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t7.t7.t43 t15.t16.t7.t7.t7.t44))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t7.t7.t42 t15.t16.t7.t7.t7.t45))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t7.t7.t7.t41 t15.t16.t7.t7.t7.t46))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t7.t7.t7.t40 t15.t16.t7.t7.t7.t47))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t7.t7.t7.t5 t15.t16.t7.t7.t7.t48 a10))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t7.t7.t4 t15.t16.t7.t7.t7.t49 t15.t16.t7.t7.t7.t12 t15.t16.t7.t7.t7.t21 a7 t15.t16.t7.t7.t7.t26 t15.t16.t7.t7.t7.t35 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t7.t7.t50))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t16.t7.t7.t7.t51 t15.t16.t7.t7.t7.t52))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t16.t7.t7.t7.t53 t15.t16.t7.t7.t7.t54))
% 0.68/0.88  (step t15.t16.t7.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t7.t55 t15.t16.t7.t7.t7.t56))
% 0.68/0.88  (step t15.t16.t7.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t7.t6 t15.t16.t7.t7.t7))
% 0.68/0.88  (step t15.t16.t7.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t16.t7.t7.t10.t4 t15.t16.t7.t7.t10.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t16.t7.t7.t10.t6 t15.t16.t7.t7.t10.t7))
% 0.68/0.88  (step t15.t16.t7.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t10.t8 t15.t16.t7.t7.t10.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t16.t7.t7.t10.t10 t15.t16.t7.t7.t10.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t7.t9 t15.t16.t7.t7.t10))
% 0.68/0.88  (step t15.t16.t7.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t7.t8 t15.t16.t7.t7.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t7.t5 t15.t16.t7.t7.t12 a11))
% 0.68/0.88  (step t15.t16.t7.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t7.t18 t15.t16.t7.t7.t19))
% 0.68/0.88  (step t15.t16.t7.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t7.t7.t17 t15.t16.t7.t7.t20 a9))
% 0.68/0.88  (step t15.t16.t7.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t7.t24.t5 t15.t16.t7.t7.t24.t6))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t7.t24.t4 t15.t16.t7.t7.t24.t7 a6))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t7.t24.t11.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t7.t24.t11.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t7.t24.t11.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t7.t24.t11.t7 t15.t16.t7.t7.t24.t11.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t7.t7.t24.t11.t6 t15.t16.t7.t7.t24.t11.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t24.t11.t10 t15.t16.t7.t7.t24.t11.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t24.t11.t12 t15.t16.t7.t7.t24.t11.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t7.t24.t10 t15.t16.t7.t7.t24.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.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)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t24.t14.t4 t15.t16.t7.t7.t24.t14.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t7.t24.t14.t8.t3 t15.t16.t7.t7.t24.t14.t8.t4))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.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 (t15.t16.t7.t7.t24.t14.t7 t15.t16.t7.t7.t24.t14.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t7.t24.t14.t6 t15.t16.t7.t7.t24.t14.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t24.t14.t10 t15.t16.t7.t7.t24.t14.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t7.t7.t24.t14.t12 t15.t16.t7.t7.t24.t14.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t24.t14.t14 t15.t16.t7.t7.t24.t14.t15))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t7.t7.t24.t14.t16 t15.t16.t7.t7.t24.t14.t17))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t7.t24.t13 t15.t16.t7.t7.t24.t14))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t7.t24.t12 t15.t16.t7.t7.t24.t15))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t7.t24.t9 t15.t16.t7.t7.t24.t16 a5))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t7.t7.t24.t3 a7 t15.t16.t7.t7.t24.t8 t15.t16.t7.t7.t24.t17 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t7.t24.t18))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t7.t7.t24.t18))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t7.t7.t24.t20 t15.t16.t7.t7.t24.t21))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t7.t7.t24.t19 t15.t16.t7.t7.t24.t22))
% 0.68/0.88  (step t15.t16.t7.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t24.t23 t15.t16.t7.t7.t24.t24))
% 0.68/0.88  (step t15.t16.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t7.t23 t15.t16.t7.t7.t24))
% 0.68/0.88  (step t15.t16.t7.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t7.t27.t3 t15.t16.t7.t7.t27.t4))
% 0.68/0.88  (step t15.t16.t7.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t16.t7.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t7.t7.t27.t7.t2))
% 0.68/0.88  (step t15.t16.t7.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t7.t27.t6 t15.t16.t7.t7.t27.t7))
% 0.68/0.88  (step t15.t16.t7.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t7.t27.t5 t15.t16.t7.t7.t27.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t27.t9 t15.t16.t7.t7.t27.t10))
% 0.68/0.88  (step t15.t16.t7.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t7.t7.t27.t11 t15.t16.t7.t7.t27.t12))
% 0.68/0.88  (step t15.t16.t7.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t7.t7.t26 t15.t16.t7.t7.t27))
% 0.68/0.88  (step t15.t16.t7.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t7.t7.t25 t15.t16.t7.t7.t28))
% 0.68/0.88  (step t15.t16.t7.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t7.t7.t22 t15.t16.t7.t7.t29 a8))
% 0.68/0.88  (step t15.t16.t7.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.88  (step t15.t16.t7.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t7.t32 t15.t16.t7.t7.t33))
% 0.68/0.88  (step t15.t16.t7.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t7.t31 t15.t16.t7.t7.t34 a6))
% 0.68/0.88  (step t15.t16.t7.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.88  (step t15.t16.t7.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t38.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))))) (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)))))) :rule and_neg)
% 0.68/0.88  (step t15.t16.t7.t7.t38.t5 (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)))))) :rule resolution :premises (t15.t16.t7.t7.t38.t4 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t7.t38.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t7.t38.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t7.t38.t7 t15.t16.t7.t7.t38.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t38.t6 t15.t16.t7.t7.t38.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t7.t7.t38.t10 t15.t16.t7.t7.t38.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t38.t12 t15.t16.t7.t7.t38.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t7.t7.t37 t15.t16.t7.t7.t38))
% 0.68/0.88  (step t15.t16.t7.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t7.t7.t41.t4 t15.t16.t7.t7.t41.t5))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t7.t41.t8.t3 t15.t16.t7.t7.t41.t8.t4))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t7.t41.t7 t15.t16.t7.t7.t41.t8))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t41.t6 t15.t16.t7.t7.t41.t9))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t7.t7.t41.t10 t15.t16.t7.t7.t41.t11))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t41.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 (t15.t16.t7.t7.t41.t12 t15.t16.t7.t7.t41.t13))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t41.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 (t15.t16.t7.t7.t41.t14 t15.t16.t7.t7.t41.t15))
% 0.68/0.88  (step t15.t16.t7.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.88  (step t15.t16.t7.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t7.t41.t16 t15.t16.t7.t7.t41.t17))
% 0.68/0.88  (step t15.t16.t7.t7.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.88  (step t15.t16.t7.t7.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t7.t40 t15.t16.t7.t7.t41))
% 0.68/0.88  (step t15.t16.t7.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t7.t39 t15.t16.t7.t7.t42))
% 0.68/0.88  (step t15.t16.t7.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t7.t36 t15.t16.t7.t7.t43 a5))
% 0.68/0.88  (step t15.t16.t7.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t7.t16 t15.t16.t7.t7.t21 t15.t16.t7.t7.t30 a7 t15.t16.t7.t7.t35 t15.t16.t7.t7.t44 a4 a3 a2))
% 0.68/0.88  (step t15.t16.t7.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t7.t7.t45))
% 0.68/0.88  (step t15.t16.t7.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t7.t7.t45))
% 0.68/0.88  (step t15.t16.t7.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t7.t46 t15.t16.t7.t7.t47))
% 0.68/0.88  (step t15.t16.t7.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t7.t7.t15 t15.t16.t7.t7.t48))
% 0.68/0.88  (step t15.t16.t7.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.88  (step t15.t16.t7.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.88  (anchor :step t15.t16.t7.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.88  (step t15.t16.t7.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t16.t7.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t7.t7.t52.t2.t2 t15.t16.t7.t7.t52.t2.t3))
% 0.68/0.89  (step t15.t16.t7.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t7.t7.t52.t2.t4 t15.t16.t7.t7.t52.t2.t5))
% 0.68/0.89  (step t15.t16.t7.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t7.t7.t52.t2 t15.t16.t7.t7.t52.t3))
% 0.68/0.89  (step t15.t16.t7.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t7.t7.t52.t4))
% 0.68/0.89  (step t15.t16.t7.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t7.t7.t52.t5 t15.t16.t7.t7.t52.t6))
% 0.68/0.89  (step t15.t16.t7.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t7.t52 t15.t16.t7.t7.t53))
% 0.68/0.89  (step t15.t16.t7.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t7.t51 t15.t16.t7.t7.t54))
% 0.68/0.89  (step t15.t16.t7.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t7.t7.t50 t15.t16.t7.t7.t55))
% 0.68/0.89  (step t15.t16.t7.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t7.t7.t49 t15.t16.t7.t7.t56))
% 0.68/0.89  (step t15.t16.t7.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t7.t7.t14 t15.t16.t7.t7.t57 a10))
% 0.68/0.89  (step t15.t16.t7.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t7.t4 t15.t16.t7.t7.t13 t15.t16.t7.t7.t58 t15.t16.t7.t7.t21 t15.t16.t7.t7.t30 a7 t15.t16.t7.t7.t35 t15.t16.t7.t7.t44 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t7.t59))
% 0.68/0.89  (step t15.t16.t7.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t7.t7.t59))
% 0.68/0.89  (step t15.t16.t7.t7.t62 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t7.t7.t61 t15.t16.t7.t7.t62))
% 0.68/0.89  (step t15.t16.t7.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t7.t7.t60 t15.t16.t7.t7.t63))
% 0.68/0.89  (step t15.t16.t7.t7.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t16.t7.t7.t61 t15.t16.t7.t7.t65))
% 0.68/0.89  (step t15.t16.t7.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t16.t7.t7.t64 t15.t16.t7.t7.t66))
% 0.68/0.89  (step t15.t16.t7.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t7.t67 t15.t16.t7.t7.t68))
% 0.68/0.89  (step t15.t16.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t6 t15.t16.t7.t7))
% 0.68/0.89  (step t15.t16.t7.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.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)
% 0.68/0.89  (step t15.t16.t7.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t10.t4 t15.t16.t7.t10.t5))
% 0.68/0.89  (step t15.t16.t7.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t16.t7.t10.t8.t3 t15.t16.t7.t10.t8.t4))
% 0.68/0.89  (step t15.t16.t7.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t16.t7.t10.t7 t15.t16.t7.t10.t8))
% 0.68/0.89  (step t15.t16.t7.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t16.t7.t10.t6 t15.t16.t7.t10.t9))
% 0.68/0.89  (step t15.t16.t7.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t16.t7.t10.t10 t15.t16.t7.t10.t11))
% 0.68/0.89  (step t15.t16.t7.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t16.t7.t10.t14.t2 t15.t16.t7.t10.t14.t3))
% 0.68/0.89  (step t15.t16.t7.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t16.t7.t10.t13 t15.t16.t7.t10.t14))
% 0.68/0.89  (step t15.t16.t7.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t16.t7.t10.t12 t15.t16.t7.t10.t15))
% 0.68/0.89  (step t15.t16.t7.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t10.t16 t15.t16.t7.t10.t17))
% 0.68/0.89  (step t15.t16.t7.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t16.t7.t10.t18 t15.t16.t7.t10.t19))
% 0.68/0.89  (step t15.t16.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t16.t7.t9 t15.t16.t7.t10))
% 0.68/0.89  (step t15.t16.t7.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t16.t7.t8 t15.t16.t7.t11))
% 0.68/0.89  (step t15.t16.t7.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t16.t7.t5 t15.t16.t7.t12 a12))
% 0.68/0.89  (step t15.t16.t7.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t16.t9 t15.t16.t7.t16.t10))
% 0.68/0.89  (step t15.t16.t7.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t7.t16.t8 t15.t16.t7.t16.t11 a9))
% 0.68/0.89  (step t15.t16.t7.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t16.t15.t5 t15.t16.t7.t16.t15.t6))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t16.t15.t4 t15.t16.t7.t16.t15.t7 a6))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t16.t7.t16.t15.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t16.t15.t11.t5))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t16.t15.t11.t5))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t16.t15.t11.t7 t15.t16.t7.t16.t15.t11.t8))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t7.t16.t15.t11.t6 t15.t16.t7.t16.t15.t11.t9))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t7.t16.t15.t11.t10 t15.t16.t7.t16.t15.t11.t11))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t16.t15.t11.t12 t15.t16.t7.t16.t15.t11.t13))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t7.t16.t15.t10 t15.t16.t7.t16.t15.t11))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t7.t16.t15.t14.t4 t15.t16.t7.t16.t15.t14.t5))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t16.t15.t14.t8.t3 t15.t16.t7.t16.t15.t14.t8.t4))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t16.t15.t14.t7 t15.t16.t7.t16.t15.t14.t8))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t16.t15.t14.t6 t15.t16.t7.t16.t15.t14.t9))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t7.t16.t15.t14.t10 t15.t16.t7.t16.t15.t14.t11))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.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 (t15.t16.t7.t16.t15.t14.t12 t15.t16.t7.t16.t15.t14.t13))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.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 (t15.t16.t7.t16.t15.t14.t14 t15.t16.t7.t16.t15.t14.t15))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t16.t15.t14.t16 t15.t16.t7.t16.t15.t14.t17))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t16.t15.t13 t15.t16.t7.t16.t15.t14))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t16.t15.t12 t15.t16.t7.t16.t15.t15))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t16.t15.t9 t15.t16.t7.t16.t15.t16 a5))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t16.t15.t3 a7 t15.t16.t7.t16.t15.t8 t15.t16.t7.t16.t15.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t16.t15.t18))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t7.t16.t15.t18))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t7.t16.t15.t20 t15.t16.t7.t16.t15.t21))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t7.t16.t15.t19 t15.t16.t7.t16.t15.t22))
% 0.68/0.89  (step t15.t16.t7.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t16.t15.t23 t15.t16.t7.t16.t15.t24))
% 0.68/0.89  (step t15.t16.t7.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t16.t14 t15.t16.t7.t16.t15))
% 0.68/0.89  (step t15.t16.t7.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t16.t18.t3 t15.t16.t7.t16.t18.t4))
% 0.68/0.89  (step t15.t16.t7.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t7.t16.t18.t7.t2))
% 0.68/0.89  (step t15.t16.t7.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t16.t18.t6 t15.t16.t7.t16.t18.t7))
% 0.68/0.89  (step t15.t16.t7.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t16.t18.t5 t15.t16.t7.t16.t18.t8))
% 0.68/0.89  (step t15.t16.t7.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t16.t18.t9 t15.t16.t7.t16.t18.t10))
% 0.68/0.89  (step t15.t16.t7.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t7.t16.t18.t11 t15.t16.t7.t16.t18.t12))
% 0.68/0.89  (step t15.t16.t7.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t7.t16.t17 t15.t16.t7.t16.t18))
% 0.68/0.89  (step t15.t16.t7.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t7.t16.t16 t15.t16.t7.t16.t19))
% 0.68/0.89  (step t15.t16.t7.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t7.t16.t13 t15.t16.t7.t16.t20 a8))
% 0.68/0.89  (step t15.t16.t7.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t7.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t16.t23 t15.t16.t7.t16.t24))
% 0.68/0.89  (step t15.t16.t7.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t16.t22 t15.t16.t7.t16.t25 a6))
% 0.68/0.89  (step t15.t16.t7.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t16.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t16.t29.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t16.t29.t5))
% 0.68/0.89  (step t15.t16.t7.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t16.t29.t5))
% 0.68/0.89  (step t15.t16.t7.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t16.t29.t7 t15.t16.t7.t16.t29.t8))
% 0.68/0.89  (step t15.t16.t7.t16.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t7.t16.t29.t6 t15.t16.t7.t16.t29.t9))
% 0.68/0.89  (step t15.t16.t7.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t16.t29.t10 t15.t16.t7.t16.t29.t11))
% 0.68/0.89  (step t15.t16.t7.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t16.t29.t12 t15.t16.t7.t16.t29.t13))
% 0.68/0.89  (step t15.t16.t7.t16.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t7.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t16.t28 t15.t16.t7.t16.t29))
% 0.68/0.89  (step t15.t16.t7.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.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)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t16.t32.t4 t15.t16.t7.t16.t32.t5))
% 0.68/0.89  (step t15.t16.t7.t16.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t16.t32.t8.t3 t15.t16.t7.t16.t32.t8.t4))
% 0.68/0.89  (step t15.t16.t7.t16.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t16.t7.t16.t32.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 (t15.t16.t7.t16.t32.t7 t15.t16.t7.t16.t32.t8))
% 0.68/0.89  (step t15.t16.t7.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t16.t32.t6 t15.t16.t7.t16.t32.t9))
% 0.68/0.89  (step t15.t16.t7.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t16.t32.t10 t15.t16.t7.t16.t32.t11))
% 0.68/0.89  (step t15.t16.t7.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t7.t16.t32.t12 t15.t16.t7.t16.t32.t13))
% 0.68/0.89  (step t15.t16.t7.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t16.t32.t14 t15.t16.t7.t16.t32.t15))
% 0.68/0.89  (step t15.t16.t7.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t7.t16.t32.t16 t15.t16.t7.t16.t32.t17))
% 0.68/0.89  (step t15.t16.t7.t16.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t7.t16.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t16.t31 t15.t16.t7.t16.t32))
% 0.68/0.89  (step t15.t16.t7.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t16.t30 t15.t16.t7.t16.t33))
% 0.68/0.89  (step t15.t16.t7.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t16.t27 t15.t16.t7.t16.t34 a5))
% 0.68/0.89  (step t15.t16.t7.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t7.t16.t7 t15.t16.t7.t16.t12 t15.t16.t7.t16.t21 a7 t15.t16.t7.t16.t26 t15.t16.t7.t16.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t7.t16.t36))
% 0.68/0.89  (step t15.t16.t7.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t7.t16.t36))
% 0.68/0.89  (step t15.t16.t7.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t16.t37 t15.t16.t7.t16.t38))
% 0.68/0.89  (step t15.t16.t7.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t7.t16.t6 t15.t16.t7.t16.t39))
% 0.68/0.89  (step t15.t16.t7.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t16.t7.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t7.t16.t43.t2.t2 t15.t16.t7.t16.t43.t2.t3))
% 0.68/0.89  (step t15.t16.t7.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t7.t16.t43.t2.t4 t15.t16.t7.t16.t43.t2.t5))
% 0.68/0.89  (step t15.t16.t7.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t7.t16.t43.t2 t15.t16.t7.t16.t43.t3))
% 0.68/0.89  (step t15.t16.t7.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t7.t16.t43.t4))
% 0.68/0.89  (step t15.t16.t7.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t7.t16.t43.t5 t15.t16.t7.t16.t43.t6))
% 0.68/0.89  (step t15.t16.t7.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t16.t43 t15.t16.t7.t16.t44))
% 0.68/0.89  (step t15.t16.t7.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t16.t42 t15.t16.t7.t16.t45))
% 0.68/0.89  (step t15.t16.t7.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t7.t16.t41 t15.t16.t7.t16.t46))
% 0.68/0.89  (step t15.t16.t7.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t7.t16.t40 t15.t16.t7.t16.t47))
% 0.68/0.89  (step t15.t16.t7.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t7.t16.t5 t15.t16.t7.t16.t48 a10))
% 0.68/0.89  (step t15.t16.t7.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t16.t4 t15.t16.t7.t16.t49 t15.t16.t7.t16.t12 t15.t16.t7.t16.t21 a7 t15.t16.t7.t16.t26 t15.t16.t7.t16.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t16.t50))
% 0.68/0.89  (step t15.t16.t7.t16.t52 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t16.t7.t16.t51 t15.t16.t7.t16.t52))
% 0.68/0.89  (step t15.t16.t7.t16.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t16.t7.t16.t53 t15.t16.t7.t16.t54))
% 0.68/0.89  (step t15.t16.t7.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t16.t55 t15.t16.t7.t16.t56))
% 0.68/0.89  (step t15.t16.t7.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t15 t15.t16.t7.t16))
% 0.68/0.89  (step t15.t16.t7.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t19.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t16.t7.t19.t4 t15.t16.t7.t19.t5))
% 0.68/0.89  (step t15.t16.t7.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t16.t7.t19.t6 t15.t16.t7.t19.t7))
% 0.68/0.89  (step t15.t16.t7.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t19.t8 t15.t16.t7.t19.t9))
% 0.68/0.89  (step t15.t16.t7.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t16.t7.t19.t10 t15.t16.t7.t19.t11))
% 0.68/0.89  (step t15.t16.t7.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t18 t15.t16.t7.t19))
% 0.68/0.89  (step t15.t16.t7.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t17 t15.t16.t7.t20))
% 0.68/0.89  (step t15.t16.t7.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t14 t15.t16.t7.t21 a11))
% 0.68/0.89  (step t15.t16.t7.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t27 t15.t16.t7.t28))
% 0.68/0.89  (step t15.t16.t7.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t7.t26 t15.t16.t7.t29 a9))
% 0.68/0.89  (step t15.t16.t7.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t7.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t33.t5 t15.t16.t7.t33.t6))
% 0.68/0.89  (step t15.t16.t7.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t33.t4 t15.t16.t7.t33.t7 a6))
% 0.68/0.89  (step t15.t16.t7.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t33.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t33.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t33.t11.t5))
% 0.68/0.89  (step t15.t16.t7.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t33.t11.t5))
% 0.68/0.89  (step t15.t16.t7.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t33.t11.t7 t15.t16.t7.t33.t11.t8))
% 0.68/0.89  (step t15.t16.t7.t33.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t7.t33.t11.t6 t15.t16.t7.t33.t11.t9))
% 0.68/0.89  (step t15.t16.t7.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t33.t11.t10 t15.t16.t7.t33.t11.t11))
% 0.68/0.89  (step t15.t16.t7.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t33.t11.t12 t15.t16.t7.t33.t11.t13))
% 0.68/0.89  (step t15.t16.t7.t33.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t7.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t33.t10 t15.t16.t7.t33.t11))
% 0.68/0.89  (step t15.t16.t7.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.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)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t33.t14.t4 t15.t16.t7.t33.t14.t5))
% 0.68/0.89  (step t15.t16.t7.t33.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t33.t14.t8.t3 t15.t16.t7.t33.t14.t8.t4))
% 0.68/0.89  (step t15.t16.t7.t33.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t16.t7.t33.t14.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 (t15.t16.t7.t33.t14.t7 t15.t16.t7.t33.t14.t8))
% 0.68/0.89  (step t15.t16.t7.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t33.t14.t6 t15.t16.t7.t33.t14.t9))
% 0.68/0.89  (step t15.t16.t7.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t33.t14.t10 t15.t16.t7.t33.t14.t11))
% 0.68/0.89  (step t15.t16.t7.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t7.t33.t14.t12 t15.t16.t7.t33.t14.t13))
% 0.68/0.89  (step t15.t16.t7.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t33.t14.t14 t15.t16.t7.t33.t14.t15))
% 0.68/0.89  (step t15.t16.t7.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t7.t33.t14.t16 t15.t16.t7.t33.t14.t17))
% 0.68/0.89  (step t15.t16.t7.t33.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t7.t33.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t33.t13 t15.t16.t7.t33.t14))
% 0.68/0.89  (step t15.t16.t7.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t33.t12 t15.t16.t7.t33.t15))
% 0.68/0.89  (step t15.t16.t7.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t33.t9 t15.t16.t7.t33.t16 a5))
% 0.68/0.89  (step t15.t16.t7.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t7.t33.t3 a7 t15.t16.t7.t33.t8 t15.t16.t7.t33.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t33.t18))
% 0.68/0.89  (step t15.t16.t7.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t7.t33.t18))
% 0.68/0.89  (step t15.t16.t7.t33.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t7.t33.t20 t15.t16.t7.t33.t21))
% 0.68/0.89  (step t15.t16.t7.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t7.t33.t19 t15.t16.t7.t33.t22))
% 0.68/0.89  (step t15.t16.t7.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t33.t23 t15.t16.t7.t33.t24))
% 0.68/0.89  (step t15.t16.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t7.t32 t15.t16.t7.t33))
% 0.68/0.89  (step t15.t16.t7.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t36.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t36.t3 t15.t16.t7.t36.t4))
% 0.68/0.89  (step t15.t16.t7.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t7.t36.t7.t2))
% 0.68/0.89  (step t15.t16.t7.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t36.t6 t15.t16.t7.t36.t7))
% 0.68/0.89  (step t15.t16.t7.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t7.t36.t5 t15.t16.t7.t36.t8))
% 0.68/0.89  (step t15.t16.t7.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t36.t9 t15.t16.t7.t36.t10))
% 0.68/0.89  (step t15.t16.t7.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t7.t36.t11 t15.t16.t7.t36.t12))
% 0.68/0.89  (step t15.t16.t7.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t7.t35 t15.t16.t7.t36))
% 0.68/0.89  (step t15.t16.t7.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t7.t34 t15.t16.t7.t37))
% 0.68/0.89  (step t15.t16.t7.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t7.t31 t15.t16.t7.t38 a8))
% 0.68/0.89  (step t15.t16.t7.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t7.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t42.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t7.t41 t15.t16.t7.t42))
% 0.68/0.89  (step t15.t16.t7.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t7.t40 t15.t16.t7.t43 a6))
% 0.68/0.89  (step t15.t16.t7.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t7.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t47.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t47.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t47.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t7.t47.t5 (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)))))) :rule resolution :premises (t15.t16.t7.t47.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t7.t47.t5))
% 0.68/0.89  (step t15.t16.t7.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t7.t47.t5))
% 0.68/0.89  (step t15.t16.t7.t47.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t7.t47.t7 t15.t16.t7.t47.t8))
% 0.68/0.89  (step t15.t16.t7.t47.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t7.t47.t6 t15.t16.t7.t47.t9))
% 0.68/0.89  (step t15.t16.t7.t47.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t47.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t7.t47.t10 t15.t16.t7.t47.t11))
% 0.68/0.89  (step t15.t16.t7.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t47.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t47.t12 t15.t16.t7.t47.t13))
% 0.68/0.89  (step t15.t16.t7.t47 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t7.t46 t15.t16.t7.t47))
% 0.68/0.89  (step t15.t16.t7.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t50.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t50.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t7.t50.t4 t15.t16.t7.t50.t5))
% 0.68/0.89  (step t15.t16.t7.t50.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t16.t7.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t7.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t7.t50.t8.t3 t15.t16.t7.t50.t8.t4))
% 0.68/0.89  (step t15.t16.t7.t50.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t50.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t7.t50.t7 t15.t16.t7.t50.t8))
% 0.68/0.89  (step t15.t16.t7.t50.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t7.t50.t6 t15.t16.t7.t50.t9))
% 0.68/0.89  (step t15.t16.t7.t50.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t7.t50.t10 t15.t16.t7.t50.t11))
% 0.68/0.89  (step t15.t16.t7.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t50.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 (t15.t16.t7.t50.t12 t15.t16.t7.t50.t13))
% 0.68/0.89  (step t15.t16.t7.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t50.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 (t15.t16.t7.t50.t14 t15.t16.t7.t50.t15))
% 0.68/0.89  (step t15.t16.t7.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t7.t50.t16 t15.t16.t7.t50.t17))
% 0.68/0.89  (step t15.t16.t7.t50 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t51 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t7.t49 t15.t16.t7.t50))
% 0.68/0.89  (step t15.t16.t7.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t7.t48 t15.t16.t7.t51))
% 0.68/0.89  (step t15.t16.t7.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t7.t45 t15.t16.t7.t52 a5))
% 0.68/0.89  (step t15.t16.t7.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t7.t25 t15.t16.t7.t30 t15.t16.t7.t39 a7 t15.t16.t7.t44 t15.t16.t7.t53 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t7.t54))
% 0.68/0.89  (step t15.t16.t7.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t7.t54))
% 0.68/0.89  (step t15.t16.t7.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t7.t55 t15.t16.t7.t56))
% 0.68/0.89  (step t15.t16.t7.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t7.t24 t15.t16.t7.t57))
% 0.68/0.89  (step t15.t16.t7.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t7.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t7.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t7.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t16.t7.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t7.t61.t2.t2 t15.t16.t7.t61.t2.t3))
% 0.68/0.89  (step t15.t16.t7.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t7.t61.t2.t4 t15.t16.t7.t61.t2.t5))
% 0.68/0.89  (step t15.t16.t7.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t7.t61.t2 t15.t16.t7.t61.t3))
% 0.68/0.89  (step t15.t16.t7.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t7.t61.t4))
% 0.68/0.89  (step t15.t16.t7.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t7.t61.t5 t15.t16.t7.t61.t6))
% 0.68/0.89  (step t15.t16.t7.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t16.t7.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t7.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t61 t15.t16.t7.t62))
% 0.68/0.89  (step t15.t16.t7.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t7.t60 t15.t16.t7.t63))
% 0.68/0.89  (step t15.t16.t7.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t7.t59 t15.t16.t7.t64))
% 0.68/0.89  (step t15.t16.t7.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t7.t58 t15.t16.t7.t65))
% 0.68/0.89  (step t15.t16.t7.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t7.t23 t15.t16.t7.t66 a10))
% 0.68/0.89  (step t15.t16.t7.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t7.t4 t15.t16.t7.t13 t15.t16.t7.t22 t15.t16.t7.t67 t15.t16.t7.t30 t15.t16.t7.t39 a7 t15.t16.t7.t44 t15.t16.t7.t53 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t7.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t15.t16.t7.t68))
% 0.68/0.89  (step t15.t16.t7.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t7.t68))
% 0.68/0.89  (step t15.t16.t7.t71 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t7.t70 t15.t16.t7.t71))
% 0.68/0.89  (step t15.t16.t7.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t7.t69 t15.t16.t7.t72))
% 0.68/0.89  (step t15.t16.t7.t74 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t16.t7.t70 t15.t16.t7.t74))
% 0.68/0.89  (step t15.t16.t7.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t16.t7.t73 t15.t16.t7.t75))
% 0.68/0.89  (step t15.t16.t7.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t7.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t16.t7.t76 t15.t16.t7.t77))
% 0.68/0.89  (step t15.t16.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t8 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t16.t6 t15.t16.t7))
% 0.68/0.89  (step t15.t16.t9 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t4 (cl (= (lambda ((U (-> $$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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t10.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t10.t4 t15.t16.t10.t5))
% 0.68/0.89  (step t15.t16.t10.t7 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t10.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t10.t8.t1 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t10.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t10.t8.t3))
% 0.68/0.89  (step t15.t16.t10.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t15.t16.t10.t8.t4 t15.t16.t10.t8.t5))
% 0.68/0.89  (step t15.t16.t10.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t10.t9 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t16.t10.t7 t15.t16.t10.t8))
% 0.68/0.89  (step t15.t16.t10.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t16.t10.t6 t15.t16.t10.t9))
% 0.68/0.89  (step t15.t16.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t10.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t16.t10.t10 t15.t16.t10.t11))
% 0.68/0.89  (step t15.t16.t10.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t10.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t10.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t10.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t15.t16.t10.t14.t2 t15.t16.t10.t14.t3))
% 0.68/0.89  (step t15.t16.t10.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t10.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t16.t10.t13 t15.t16.t10.t14))
% 0.68/0.89  (step t15.t16.t10.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t16.t10.t12 t15.t16.t10.t15))
% 0.68/0.89  (step t15.t16.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t10.t16 t15.t16.t10.t17))
% 0.68/0.89  (step t15.t16.t10.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t10.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t16.t10.t18 t15.t16.t10.t19))
% 0.68/0.89  (step t15.t16.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t11 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t16.t9 t15.t16.t10))
% 0.68/0.89  (step t15.t16.t12 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t16.t8 t15.t16.t11))
% 0.68/0.89  (step t15.t16.t13 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t16.t5 t15.t16.t12 a13))
% 0.68/0.89  (step t15.t16.t14 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t15 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t16.t7.t9 t15.t16.t16.t7.t10))
% 0.68/0.89  (step t15.t16.t16.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t16.t7.t8 t15.t16.t16.t7.t11 a9))
% 0.68/0.89  (step t15.t16.t16.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t16.t7.t15.t5 t15.t16.t16.t7.t15.t6))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t16.t7.t15.t4 t15.t16.t16.t7.t15.t7 a6))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t16.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t16.t7.t15.t11.t5))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t16.t7.t15.t11.t5))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t16.t7.t15.t11.t7 t15.t16.t16.t7.t15.t11.t8))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t16.t7.t15.t11.t6 t15.t16.t16.t7.t15.t11.t9))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t7.t15.t11.t10 t15.t16.t16.t7.t15.t11.t11))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t7.t15.t11.t12 t15.t16.t16.t7.t15.t11.t13))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t16.t7.t15.t10 t15.t16.t16.t7.t15.t11))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.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)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t16.t7.t15.t14.t4 t15.t16.t16.t7.t15.t14.t5))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t16.t7.t15.t14.t8.t3 t15.t16.t16.t7.t15.t14.t8.t4))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.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 (t15.t16.t16.t7.t15.t14.t7 t15.t16.t16.t7.t15.t14.t8))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t16.t7.t15.t14.t6 t15.t16.t16.t7.t15.t14.t9))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t7.t15.t14.t10 t15.t16.t16.t7.t15.t14.t11))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t16.t7.t15.t14.t12 t15.t16.t16.t7.t15.t14.t13))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t7.t15.t14.t14 t15.t16.t16.t7.t15.t14.t15))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t16.t7.t15.t14.t16 t15.t16.t16.t7.t15.t14.t17))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t16.t7.t15.t13 t15.t16.t16.t7.t15.t14))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t16.t7.t15.t12 t15.t16.t16.t7.t15.t15))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t16.t7.t15.t9 t15.t16.t16.t7.t15.t16 a5))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t16.t7.t15.t3 a7 t15.t16.t16.t7.t15.t8 t15.t16.t16.t7.t15.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t16.t7.t15.t18))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t16.t7.t15.t18))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t16.t7.t15.t20 t15.t16.t16.t7.t15.t21))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t16.t7.t15.t19 t15.t16.t16.t7.t15.t22))
% 0.68/0.89  (step t15.t16.t16.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t7.t15.t23 t15.t16.t16.t7.t15.t24))
% 0.68/0.89  (step t15.t16.t16.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t16.t7.t14 t15.t16.t16.t7.t15))
% 0.68/0.89  (step t15.t16.t16.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t16.t7.t18.t3 t15.t16.t16.t7.t18.t4))
% 0.68/0.89  (step t15.t16.t16.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t16.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t16.t7.t18.t7.t2))
% 0.68/0.89  (step t15.t16.t16.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t16.t7.t18.t6 t15.t16.t16.t7.t18.t7))
% 0.68/0.89  (step t15.t16.t16.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t16.t7.t18.t5 t15.t16.t16.t7.t18.t8))
% 0.68/0.89  (step t15.t16.t16.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t7.t18.t9 t15.t16.t16.t7.t18.t10))
% 0.68/0.89  (step t15.t16.t16.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t16.t7.t18.t11 t15.t16.t16.t7.t18.t12))
% 0.68/0.89  (step t15.t16.t16.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t16.t7.t17 t15.t16.t16.t7.t18))
% 0.68/0.89  (step t15.t16.t16.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t16.t7.t16 t15.t16.t16.t7.t19))
% 0.68/0.89  (step t15.t16.t16.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t16.t7.t13 t15.t16.t16.t7.t20 a8))
% 0.68/0.89  (step t15.t16.t16.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t16.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t16.t7.t23 t15.t16.t16.t7.t24))
% 0.68/0.89  (step t15.t16.t16.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t16.t7.t22 t15.t16.t16.t7.t25 a6))
% 0.68/0.89  (step t15.t16.t16.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t7.t29.t5 (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)))))) :rule resolution :premises (t15.t16.t16.t7.t29.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t16.t7.t29.t5))
% 0.68/0.89  (step t15.t16.t16.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t16.t7.t29.t5))
% 0.68/0.89  (step t15.t16.t16.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t16.t7.t29.t7 t15.t16.t16.t7.t29.t8))
% 0.68/0.89  (step t15.t16.t16.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t16.t7.t29.t6 t15.t16.t16.t7.t29.t9))
% 0.68/0.89  (step t15.t16.t16.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t16.t7.t29.t10 t15.t16.t16.t7.t29.t11))
% 0.68/0.89  (step t15.t16.t16.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t7.t29.t12 t15.t16.t16.t7.t29.t13))
% 0.68/0.89  (step t15.t16.t16.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t16.t7.t28 t15.t16.t16.t7.t29))
% 0.68/0.89  (step t15.t16.t16.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t16.t7.t32.t4 t15.t16.t16.t7.t32.t5))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t16.t7.t32.t8.t3 t15.t16.t16.t7.t32.t8.t4))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t16.t7.t32.t7 t15.t16.t16.t7.t32.t8))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t16.t7.t32.t6 t15.t16.t16.t7.t32.t9))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t16.t7.t32.t10 t15.t16.t16.t7.t32.t11))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t32.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 (t15.t16.t16.t7.t32.t12 t15.t16.t16.t7.t32.t13))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t32.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 (t15.t16.t16.t7.t32.t14 t15.t16.t16.t7.t32.t15))
% 0.68/0.89  (step t15.t16.t16.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t7.t32.t16 t15.t16.t16.t7.t32.t17))
% 0.68/0.89  (step t15.t16.t16.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t16.t7.t31 t15.t16.t16.t7.t32))
% 0.68/0.89  (step t15.t16.t16.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t16.t7.t30 t15.t16.t16.t7.t33))
% 0.68/0.89  (step t15.t16.t16.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t16.t7.t27 t15.t16.t16.t7.t34 a5))
% 0.68/0.89  (step t15.t16.t16.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t16.t7.t7 t15.t16.t16.t7.t12 t15.t16.t16.t7.t21 a7 t15.t16.t16.t7.t26 t15.t16.t16.t7.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t16.t7.t36))
% 0.68/0.89  (step t15.t16.t16.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t16.t7.t36))
% 0.68/0.89  (step t15.t16.t16.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t16.t7.t37 t15.t16.t16.t7.t38))
% 0.68/0.89  (step t15.t16.t16.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t16.t7.t6 t15.t16.t16.t7.t39))
% 0.68/0.89  (step t15.t16.t16.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t16.t16.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t16.t7.t43.t2.t2 t15.t16.t16.t7.t43.t2.t3))
% 0.68/0.89  (step t15.t16.t16.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t16.t7.t43.t2.t4 t15.t16.t16.t7.t43.t2.t5))
% 0.68/0.89  (step t15.t16.t16.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t16.t7.t43.t2 t15.t16.t16.t7.t43.t3))
% 0.68/0.89  (step t15.t16.t16.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t16.t7.t43.t4))
% 0.68/0.89  (step t15.t16.t16.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t16.t7.t43.t5 t15.t16.t16.t7.t43.t6))
% 0.68/0.89  (step t15.t16.t16.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t16.t7.t43 t15.t16.t16.t7.t44))
% 0.68/0.89  (step t15.t16.t16.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t16.t7.t42 t15.t16.t16.t7.t45))
% 0.68/0.89  (step t15.t16.t16.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t16.t7.t41 t15.t16.t16.t7.t46))
% 0.68/0.89  (step t15.t16.t16.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t16.t7.t40 t15.t16.t16.t7.t47))
% 0.68/0.89  (step t15.t16.t16.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t16.t7.t5 t15.t16.t16.t7.t48 a10))
% 0.68/0.89  (step t15.t16.t16.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t16.t7.t4 t15.t16.t16.t7.t49 t15.t16.t16.t7.t12 t15.t16.t16.t7.t21 a7 t15.t16.t16.t7.t26 t15.t16.t16.t7.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t16.t7.t50))
% 0.68/0.89  (step t15.t16.t16.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t16.t16.t7.t51 t15.t16.t16.t7.t52))
% 0.68/0.89  (step t15.t16.t16.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t16.t16.t7.t53 t15.t16.t16.t7.t54))
% 0.68/0.89  (step t15.t16.t16.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t7.t55 t15.t16.t16.t7.t56))
% 0.68/0.89  (step t15.t16.t16.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t16.t16.t6 t15.t16.t16.t7))
% 0.68/0.89  (step t15.t16.t16.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t16.t16.t10.t4 t15.t16.t16.t10.t5))
% 0.68/0.89  (step t15.t16.t16.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t16.t16.t10.t6 t15.t16.t16.t10.t7))
% 0.68/0.89  (step t15.t16.t16.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t10.t8 t15.t16.t16.t10.t9))
% 0.68/0.89  (step t15.t16.t16.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t16.t16.t10.t10 t15.t16.t16.t10.t11))
% 0.68/0.89  (step t15.t16.t16.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t16.t16.t9 t15.t16.t16.t10))
% 0.68/0.89  (step t15.t16.t16.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t16.t16.t8 t15.t16.t16.t11))
% 0.68/0.89  (step t15.t16.t16.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t16.t16.t5 t15.t16.t16.t12 a11))
% 0.68/0.89  (step t15.t16.t16.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t16.t18 t15.t16.t16.t19))
% 0.68/0.89  (step t15.t16.t16.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t16.t17 t15.t16.t16.t20 a9))
% 0.68/0.89  (step t15.t16.t16.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t16.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t16.t24.t5 t15.t16.t16.t24.t6))
% 0.68/0.89  (step t15.t16.t16.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t16.t24.t4 t15.t16.t16.t24.t7 a6))
% 0.68/0.89  (step t15.t16.t16.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t24.t11.t5 (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)))))) :rule resolution :premises (t15.t16.t16.t24.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t16.t24.t11.t5))
% 0.68/0.89  (step t15.t16.t16.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t16.t24.t11.t5))
% 0.68/0.89  (step t15.t16.t16.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t16.t24.t11.t7 t15.t16.t16.t24.t11.t8))
% 0.68/0.89  (step t15.t16.t16.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t16.t24.t11.t6 t15.t16.t16.t24.t11.t9))
% 0.68/0.89  (step t15.t16.t16.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t16.t24.t11.t10 t15.t16.t16.t24.t11.t11))
% 0.68/0.89  (step t15.t16.t16.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t24.t11.t12 t15.t16.t16.t24.t11.t13))
% 0.68/0.89  (step t15.t16.t16.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t16.t24.t10 t15.t16.t16.t24.t11))
% 0.68/0.89  (step t15.t16.t16.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t16.t24.t14.t4 t15.t16.t16.t24.t14.t5))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t16.t16.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t16.t24.t14.t8.t3 t15.t16.t16.t24.t14.t8.t4))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t16.t24.t14.t7 t15.t16.t16.t24.t14.t8))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t16.t24.t14.t6 t15.t16.t16.t24.t14.t9))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t16.t24.t14.t10 t15.t16.t16.t24.t14.t11))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t24.t14.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 (t15.t16.t16.t24.t14.t12 t15.t16.t16.t24.t14.t13))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t14.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 (t15.t16.t16.t24.t14.t14 t15.t16.t16.t24.t14.t15))
% 0.68/0.89  (step t15.t16.t16.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t24.t14.t16 t15.t16.t16.t24.t14.t17))
% 0.68/0.89  (step t15.t16.t16.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t16.t24.t13 t15.t16.t16.t24.t14))
% 0.68/0.89  (step t15.t16.t16.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t16.t24.t12 t15.t16.t16.t24.t15))
% 0.68/0.89  (step t15.t16.t16.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t16.t24.t9 t15.t16.t16.t24.t16 a5))
% 0.68/0.89  (step t15.t16.t16.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t16.t24.t3 a7 t15.t16.t16.t24.t8 t15.t16.t16.t24.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t16.t24.t18))
% 0.68/0.89  (step t15.t16.t16.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t16.t24.t18))
% 0.68/0.89  (step t15.t16.t16.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t16.t24.t20 t15.t16.t16.t24.t21))
% 0.68/0.89  (step t15.t16.t16.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t16.t24.t19 t15.t16.t16.t24.t22))
% 0.68/0.89  (step t15.t16.t16.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t24.t23 t15.t16.t16.t24.t24))
% 0.68/0.89  (step t15.t16.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t16.t23 t15.t16.t16.t24))
% 0.68/0.89  (step t15.t16.t16.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t16.t27.t3 t15.t16.t16.t27.t4))
% 0.68/0.89  (step t15.t16.t16.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t16.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t16.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t16.t27.t7.t2))
% 0.68/0.89  (step t15.t16.t16.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t16.t27.t6 t15.t16.t16.t27.t7))
% 0.68/0.89  (step t15.t16.t16.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t16.t27.t5 t15.t16.t16.t27.t8))
% 0.68/0.89  (step t15.t16.t16.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t27.t9 t15.t16.t16.t27.t10))
% 0.68/0.89  (step t15.t16.t16.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t16.t27.t11 t15.t16.t16.t27.t12))
% 0.68/0.89  (step t15.t16.t16.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t16.t26 t15.t16.t16.t27))
% 0.68/0.89  (step t15.t16.t16.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t16.t25 t15.t16.t16.t28))
% 0.68/0.89  (step t15.t16.t16.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t16.t22 t15.t16.t16.t29 a8))
% 0.68/0.89  (step t15.t16.t16.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t16.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t16.t32 t15.t16.t16.t33))
% 0.68/0.89  (step t15.t16.t16.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t16.t31 t15.t16.t16.t34 a6))
% 0.68/0.89  (step t15.t16.t16.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t16.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t16.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t16.t38.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t16.t38.t5))
% 0.68/0.89  (step t15.t16.t16.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t16.t38.t5))
% 0.68/0.89  (step t15.t16.t16.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t16.t38.t7 t15.t16.t16.t38.t8))
% 0.68/0.89  (step t15.t16.t16.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t16.t38.t6 t15.t16.t16.t38.t9))
% 0.68/0.89  (step t15.t16.t16.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t38.t10 t15.t16.t16.t38.t11))
% 0.68/0.89  (step t15.t16.t16.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t38.t12 t15.t16.t16.t38.t13))
% 0.68/0.89  (step t15.t16.t16.t38 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t16.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t16.t37 t15.t16.t16.t38))
% 0.68/0.89  (step t15.t16.t16.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.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)
% 0.68/0.89  (step t15.t16.t16.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t16.t41.t4 t15.t16.t16.t41.t5))
% 0.68/0.89  (step t15.t16.t16.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t16.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t16.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t16.t41.t8.t3 t15.t16.t16.t41.t8.t4))
% 0.68/0.89  (step t15.t16.t16.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t16.t16.t41.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 (t15.t16.t16.t41.t7 t15.t16.t16.t41.t8))
% 0.68/0.89  (step t15.t16.t16.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t16.t41.t6 t15.t16.t16.t41.t9))
% 0.68/0.89  (step t15.t16.t16.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t16.t41.t10 t15.t16.t16.t41.t11))
% 0.68/0.89  (step t15.t16.t16.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t16.t41.t12 t15.t16.t16.t41.t13))
% 0.68/0.89  (step t15.t16.t16.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t41.t14 t15.t16.t16.t41.t15))
% 0.68/0.89  (step t15.t16.t16.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t16.t41.t16 t15.t16.t16.t41.t17))
% 0.68/0.89  (step t15.t16.t16.t41 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t16.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t16.t40 t15.t16.t16.t41))
% 0.68/0.89  (step t15.t16.t16.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t16.t39 t15.t16.t16.t42))
% 0.68/0.89  (step t15.t16.t16.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t16.t36 t15.t16.t16.t43 a5))
% 0.68/0.89  (step t15.t16.t16.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t16.t16 t15.t16.t16.t21 t15.t16.t16.t30 a7 t15.t16.t16.t35 t15.t16.t16.t44 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t16.t45))
% 0.68/0.89  (step t15.t16.t16.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t16.t45))
% 0.68/0.89  (step t15.t16.t16.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t16.t46 t15.t16.t16.t47))
% 0.68/0.89  (step t15.t16.t16.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t16.t15 t15.t16.t16.t48))
% 0.68/0.89  (step t15.t16.t16.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t16.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t16.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t16.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t16.t16.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t16.t52.t2.t2 t15.t16.t16.t52.t2.t3))
% 0.68/0.89  (step t15.t16.t16.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t16.t52.t2.t4 t15.t16.t16.t52.t2.t5))
% 0.68/0.89  (step t15.t16.t16.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t16.t52.t2 t15.t16.t16.t52.t3))
% 0.68/0.89  (step t15.t16.t16.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t16.t52.t4))
% 0.68/0.89  (step t15.t16.t16.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t16.t52.t5 t15.t16.t16.t52.t6))
% 0.68/0.89  (step t15.t16.t16.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t16.t16.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t16.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t16.t52 t15.t16.t16.t53))
% 0.68/0.89  (step t15.t16.t16.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t16.t51 t15.t16.t16.t54))
% 0.68/0.89  (step t15.t16.t16.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t16.t50 t15.t16.t16.t55))
% 0.68/0.89  (step t15.t16.t16.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t16.t49 t15.t16.t16.t56))
% 0.68/0.89  (step t15.t16.t16.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t16.t14 t15.t16.t16.t57 a10))
% 0.68/0.89  (step t15.t16.t16.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t16.t4 t15.t16.t16.t13 t15.t16.t16.t58 t15.t16.t16.t21 t15.t16.t16.t30 a7 t15.t16.t16.t35 t15.t16.t16.t44 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t16.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t16.t59))
% 0.68/0.89  (step t15.t16.t16.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t16.t59))
% 0.68/0.89  (step t15.t16.t16.t62 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t16.t61 t15.t16.t16.t62))
% 0.68/0.89  (step t15.t16.t16.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t16.t60 t15.t16.t16.t63))
% 0.68/0.89  (step t15.t16.t16.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t16.t16.t61 t15.t16.t16.t65))
% 0.68/0.89  (step t15.t16.t16.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t16.t16.t64 t15.t16.t16.t66))
% 0.68/0.89  (step t15.t16.t16.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t16.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t16.t16.t67 t15.t16.t16.t68))
% 0.68/0.89  (step t15.t16.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t17 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t16.t15 t15.t16.t16))
% 0.68/0.89  (step t15.t16.t18 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t19.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t19.t4 t15.t16.t19.t5))
% 0.68/0.89  (step t15.t16.t19.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t19.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t19.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t19.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t16.t19.t8.t3 t15.t16.t19.t8.t4))
% 0.68/0.89  (step t15.t16.t19.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t19.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t16.t19.t7 t15.t16.t19.t8))
% 0.68/0.89  (step t15.t16.t19.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t16.t19.t6 t15.t16.t19.t9))
% 0.68/0.89  (step t15.t16.t19.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t19.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t16.t19.t10 t15.t16.t19.t11))
% 0.68/0.89  (step t15.t16.t19.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t19.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t19.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t19.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t16.t19.t14.t2 t15.t16.t19.t14.t3))
% 0.68/0.89  (step t15.t16.t19.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t19.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t16.t19.t13 t15.t16.t19.t14))
% 0.68/0.89  (step t15.t16.t19.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t16.t19.t12 t15.t16.t19.t15))
% 0.68/0.89  (step t15.t16.t19.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t19.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t19.t16 t15.t16.t19.t17))
% 0.68/0.89  (step t15.t16.t19.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t19.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t16.t19.t18 t15.t16.t19.t19))
% 0.68/0.89  (step t15.t16.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t20 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t16.t18 t15.t16.t19))
% 0.68/0.89  (step t15.t16.t21 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t16.t17 t15.t16.t20))
% 0.68/0.89  (step t15.t16.t22 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t16.t14 t15.t16.t21 a12))
% 0.68/0.89  (step t15.t16.t23 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t24 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t25.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t25.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t25.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t25.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t25.t9 t15.t16.t25.t10))
% 0.68/0.89  (step t15.t16.t25.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t25.t8 t15.t16.t25.t11 a9))
% 0.68/0.89  (step t15.t16.t25.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t25.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t25.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t25.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t25.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t25.t15.t5 t15.t16.t25.t15.t6))
% 0.68/0.89  (step t15.t16.t25.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t25.t15.t4 t15.t16.t25.t15.t7 a6))
% 0.68/0.89  (step t15.t16.t25.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t25.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t25.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t25.t15.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t25.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t25.t15.t11.t5))
% 0.68/0.89  (step t15.t16.t25.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t25.t15.t11.t5))
% 0.68/0.89  (step t15.t16.t25.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t25.t15.t11.t7 t15.t16.t25.t15.t11.t8))
% 0.68/0.89  (step t15.t16.t25.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t25.t15.t11.t6 t15.t16.t25.t15.t11.t9))
% 0.68/0.89  (step t15.t16.t25.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t25.t15.t11.t10 t15.t16.t25.t15.t11.t11))
% 0.68/0.89  (step t15.t16.t25.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t25.t15.t11.t12 t15.t16.t25.t15.t11.t13))
% 0.68/0.89  (step t15.t16.t25.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t25.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t25.t15.t10 t15.t16.t25.t15.t11))
% 0.68/0.89  (step t15.t16.t25.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.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)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t25.t15.t14.t4 t15.t16.t25.t15.t14.t5))
% 0.68/0.89  (step t15.t16.t25.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t25.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t25.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t25.t15.t14.t8.t3 t15.t16.t25.t15.t14.t8.t4))
% 0.68/0.89  (step t15.t16.t25.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t16.t25.t15.t14.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 (t15.t16.t25.t15.t14.t7 t15.t16.t25.t15.t14.t8))
% 0.68/0.89  (step t15.t16.t25.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t25.t15.t14.t6 t15.t16.t25.t15.t14.t9))
% 0.68/0.89  (step t15.t16.t25.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t25.t15.t14.t10 t15.t16.t25.t15.t14.t11))
% 0.68/0.89  (step t15.t16.t25.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t25.t15.t14.t12 t15.t16.t25.t15.t14.t13))
% 0.68/0.89  (step t15.t16.t25.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t25.t15.t14.t14 t15.t16.t25.t15.t14.t15))
% 0.68/0.89  (step t15.t16.t25.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t25.t15.t14.t16 t15.t16.t25.t15.t14.t17))
% 0.68/0.89  (step t15.t16.t25.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t25.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t25.t15.t13 t15.t16.t25.t15.t14))
% 0.68/0.89  (step t15.t16.t25.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t25.t15.t12 t15.t16.t25.t15.t15))
% 0.68/0.89  (step t15.t16.t25.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t25.t15.t9 t15.t16.t25.t15.t16 a5))
% 0.68/0.89  (step t15.t16.t25.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t25.t15.t3 a7 t15.t16.t25.t15.t8 t15.t16.t25.t15.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t25.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t25.t15.t18))
% 0.68/0.89  (step t15.t16.t25.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t25.t15.t18))
% 0.68/0.89  (step t15.t16.t25.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t25.t15.t20 t15.t16.t25.t15.t21))
% 0.68/0.89  (step t15.t16.t25.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t25.t15.t19 t15.t16.t25.t15.t22))
% 0.68/0.89  (step t15.t16.t25.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t25.t15.t23 t15.t16.t25.t15.t24))
% 0.68/0.89  (step t15.t16.t25.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t25.t14 t15.t16.t25.t15))
% 0.68/0.89  (step t15.t16.t25.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t25.t18.t3 t15.t16.t25.t18.t4))
% 0.68/0.89  (step t15.t16.t25.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t25.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t25.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t25.t18.t7.t2))
% 0.68/0.89  (step t15.t16.t25.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t25.t18.t6 t15.t16.t25.t18.t7))
% 0.68/0.89  (step t15.t16.t25.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t25.t18.t5 t15.t16.t25.t18.t8))
% 0.68/0.89  (step t15.t16.t25.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t25.t18.t9 t15.t16.t25.t18.t10))
% 0.68/0.89  (step t15.t16.t25.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t25.t18.t11 t15.t16.t25.t18.t12))
% 0.68/0.89  (step t15.t16.t25.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t25.t17 t15.t16.t25.t18))
% 0.68/0.89  (step t15.t16.t25.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t25.t16 t15.t16.t25.t19))
% 0.68/0.89  (step t15.t16.t25.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t25.t13 t15.t16.t25.t20 a8))
% 0.68/0.89  (step t15.t16.t25.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t25.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t25.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t25.t23 t15.t16.t25.t24))
% 0.68/0.89  (step t15.t16.t25.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t25.t22 t15.t16.t25.t25 a6))
% 0.68/0.89  (step t15.t16.t25.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t25.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t25.t29.t5 (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)))))) :rule resolution :premises (t15.t16.t25.t29.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t25.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t25.t29.t5))
% 0.68/0.89  (step t15.t16.t25.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t25.t29.t5))
% 0.68/0.89  (step t15.t16.t25.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t25.t29.t7 t15.t16.t25.t29.t8))
% 0.68/0.89  (step t15.t16.t25.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t25.t29.t6 t15.t16.t25.t29.t9))
% 0.68/0.89  (step t15.t16.t25.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t25.t29.t10 t15.t16.t25.t29.t11))
% 0.68/0.89  (step t15.t16.t25.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t25.t29.t12 t15.t16.t25.t29.t13))
% 0.68/0.89  (step t15.t16.t25.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t25.t28 t15.t16.t25.t29))
% 0.68/0.89  (step t15.t16.t25.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t25.t32.t4 t15.t16.t25.t32.t5))
% 0.68/0.89  (step t15.t16.t25.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t16.t25.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t25.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t25.t32.t8.t3 t15.t16.t25.t32.t8.t4))
% 0.68/0.89  (step t15.t16.t25.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t25.t32.t7 t15.t16.t25.t32.t8))
% 0.68/0.89  (step t15.t16.t25.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t25.t32.t6 t15.t16.t25.t32.t9))
% 0.68/0.89  (step t15.t16.t25.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t25.t32.t10 t15.t16.t25.t32.t11))
% 0.68/0.89  (step t15.t16.t25.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t32.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 (t15.t16.t25.t32.t12 t15.t16.t25.t32.t13))
% 0.68/0.89  (step t15.t16.t25.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t32.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 (t15.t16.t25.t32.t14 t15.t16.t25.t32.t15))
% 0.68/0.89  (step t15.t16.t25.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t25.t32.t16 t15.t16.t25.t32.t17))
% 0.68/0.89  (step t15.t16.t25.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t25.t31 t15.t16.t25.t32))
% 0.68/0.89  (step t15.t16.t25.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t25.t30 t15.t16.t25.t33))
% 0.68/0.89  (step t15.t16.t25.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t25.t27 t15.t16.t25.t34 a5))
% 0.68/0.89  (step t15.t16.t25.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t25.t7 t15.t16.t25.t12 t15.t16.t25.t21 a7 t15.t16.t25.t26 t15.t16.t25.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t25.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t25.t36))
% 0.68/0.89  (step t15.t16.t25.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t25.t36))
% 0.68/0.89  (step t15.t16.t25.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t25.t37 t15.t16.t25.t38))
% 0.68/0.89  (step t15.t16.t25.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t25.t6 t15.t16.t25.t39))
% 0.68/0.89  (step t15.t16.t25.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t25.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t25.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t25.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t16.t25.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t25.t43.t2.t2 t15.t16.t25.t43.t2.t3))
% 0.68/0.89  (step t15.t16.t25.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t25.t43.t2.t4 t15.t16.t25.t43.t2.t5))
% 0.68/0.89  (step t15.t16.t25.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t25.t43.t2 t15.t16.t25.t43.t3))
% 0.68/0.89  (step t15.t16.t25.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t25.t43.t4))
% 0.68/0.89  (step t15.t16.t25.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t25.t43.t5 t15.t16.t25.t43.t6))
% 0.68/0.89  (step t15.t16.t25.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t16.t25.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t25.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t25.t43 t15.t16.t25.t44))
% 0.68/0.89  (step t15.t16.t25.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t25.t42 t15.t16.t25.t45))
% 0.68/0.89  (step t15.t16.t25.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t25.t41 t15.t16.t25.t46))
% 0.68/0.89  (step t15.t16.t25.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t25.t40 t15.t16.t25.t47))
% 0.68/0.89  (step t15.t16.t25.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t25.t5 t15.t16.t25.t48 a10))
% 0.68/0.89  (step t15.t16.t25.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t25.t4 t15.t16.t25.t49 t15.t16.t25.t12 t15.t16.t25.t21 a7 t15.t16.t25.t26 t15.t16.t25.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t25.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t25.t50))
% 0.68/0.89  (step t15.t16.t25.t52 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t16.t25.t51 t15.t16.t25.t52))
% 0.68/0.89  (step t15.t16.t25.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t16.t25.t53 t15.t16.t25.t54))
% 0.68/0.89  (step t15.t16.t25.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t25.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t16.t25.t55 t15.t16.t25.t56))
% 0.68/0.89  (step t15.t16.t25 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t26 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t16.t24 t15.t16.t25))
% 0.68/0.89  (step t15.t16.t27 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t28 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t28.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t28.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t28.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t28.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t28.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t16.t28.t4 t15.t16.t28.t5))
% 0.68/0.89  (step t15.t16.t28.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t28.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t16.t28.t6 t15.t16.t28.t7))
% 0.68/0.89  (step t15.t16.t28.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t28.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t16.t28.t8 t15.t16.t28.t9))
% 0.68/0.89  (step t15.t16.t28.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t28.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t16.t28.t10 t15.t16.t28.t11))
% 0.68/0.89  (step t15.t16.t28 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t29 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t16.t27 t15.t16.t28))
% 0.68/0.89  (step t15.t16.t30 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t16.t26 t15.t16.t29))
% 0.68/0.89  (step t15.t16.t31 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t16.t23 t15.t16.t30 a11))
% 0.68/0.89  (step t15.t16.t32 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t33 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t34 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t35 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t36 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t16.t37 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t38 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t36 t15.t16.t37))
% 0.68/0.89  (step t15.t16.t39 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t16.t35 t15.t16.t38 a9))
% 0.68/0.89  (step t15.t16.t40 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t41 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t42.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t42.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t42.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t42.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t42.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t42.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t42.t5 t15.t16.t42.t6))
% 0.68/0.89  (step t15.t16.t42.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t42.t4 t15.t16.t42.t7 a6))
% 0.68/0.89  (step t15.t16.t42.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t42.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t42.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t42.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t42.t11.t5 (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)))))) :rule resolution :premises (t15.t16.t42.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t42.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t42.t11.t5))
% 0.68/0.89  (step t15.t16.t42.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t42.t11.t5))
% 0.68/0.89  (step t15.t16.t42.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t42.t11.t7 t15.t16.t42.t11.t8))
% 0.68/0.89  (step t15.t16.t42.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t16.t42.t11.t6 t15.t16.t42.t11.t9))
% 0.68/0.89  (step t15.t16.t42.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t16.t42.t11.t10 t15.t16.t42.t11.t11))
% 0.68/0.89  (step t15.t16.t42.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t42.t11.t12 t15.t16.t42.t11.t13))
% 0.68/0.89  (step t15.t16.t42.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t42.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t16.t42.t10 t15.t16.t42.t11))
% 0.68/0.89  (step t15.t16.t42.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t42.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t42.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t42.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t16.t42.t14.t4 t15.t16.t42.t14.t5))
% 0.68/0.89  (step t15.t16.t42.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t16.t42.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t42.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t42.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t42.t14.t8.t3 t15.t16.t42.t14.t8.t4))
% 0.68/0.89  (step t15.t16.t42.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t16.t42.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t42.t14.t7 t15.t16.t42.t14.t8))
% 0.68/0.89  (step t15.t16.t42.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t42.t14.t6 t15.t16.t42.t14.t9))
% 0.68/0.89  (step t15.t16.t42.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t16.t42.t14.t10 t15.t16.t42.t14.t11))
% 0.68/0.89  (step t15.t16.t42.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t42.t14.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 (t15.t16.t42.t14.t12 t15.t16.t42.t14.t13))
% 0.68/0.89  (step t15.t16.t42.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t14.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 (t15.t16.t42.t14.t14 t15.t16.t42.t14.t15))
% 0.68/0.89  (step t15.t16.t42.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t42.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t16.t42.t14.t16 t15.t16.t42.t14.t17))
% 0.68/0.89  (step t15.t16.t42.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t16.t42.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t42.t13 t15.t16.t42.t14))
% 0.68/0.89  (step t15.t16.t42.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t42.t12 t15.t16.t42.t15))
% 0.68/0.89  (step t15.t16.t42.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t42.t9 t15.t16.t42.t16 a5))
% 0.68/0.89  (step t15.t16.t42.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t42.t3 a7 t15.t16.t42.t8 t15.t16.t42.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t42.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t42.t18))
% 0.68/0.89  (step t15.t16.t42.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t16.t42.t18))
% 0.68/0.89  (step t15.t16.t42.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t16.t42.t20 t15.t16.t42.t21))
% 0.68/0.89  (step t15.t16.t42.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t16.t42.t19 t15.t16.t42.t22))
% 0.68/0.89  (step t15.t16.t42.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t42.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t16.t42.t23 t15.t16.t42.t24))
% 0.68/0.89  (step t15.t16.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t16.t43 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t16.t41 t15.t16.t42))
% 0.68/0.89  (step t15.t16.t44 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t45 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t45.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t45.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t45.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t16.t45.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t45.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t45.t3 t15.t16.t45.t4))
% 0.68/0.89  (step t15.t16.t45.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t45.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t45.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t45.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t45.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t16.t45.t7.t2))
% 0.68/0.89  (step t15.t16.t45.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t45.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t45.t6 t15.t16.t45.t7))
% 0.68/0.89  (step t15.t16.t45.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t16.t45.t5 t15.t16.t45.t8))
% 0.68/0.89  (step t15.t16.t45.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t45.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t16.t45.t9 t15.t16.t45.t10))
% 0.68/0.89  (step t15.t16.t45.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t45.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t16.t45.t11 t15.t16.t45.t12))
% 0.68/0.89  (step t15.t16.t45 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t16.t46 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t16.t44 t15.t16.t45))
% 0.68/0.89  (step t15.t16.t47 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t16.t43 t15.t16.t46))
% 0.68/0.89  (step t15.t16.t48 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t16.t40 t15.t16.t47 a8))
% 0.68/0.89  (step t15.t16.t49 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t50 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t51 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t16.t51.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t51.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t16.t51.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t51 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t16.t52 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t16.t50 t15.t16.t51))
% 0.68/0.89  (step t15.t16.t53 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t16.t49 t15.t16.t52 a6))
% 0.68/0.89  (step t15.t16.t54 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t16.t55 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t56 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t56.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t56.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t56.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t56.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t16.t56.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t16.t56.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t56.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t16.t56.t5))
% 0.68/0.89  (step t15.t16.t56.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t16.t56.t5))
% 0.68/0.89  (step t15.t16.t56.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t56.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t16.t56.t7 t15.t16.t56.t8))
% 0.68/0.89  (step t15.t16.t56.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t16.t56.t6 t15.t16.t56.t9))
% 0.68/0.89  (step t15.t16.t56.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t56.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t16.t56.t10 t15.t16.t56.t11))
% 0.68/0.89  (step t15.t16.t56.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t56.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t16.t56.t12 t15.t16.t56.t13))
% 0.68/0.89  (step t15.t16.t56 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t57 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t16.t55 t15.t16.t56))
% 0.68/0.89  (step t15.t16.t58 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t59 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t59.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t59.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t59.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t59.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)
% 0.68/0.89  (step t15.t16.t59.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t59.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t16.t59.t4 t15.t16.t59.t5))
% 0.68/0.89  (step t15.t16.t59.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t59.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t16.t59.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t59.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t16.t59.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t59.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t16.t59.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t16.t59.t8.t3 t15.t16.t59.t8.t4))
% 0.68/0.89  (step t15.t16.t59.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t16.t59.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 (t15.t16.t59.t7 t15.t16.t59.t8))
% 0.68/0.89  (step t15.t16.t59.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t16.t59.t6 t15.t16.t59.t9))
% 0.68/0.89  (step t15.t16.t59.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t16.t59.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t16.t59.t10 t15.t16.t59.t11))
% 0.68/0.89  (step t15.t16.t59.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t59.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t16.t59.t12 t15.t16.t59.t13))
% 0.68/0.89  (step t15.t16.t59.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t59.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t16.t59.t14 t15.t16.t59.t15))
% 0.68/0.89  (step t15.t16.t59.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t59.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t16.t59.t16 t15.t16.t59.t17))
% 0.68/0.89  (step t15.t16.t59 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t16.t60 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t16.t58 t15.t16.t59))
% 0.68/0.89  (step t15.t16.t61 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t16.t57 t15.t16.t60))
% 0.68/0.89  (step t15.t16.t62 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t16.t54 t15.t16.t61 a5))
% 0.68/0.89  (step t15.t16.t63 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t34 t15.t16.t39 t15.t16.t48 a7 t15.t16.t53 t15.t16.t62 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t64 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t16.t63))
% 0.68/0.89  (step t15.t16.t65 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t16.t63))
% 0.68/0.89  (step t15.t16.t66 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t16.t64 t15.t16.t65))
% 0.68/0.89  (step t15.t16.t67 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t16.t33 t15.t16.t66))
% 0.68/0.89  (step t15.t16.t68 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t16.t69 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t16.t70 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t16.t70.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t16.t70.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t16.t70.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t16.t70.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t16.t70.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t70.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t16.t70.t2.t2 t15.t16.t70.t2.t3))
% 0.68/0.89  (step t15.t16.t70.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t70.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t16.t70.t2.t4 t15.t16.t70.t2.t5))
% 0.68/0.89  (step t15.t16.t70.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t16.t70.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t70.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t16.t70.t2 t15.t16.t70.t3))
% 0.68/0.89  (step t15.t16.t70.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t16.t70.t4))
% 0.68/0.89  (step t15.t16.t70.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t70.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t16.t70.t5 t15.t16.t70.t6))
% 0.68/0.89  (step t15.t16.t70 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t16.t71 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t16.t72 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t70 t15.t16.t71))
% 0.68/0.89  (step t15.t16.t73 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t16.t69 t15.t16.t72))
% 0.68/0.89  (step t15.t16.t74 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t16.t68 t15.t16.t73))
% 0.68/0.89  (step t15.t16.t75 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t16.t67 t15.t16.t74))
% 0.68/0.89  (step t15.t16.t76 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t16.t32 t15.t16.t75 a10))
% 0.68/0.89  (step t15.t16.t77 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t16.t4 t15.t16.t13 t15.t16.t22 t15.t16.t31 t15.t16.t76 t15.t16.t39 t15.t16.t48 a7 t15.t16.t53 t15.t16.t62 a4 a3 a2))
% 0.68/0.89  (step t15.t16.t78 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule and :premises (t15.t16.t77))
% 0.68/0.89  (step t15.t16.t79 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t16.t80 (cl (= (@ tptp.iimplies Q) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t15.t16.t78 t15.t16.t79))
% 0.68/0.89  (step t15.t16.t81 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t16.t82 (cl (= (@ (@ tptp.iimplies Q) P) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P))) :rule cong :premises (t15.t16.t80 t15.t16.t81))
% 0.68/0.89  (step t15.t16.t83 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t16.t84 (cl (= (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) :rule cong :premises (t15.t16.t82 t15.t16.t83))
% 0.68/0.89  (step t15.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t17 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))))) :rule cong :premises (t15.t15 t15.t16))
% 0.68/0.89  (step t15.t18 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.68/0.89  (anchor :step t15.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t19.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.89  (step t15.t19.t5 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t19.t6 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t15.t19.t4 t15.t19.t5))
% 0.68/0.89  (step t15.t19.t7 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.89  (step t15.t19.t8 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t15.t19.t6 t15.t19.t7))
% 0.68/0.89  (step t15.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t19.t10 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t19.t8 t15.t19.t9))
% 0.68/0.89  (step t15.t19.t11 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t19.t12 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t19.t10 t15.t19.t11))
% 0.68/0.89  (step t15.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t20 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t18 t15.t19))
% 0.68/0.89  (step t15.t21 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t17 t15.t20))
% 0.68/0.89  (step t15.t22 (cl (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t14 t15.t21 a14))
% 0.68/0.89  (step t15.t23 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t24 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t7.t7.t9 t15.t25.t7.t7.t10))
% 0.68/0.89  (step t15.t25.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t25.t7.t7.t8 t15.t25.t7.t7.t11 a9))
% 0.68/0.89  (step t15.t25.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t7.t7.t15.t5 t15.t25.t7.t7.t15.t6))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t7.t7.t15.t4 t15.t25.t7.t7.t15.t7 a6))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t7.t7.t15.t11.t5))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t7.t7.t15.t11.t5))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t7.t7.t15.t11.t7 t15.t25.t7.t7.t15.t11.t8))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t25.t7.t7.t15.t11.t6 t15.t25.t7.t7.t15.t11.t9))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t7.t15.t11.t10 t15.t25.t7.t7.t15.t11.t11))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t7.t15.t11.t12 t15.t25.t7.t7.t15.t11.t13))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t25.t7.t7.t15.t10 t15.t25.t7.t7.t15.t11))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.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)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t7.t7.t15.t14.t4 t15.t25.t7.t7.t15.t14.t5))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t7.t7.t15.t14.t8.t3 t15.t25.t7.t7.t15.t14.t8.t4))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.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 (t15.t25.t7.t7.t15.t14.t7 t15.t25.t7.t7.t15.t14.t8))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t7.t7.t15.t14.t6 t15.t25.t7.t7.t15.t14.t9))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t7.t15.t14.t10 t15.t25.t7.t7.t15.t14.t11))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t25.t7.t7.t15.t14.t12 t15.t25.t7.t7.t15.t14.t13))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t7.t15.t14.t14 t15.t25.t7.t7.t15.t14.t15))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t25.t7.t7.t15.t14.t16 t15.t25.t7.t7.t15.t14.t17))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t7.t7.t15.t13 t15.t25.t7.t7.t15.t14))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t7.t7.t15.t12 t15.t25.t7.t7.t15.t15))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t7.t7.t15.t9 t15.t25.t7.t7.t15.t16 a5))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t25.t7.t7.t15.t3 a7 t15.t25.t7.t7.t15.t8 t15.t25.t7.t7.t15.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t7.t7.t15.t18))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t25.t7.t7.t15.t18))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t25.t7.t7.t15.t20 t15.t25.t7.t7.t15.t21))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t25.t7.t7.t15.t19 t15.t25.t7.t7.t15.t22))
% 0.68/0.89  (step t15.t25.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t7.t15.t23 t15.t25.t7.t7.t15.t24))
% 0.68/0.89  (step t15.t25.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t25.t7.t7.t14 t15.t25.t7.t7.t15))
% 0.68/0.89  (step t15.t25.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t7.t7.t18.t3 t15.t25.t7.t7.t18.t4))
% 0.68/0.89  (step t15.t25.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t25.t7.t7.t18.t7.t2))
% 0.68/0.89  (step t15.t25.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t7.t7.t18.t6 t15.t25.t7.t7.t18.t7))
% 0.68/0.89  (step t15.t25.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t7.t7.t18.t5 t15.t25.t7.t7.t18.t8))
% 0.68/0.89  (step t15.t25.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t7.t18.t9 t15.t25.t7.t7.t18.t10))
% 0.68/0.89  (step t15.t25.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t25.t7.t7.t18.t11 t15.t25.t7.t7.t18.t12))
% 0.68/0.89  (step t15.t25.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t25.t7.t7.t17 t15.t25.t7.t7.t18))
% 0.68/0.89  (step t15.t25.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t25.t7.t7.t16 t15.t25.t7.t7.t19))
% 0.68/0.89  (step t15.t25.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t25.t7.t7.t13 t15.t25.t7.t7.t20 a8))
% 0.68/0.89  (step t15.t25.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t25.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t7.t7.t23 t15.t25.t7.t7.t24))
% 0.68/0.89  (step t15.t25.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t7.t7.t22 t15.t25.t7.t7.t25 a6))
% 0.68/0.89  (step t15.t25.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t7.t29.t5 (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)))))) :rule resolution :premises (t15.t25.t7.t7.t29.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t7.t7.t29.t5))
% 0.68/0.89  (step t15.t25.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t7.t7.t29.t5))
% 0.68/0.89  (step t15.t25.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t7.t7.t29.t7 t15.t25.t7.t7.t29.t8))
% 0.68/0.89  (step t15.t25.t7.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t25.t7.t7.t29.t6 t15.t25.t7.t7.t29.t9))
% 0.68/0.89  (step t15.t25.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t25.t7.t7.t29.t10 t15.t25.t7.t7.t29.t11))
% 0.68/0.89  (step t15.t25.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t7.t29.t12 t15.t25.t7.t7.t29.t13))
% 0.68/0.89  (step t15.t25.t7.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t25.t7.t7.t28 t15.t25.t7.t7.t29))
% 0.68/0.89  (step t15.t25.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t25.t7.t7.t32.t4 t15.t25.t7.t7.t32.t5))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t7.t7.t32.t8.t3 t15.t25.t7.t7.t32.t8.t4))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t7.t7.t32.t7 t15.t25.t7.t7.t32.t8))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t7.t7.t32.t6 t15.t25.t7.t7.t32.t9))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t25.t7.t7.t32.t10 t15.t25.t7.t7.t32.t11))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t32.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 (t15.t25.t7.t7.t32.t12 t15.t25.t7.t7.t32.t13))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t32.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 (t15.t25.t7.t7.t32.t14 t15.t25.t7.t7.t32.t15))
% 0.68/0.89  (step t15.t25.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t7.t32.t16 t15.t25.t7.t7.t32.t17))
% 0.68/0.89  (step t15.t25.t7.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t7.t7.t31 t15.t25.t7.t7.t32))
% 0.68/0.89  (step t15.t25.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t7.t7.t30 t15.t25.t7.t7.t33))
% 0.68/0.89  (step t15.t25.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t7.t7.t27 t15.t25.t7.t7.t34 a5))
% 0.68/0.89  (step t15.t25.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t7.t7.t7 t15.t25.t7.t7.t12 t15.t25.t7.t7.t21 a7 t15.t25.t7.t7.t26 t15.t25.t7.t7.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t25.t7.t7.t36))
% 0.68/0.89  (step t15.t25.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t25.t7.t7.t36))
% 0.68/0.89  (step t15.t25.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t7.t7.t37 t15.t25.t7.t7.t38))
% 0.68/0.89  (step t15.t25.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t25.t7.t7.t6 t15.t25.t7.t7.t39))
% 0.68/0.89  (step t15.t25.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t25.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t25.t7.t7.t43.t2.t2 t15.t25.t7.t7.t43.t2.t3))
% 0.68/0.89  (step t15.t25.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t25.t7.t7.t43.t2.t4 t15.t25.t7.t7.t43.t2.t5))
% 0.68/0.89  (step t15.t25.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t25.t7.t7.t43.t2 t15.t25.t7.t7.t43.t3))
% 0.68/0.89  (step t15.t25.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t25.t7.t7.t43.t4))
% 0.68/0.89  (step t15.t25.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t25.t7.t7.t43.t5 t15.t25.t7.t7.t43.t6))
% 0.68/0.89  (step t15.t25.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t7.t7.t43 t15.t25.t7.t7.t44))
% 0.68/0.89  (step t15.t25.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t7.t7.t42 t15.t25.t7.t7.t45))
% 0.68/0.89  (step t15.t25.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t25.t7.t7.t41 t15.t25.t7.t7.t46))
% 0.68/0.89  (step t15.t25.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t25.t7.t7.t40 t15.t25.t7.t7.t47))
% 0.68/0.89  (step t15.t25.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t25.t7.t7.t5 t15.t25.t7.t7.t48 a10))
% 0.68/0.89  (step t15.t25.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t25.t7.t7.t4 t15.t25.t7.t7.t49 t15.t25.t7.t7.t12 t15.t25.t7.t7.t21 a7 t15.t25.t7.t7.t26 t15.t25.t7.t7.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t7.t7.t50))
% 0.68/0.89  (step t15.t25.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t25.t7.t7.t51 t15.t25.t7.t7.t52))
% 0.68/0.89  (step t15.t25.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t25.t7.t7.t53 t15.t25.t7.t7.t54))
% 0.68/0.89  (step t15.t25.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t7.t55 t15.t25.t7.t7.t56))
% 0.68/0.89  (step t15.t25.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t25.t7.t6 t15.t25.t7.t7))
% 0.68/0.89  (step t15.t25.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t25.t7.t10.t4 t15.t25.t7.t10.t5))
% 0.68/0.89  (step t15.t25.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t25.t7.t10.t6 t15.t25.t7.t10.t7))
% 0.68/0.89  (step t15.t25.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t10.t8 t15.t25.t7.t10.t9))
% 0.68/0.89  (step t15.t25.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t25.t7.t10.t10 t15.t25.t7.t10.t11))
% 0.68/0.89  (step t15.t25.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t25.t7.t9 t15.t25.t7.t10))
% 0.68/0.89  (step t15.t25.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t25.t7.t8 t15.t25.t7.t11))
% 0.68/0.89  (step t15.t25.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t25.t7.t5 t15.t25.t7.t12 a11))
% 0.68/0.89  (step t15.t25.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t7.t18 t15.t25.t7.t19))
% 0.68/0.89  (step t15.t25.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t25.t7.t17 t15.t25.t7.t20 a9))
% 0.68/0.89  (step t15.t25.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t25.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t7.t24.t5 t15.t25.t7.t24.t6))
% 0.68/0.89  (step t15.t25.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t7.t24.t4 t15.t25.t7.t24.t7 a6))
% 0.68/0.89  (step t15.t25.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t24.t11.t5 (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)))))) :rule resolution :premises (t15.t25.t7.t24.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t7.t24.t11.t5))
% 0.68/0.89  (step t15.t25.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t7.t24.t11.t5))
% 0.68/0.89  (step t15.t25.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t7.t24.t11.t7 t15.t25.t7.t24.t11.t8))
% 0.68/0.89  (step t15.t25.t7.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t25.t7.t24.t11.t6 t15.t25.t7.t24.t11.t9))
% 0.68/0.89  (step t15.t25.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t25.t7.t24.t11.t10 t15.t25.t7.t24.t11.t11))
% 0.68/0.89  (step t15.t25.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t24.t11.t12 t15.t25.t7.t24.t11.t13))
% 0.68/0.89  (step t15.t25.t7.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t25.t7.t24.t10 t15.t25.t7.t24.t11))
% 0.68/0.89  (step t15.t25.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t25.t7.t24.t14.t4 t15.t25.t7.t24.t14.t5))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t25.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t7.t24.t14.t8.t3 t15.t25.t7.t24.t14.t8.t4))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t7.t24.t14.t7 t15.t25.t7.t24.t14.t8))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t7.t24.t14.t6 t15.t25.t7.t24.t14.t9))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t25.t7.t24.t14.t10 t15.t25.t7.t24.t14.t11))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t24.t14.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 (t15.t25.t7.t24.t14.t12 t15.t25.t7.t24.t14.t13))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t14.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 (t15.t25.t7.t24.t14.t14 t15.t25.t7.t24.t14.t15))
% 0.68/0.89  (step t15.t25.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t24.t14.t16 t15.t25.t7.t24.t14.t17))
% 0.68/0.89  (step t15.t25.t7.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t7.t24.t13 t15.t25.t7.t24.t14))
% 0.68/0.89  (step t15.t25.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t7.t24.t12 t15.t25.t7.t24.t15))
% 0.68/0.89  (step t15.t25.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t7.t24.t9 t15.t25.t7.t24.t16 a5))
% 0.68/0.89  (step t15.t25.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t7.t24.t3 a7 t15.t25.t7.t24.t8 t15.t25.t7.t24.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t7.t24.t18))
% 0.68/0.89  (step t15.t25.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t25.t7.t24.t18))
% 0.68/0.89  (step t15.t25.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t25.t7.t24.t20 t15.t25.t7.t24.t21))
% 0.68/0.89  (step t15.t25.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t25.t7.t24.t19 t15.t25.t7.t24.t22))
% 0.68/0.89  (step t15.t25.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t24.t23 t15.t25.t7.t24.t24))
% 0.68/0.89  (step t15.t25.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t25.t7.t23 t15.t25.t7.t24))
% 0.68/0.89  (step t15.t25.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t7.t27.t3 t15.t25.t7.t27.t4))
% 0.68/0.89  (step t15.t25.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t25.t7.t27.t7.t2))
% 0.68/0.89  (step t15.t25.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t7.t27.t6 t15.t25.t7.t27.t7))
% 0.68/0.89  (step t15.t25.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t7.t27.t5 t15.t25.t7.t27.t8))
% 0.68/0.89  (step t15.t25.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t27.t9 t15.t25.t7.t27.t10))
% 0.68/0.89  (step t15.t25.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t25.t7.t27.t11 t15.t25.t7.t27.t12))
% 0.68/0.89  (step t15.t25.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t25.t7.t26 t15.t25.t7.t27))
% 0.68/0.89  (step t15.t25.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t25.t7.t25 t15.t25.t7.t28))
% 0.68/0.89  (step t15.t25.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t25.t7.t22 t15.t25.t7.t29 a8))
% 0.68/0.89  (step t15.t25.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t25.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t7.t32 t15.t25.t7.t33))
% 0.68/0.89  (step t15.t25.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t7.t31 t15.t25.t7.t34 a6))
% 0.68/0.89  (step t15.t25.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t7.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t7.t38.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t7.t38.t5))
% 0.68/0.89  (step t15.t25.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t7.t38.t5))
% 0.68/0.89  (step t15.t25.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t7.t38.t7 t15.t25.t7.t38.t8))
% 0.68/0.89  (step t15.t25.t7.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t25.t7.t38.t6 t15.t25.t7.t38.t9))
% 0.68/0.89  (step t15.t25.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t38.t10 t15.t25.t7.t38.t11))
% 0.68/0.89  (step t15.t25.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t38.t12 t15.t25.t7.t38.t13))
% 0.68/0.89  (step t15.t25.t7.t38 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t25.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t25.t7.t37 t15.t25.t7.t38))
% 0.68/0.89  (step t15.t25.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.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)
% 0.68/0.89  (step t15.t25.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t7.t41.t4 t15.t25.t7.t41.t5))
% 0.68/0.89  (step t15.t25.t7.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t7.t41.t8.t3 t15.t25.t7.t41.t8.t4))
% 0.68/0.89  (step t15.t25.t7.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t25.t7.t41.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 (t15.t25.t7.t41.t7 t15.t25.t7.t41.t8))
% 0.68/0.89  (step t15.t25.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t7.t41.t6 t15.t25.t7.t41.t9))
% 0.68/0.89  (step t15.t25.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t25.t7.t41.t10 t15.t25.t7.t41.t11))
% 0.68/0.89  (step t15.t25.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t25.t7.t41.t12 t15.t25.t7.t41.t13))
% 0.68/0.89  (step t15.t25.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t41.t14 t15.t25.t7.t41.t15))
% 0.68/0.89  (step t15.t25.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t25.t7.t41.t16 t15.t25.t7.t41.t17))
% 0.68/0.89  (step t15.t25.t7.t41 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t25.t7.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t7.t40 t15.t25.t7.t41))
% 0.68/0.89  (step t15.t25.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t7.t39 t15.t25.t7.t42))
% 0.68/0.89  (step t15.t25.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t7.t36 t15.t25.t7.t43 a5))
% 0.68/0.89  (step t15.t25.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t25.t7.t16 t15.t25.t7.t21 t15.t25.t7.t30 a7 t15.t25.t7.t35 t15.t25.t7.t44 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t25.t7.t45))
% 0.68/0.89  (step t15.t25.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t25.t7.t45))
% 0.68/0.89  (step t15.t25.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t7.t46 t15.t25.t7.t47))
% 0.68/0.89  (step t15.t25.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t25.t7.t15 t15.t25.t7.t48))
% 0.68/0.89  (step t15.t25.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t25.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t25.t7.t52.t2.t2 t15.t25.t7.t52.t2.t3))
% 0.68/0.89  (step t15.t25.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t25.t7.t52.t2.t4 t15.t25.t7.t52.t2.t5))
% 0.68/0.89  (step t15.t25.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t25.t7.t52.t2 t15.t25.t7.t52.t3))
% 0.68/0.89  (step t15.t25.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t25.t7.t52.t4))
% 0.68/0.89  (step t15.t25.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t25.t7.t52.t5 t15.t25.t7.t52.t6))
% 0.68/0.89  (step t15.t25.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.89  (step t15.t25.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t7.t52 t15.t25.t7.t53))
% 0.68/0.89  (step t15.t25.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t7.t51 t15.t25.t7.t54))
% 0.68/0.89  (step t15.t25.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t25.t7.t50 t15.t25.t7.t55))
% 0.68/0.89  (step t15.t25.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t25.t7.t49 t15.t25.t7.t56))
% 0.68/0.89  (step t15.t25.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t25.t7.t14 t15.t25.t7.t57 a10))
% 0.68/0.89  (step t15.t25.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t25.t7.t4 t15.t25.t7.t13 t15.t25.t7.t58 t15.t25.t7.t21 t15.t25.t7.t30 a7 t15.t25.t7.t35 t15.t25.t7.t44 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t7.t59))
% 0.68/0.89  (step t15.t25.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t25.t7.t59))
% 0.68/0.89  (step t15.t25.t7.t62 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t25.t7.t61 t15.t25.t7.t62))
% 0.68/0.89  (step t15.t25.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t25.t7.t60 t15.t25.t7.t63))
% 0.68/0.89  (step t15.t25.t7.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t25.t7.t61 t15.t25.t7.t65))
% 0.68/0.89  (step t15.t25.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t25.t7.t64 t15.t25.t7.t66))
% 0.68/0.89  (step t15.t25.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t25.t7.t67 t15.t25.t7.t68))
% 0.68/0.89  (step t15.t25.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t25.t6 t15.t25.t7))
% 0.68/0.89  (step t15.t25.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t10.t4 t15.t25.t10.t5))
% 0.68/0.89  (step t15.t25.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t25.t10.t8.t3 t15.t25.t10.t8.t4))
% 0.68/0.89  (step t15.t25.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t25.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t25.t10.t7 t15.t25.t10.t8))
% 0.68/0.89  (step t15.t25.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t25.t10.t6 t15.t25.t10.t9))
% 0.68/0.89  (step t15.t25.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t25.t10.t10 t15.t25.t10.t11))
% 0.68/0.89  (step t15.t25.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t25.t10.t14.t2 t15.t25.t10.t14.t3))
% 0.68/0.89  (step t15.t25.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t25.t10.t13 t15.t25.t10.t14))
% 0.68/0.89  (step t15.t25.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t25.t10.t12 t15.t25.t10.t15))
% 0.68/0.89  (step t15.t25.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t25.t10.t16 t15.t25.t10.t17))
% 0.68/0.89  (step t15.t25.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t25.t10.t18 t15.t25.t10.t19))
% 0.68/0.89  (step t15.t25.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t25.t9 t15.t25.t10))
% 0.68/0.89  (step t15.t25.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t25.t8 t15.t25.t11))
% 0.68/0.89  (step t15.t25.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t25.t5 t15.t25.t12 a12))
% 0.68/0.89  (step t15.t25.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t16.t9 t15.t25.t16.t10))
% 0.68/0.89  (step t15.t25.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t25.t16.t8 t15.t25.t16.t11 a9))
% 0.68/0.89  (step t15.t25.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t25.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t16.t15.t5 t15.t25.t16.t15.t6))
% 0.68/0.89  (step t15.t25.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t16.t15.t4 t15.t25.t16.t15.t7 a6))
% 0.68/0.89  (step t15.t25.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t16.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t16.t15.t11.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t16.t15.t11.t5))
% 0.68/0.89  (step t15.t25.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t16.t15.t11.t5))
% 0.68/0.89  (step t15.t25.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t16.t15.t11.t7 t15.t25.t16.t15.t11.t8))
% 0.68/0.89  (step t15.t25.t16.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t25.t16.t15.t11.t6 t15.t25.t16.t15.t11.t9))
% 0.68/0.89  (step t15.t25.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t25.t16.t15.t11.t10 t15.t25.t16.t15.t11.t11))
% 0.68/0.89  (step t15.t25.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t25.t16.t15.t11.t12 t15.t25.t16.t15.t11.t13))
% 0.68/0.89  (step t15.t25.t16.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t25.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t25.t16.t15.t10 t15.t25.t16.t15.t11))
% 0.68/0.89  (step t15.t25.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.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)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t16.t15.t14.t4 t15.t25.t16.t15.t14.t5))
% 0.68/0.89  (step t15.t25.t16.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t16.t15.t14.t8.t3 t15.t25.t16.t15.t14.t8.t4))
% 0.68/0.89  (step t15.t25.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.89  (step t15.t25.t16.t15.t14.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 (t15.t25.t16.t15.t14.t7 t15.t25.t16.t15.t14.t8))
% 0.68/0.89  (step t15.t25.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t16.t15.t14.t6 t15.t25.t16.t15.t14.t9))
% 0.68/0.89  (step t15.t25.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t25.t16.t15.t14.t10 t15.t25.t16.t15.t14.t11))
% 0.68/0.89  (step t15.t25.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t25.t16.t15.t14.t12 t15.t25.t16.t15.t14.t13))
% 0.68/0.89  (step t15.t25.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t25.t16.t15.t14.t14 t15.t25.t16.t15.t14.t15))
% 0.68/0.89  (step t15.t25.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t25.t16.t15.t14.t16 t15.t25.t16.t15.t14.t17))
% 0.68/0.89  (step t15.t25.t16.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.89  (step t15.t25.t16.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t16.t15.t13 t15.t25.t16.t15.t14))
% 0.68/0.89  (step t15.t25.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t16.t15.t12 t15.t25.t16.t15.t15))
% 0.68/0.89  (step t15.t25.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t16.t15.t9 t15.t25.t16.t15.t16 a5))
% 0.68/0.89  (step t15.t25.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t25.t16.t15.t3 a7 t15.t25.t16.t15.t8 t15.t25.t16.t15.t17 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t16.t15.t18))
% 0.68/0.89  (step t15.t25.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t25.t16.t15.t18))
% 0.68/0.89  (step t15.t25.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t25.t16.t15.t20 t15.t25.t16.t15.t21))
% 0.68/0.89  (step t15.t25.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t25.t16.t15.t19 t15.t25.t16.t15.t22))
% 0.68/0.89  (step t15.t25.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t25.t16.t15.t23 t15.t25.t16.t15.t24))
% 0.68/0.89  (step t15.t25.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t25.t16.t14 t15.t25.t16.t15))
% 0.68/0.89  (step t15.t25.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t16.t18.t3 t15.t25.t16.t18.t4))
% 0.68/0.89  (step t15.t25.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t25.t16.t18.t7.t2))
% 0.68/0.89  (step t15.t25.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t16.t18.t6 t15.t25.t16.t18.t7))
% 0.68/0.89  (step t15.t25.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t16.t18.t5 t15.t25.t16.t18.t8))
% 0.68/0.89  (step t15.t25.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t25.t16.t18.t9 t15.t25.t16.t18.t10))
% 0.68/0.89  (step t15.t25.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t25.t16.t18.t11 t15.t25.t16.t18.t12))
% 0.68/0.89  (step t15.t25.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t25.t16.t17 t15.t25.t16.t18))
% 0.68/0.89  (step t15.t25.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t25.t16.t16 t15.t25.t16.t19))
% 0.68/0.89  (step t15.t25.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t25.t16.t13 t15.t25.t16.t20 a8))
% 0.68/0.89  (step t15.t25.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.89  (step t15.t25.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t16.t23 t15.t25.t16.t24))
% 0.68/0.89  (step t15.t25.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t16.t22 t15.t25.t16.t25 a6))
% 0.68/0.89  (step t15.t25.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.89  (step t15.t25.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.89  (step t15.t25.t16.t29.t5 (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)))))) :rule resolution :premises (t15.t25.t16.t29.t4 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t16.t29.t5))
% 0.68/0.89  (step t15.t25.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t16.t29.t5))
% 0.68/0.89  (step t15.t25.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t16.t29.t7 t15.t25.t16.t29.t8))
% 0.68/0.89  (step t15.t25.t16.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t25.t16.t29.t6 t15.t25.t16.t29.t9))
% 0.68/0.89  (step t15.t25.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t25.t16.t29.t10 t15.t25.t16.t29.t11))
% 0.68/0.89  (step t15.t25.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t16.t29.t12 t15.t25.t16.t29.t13))
% 0.68/0.89  (step t15.t25.t16.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t25.t16.t28 t15.t25.t16.t29))
% 0.68/0.89  (step t15.t25.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t25.t16.t32.t4 t15.t25.t16.t32.t5))
% 0.68/0.89  (step t15.t25.t16.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.89  (anchor :step t15.t25.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.89  (step t15.t25.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t16.t32.t8.t3 t15.t25.t16.t32.t8.t4))
% 0.68/0.89  (step t15.t25.t16.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t16.t32.t7 t15.t25.t16.t32.t8))
% 0.68/0.89  (step t15.t25.t16.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t16.t32.t6 t15.t25.t16.t32.t9))
% 0.68/0.89  (step t15.t25.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t25.t16.t32.t10 t15.t25.t16.t32.t11))
% 0.68/0.89  (step t15.t25.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t32.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 (t15.t25.t16.t32.t12 t15.t25.t16.t32.t13))
% 0.68/0.89  (step t15.t25.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t32.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 (t15.t25.t16.t32.t14 t15.t25.t16.t32.t15))
% 0.68/0.89  (step t15.t25.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t16.t32.t16 t15.t25.t16.t32.t17))
% 0.68/0.89  (step t15.t25.t16.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t16.t31 t15.t25.t16.t32))
% 0.68/0.89  (step t15.t25.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t16.t30 t15.t25.t16.t33))
% 0.68/0.89  (step t15.t25.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t16.t27 t15.t25.t16.t34 a5))
% 0.68/0.89  (step t15.t25.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t16.t7 t15.t25.t16.t12 t15.t25.t16.t21 a7 t15.t25.t16.t26 t15.t25.t16.t35 a4 a3 a2))
% 0.68/0.89  (step t15.t25.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t25.t16.t36))
% 0.68/0.89  (step t15.t25.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t25.t16.t36))
% 0.68/0.89  (step t15.t25.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t16.t37 t15.t25.t16.t38))
% 0.68/0.89  (step t15.t25.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t25.t16.t6 t15.t25.t16.t39))
% 0.68/0.89  (step t15.t25.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.89  (anchor :step t15.t25.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.89  (step t15.t25.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.89  (anchor :step t15.t25.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.89  (step t15.t25.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.89  (step t15.t25.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t25.t16.t43.t2.t2 t15.t25.t16.t43.t2.t3))
% 0.68/0.89  (step t15.t25.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t25.t16.t43.t2.t4 t15.t25.t16.t43.t2.t5))
% 0.68/0.89  (step t15.t25.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.89  (step t15.t25.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.89  (step t15.t25.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t25.t16.t43.t2 t15.t25.t16.t43.t3))
% 0.68/0.89  (step t15.t25.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t25.t16.t43.t4))
% 0.68/0.90  (step t15.t25.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t25.t16.t43.t5 t15.t25.t16.t43.t6))
% 0.68/0.90  (step t15.t25.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t15.t25.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t16.t43 t15.t25.t16.t44))
% 0.68/0.90  (step t15.t25.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t16.t42 t15.t25.t16.t45))
% 0.68/0.90  (step t15.t25.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t25.t16.t41 t15.t25.t16.t46))
% 0.68/0.90  (step t15.t25.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t25.t16.t40 t15.t25.t16.t47))
% 0.68/0.90  (step t15.t25.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t25.t16.t5 t15.t25.t16.t48 a10))
% 0.68/0.90  (step t15.t25.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t25.t16.t4 t15.t25.t16.t49 t15.t25.t16.t12 t15.t25.t16.t21 a7 t15.t25.t16.t26 t15.t25.t16.t35 a4 a3 a2))
% 0.68/0.90  (step t15.t25.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t16.t50))
% 0.68/0.90  (step t15.t25.t16.t52 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t25.t16.t51 t15.t25.t16.t52))
% 0.68/0.90  (step t15.t25.t16.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t25.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t25.t16.t53 t15.t25.t16.t54))
% 0.68/0.90  (step t15.t25.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t25.t16.t55 t15.t25.t16.t56))
% 0.68/0.90  (step t15.t25.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t25.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t25.t15 t15.t25.t16))
% 0.68/0.90  (step t15.t25.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t25.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t19.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t25.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t25.t19.t4 t15.t25.t19.t5))
% 0.68/0.90  (step t15.t25.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t25.t19.t6 t15.t25.t19.t7))
% 0.68/0.90  (step t15.t25.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t25.t19.t8 t15.t25.t19.t9))
% 0.68/0.90  (step t15.t25.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t25.t19.t10 t15.t25.t19.t11))
% 0.68/0.90  (step t15.t25.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t25.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t25.t18 t15.t25.t19))
% 0.68/0.90  (step t15.t25.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t25.t17 t15.t25.t20))
% 0.68/0.90  (step t15.t25.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t25.t14 t15.t25.t21 a11))
% 0.68/0.90  (step t15.t25.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t25.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t25.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t25.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t25.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t15.t25.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t27 t15.t25.t28))
% 0.68/0.90  (step t15.t25.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t25.t26 t15.t25.t29 a9))
% 0.68/0.90  (step t15.t25.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t25.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t25.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t25.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t25.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t25.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t33.t5 t15.t25.t33.t6))
% 0.68/0.90  (step t15.t25.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t33.t4 t15.t25.t33.t7 a6))
% 0.68/0.90  (step t15.t25.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t25.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t25.t33.t11.t5 (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)))))) :rule resolution :premises (t15.t25.t33.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t25.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t33.t11.t5))
% 0.68/0.90  (step t15.t25.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t33.t11.t5))
% 0.68/0.90  (step t15.t25.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t33.t11.t7 t15.t25.t33.t11.t8))
% 0.68/0.90  (step t15.t25.t33.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t25.t33.t11.t6 t15.t25.t33.t11.t9))
% 0.68/0.90  (step t15.t25.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t25.t33.t11.t10 t15.t25.t33.t11.t11))
% 0.68/0.90  (step t15.t25.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t33.t11.t12 t15.t25.t33.t11.t13))
% 0.68/0.90  (step t15.t25.t33.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t25.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t25.t33.t10 t15.t25.t33.t11))
% 0.68/0.90  (step t15.t25.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t33.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t25.t33.t14.t4 t15.t25.t33.t14.t5))
% 0.68/0.90  (step t15.t25.t33.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t15.t25.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t25.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t33.t14.t8.t3 t15.t25.t33.t14.t8.t4))
% 0.68/0.90  (step t15.t25.t33.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t15.t25.t33.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t33.t14.t7 t15.t25.t33.t14.t8))
% 0.68/0.90  (step t15.t25.t33.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t33.t14.t6 t15.t25.t33.t14.t9))
% 0.68/0.90  (step t15.t25.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t25.t33.t14.t10 t15.t25.t33.t14.t11))
% 0.68/0.90  (step t15.t25.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t33.t14.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 (t15.t25.t33.t14.t12 t15.t25.t33.t14.t13))
% 0.68/0.90  (step t15.t25.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t14.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 (t15.t25.t33.t14.t14 t15.t25.t33.t14.t15))
% 0.68/0.90  (step t15.t25.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t25.t33.t14.t16 t15.t25.t33.t14.t17))
% 0.68/0.90  (step t15.t25.t33.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t25.t33.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t33.t13 t15.t25.t33.t14))
% 0.68/0.90  (step t15.t25.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t33.t12 t15.t25.t33.t15))
% 0.68/0.90  (step t15.t25.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t33.t9 t15.t25.t33.t16 a5))
% 0.68/0.90  (step t15.t25.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t33.t3 a7 t15.t25.t33.t8 t15.t25.t33.t17 a4 a3 a2))
% 0.68/0.90  (step t15.t25.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t33.t18))
% 0.68/0.90  (step t15.t25.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t25.t33.t18))
% 0.68/0.90  (step t15.t25.t33.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t25.t33.t20 t15.t25.t33.t21))
% 0.68/0.90  (step t15.t25.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t25.t33.t19 t15.t25.t33.t22))
% 0.68/0.90  (step t15.t25.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t25.t33.t23 t15.t25.t33.t24))
% 0.68/0.90  (step t15.t25.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t25.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t25.t32 t15.t25.t33))
% 0.68/0.90  (step t15.t25.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t36.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t15.t25.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t36.t3 t15.t25.t36.t4))
% 0.68/0.90  (step t15.t25.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t25.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t25.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t25.t36.t7.t2))
% 0.68/0.90  (step t15.t25.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t25.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t36.t6 t15.t25.t36.t7))
% 0.68/0.90  (step t15.t25.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t25.t36.t5 t15.t25.t36.t8))
% 0.68/0.90  (step t15.t25.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t25.t36.t9 t15.t25.t36.t10))
% 0.68/0.90  (step t15.t25.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t25.t36.t11 t15.t25.t36.t12))
% 0.68/0.90  (step t15.t25.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t25.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t25.t35 t15.t25.t36))
% 0.68/0.90  (step t15.t25.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t25.t34 t15.t25.t37))
% 0.68/0.90  (step t15.t25.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t25.t31 t15.t25.t38 a8))
% 0.68/0.90  (step t15.t25.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t25.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t25.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t42.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t25.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t25.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t25.t41 t15.t25.t42))
% 0.68/0.90  (step t15.t25.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t25.t40 t15.t25.t43 a6))
% 0.68/0.90  (step t15.t25.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t25.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t47.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t47.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t47.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t25.t47.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t47.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t25.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t25.t47.t5))
% 0.68/0.90  (step t15.t25.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t25.t47.t5))
% 0.68/0.90  (step t15.t25.t47.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t25.t47.t7 t15.t25.t47.t8))
% 0.68/0.90  (step t15.t25.t47.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t25.t47.t6 t15.t25.t47.t9))
% 0.68/0.90  (step t15.t25.t47.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t47.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t25.t47.t10 t15.t25.t47.t11))
% 0.68/0.90  (step t15.t25.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t47.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t25.t47.t12 t15.t25.t47.t13))
% 0.68/0.90  (step t15.t25.t47 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t25.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t25.t46 t15.t25.t47))
% 0.68/0.90  (step t15.t25.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t50.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t50.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t50.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)
% 0.68/0.90  (step t15.t25.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t50.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t25.t50.t4 t15.t25.t50.t5))
% 0.68/0.90  (step t15.t25.t50.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t25.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t25.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t25.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t25.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t25.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t25.t50.t8.t3 t15.t25.t50.t8.t4))
% 0.68/0.90  (step t15.t25.t50.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t15.t25.t50.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 (t15.t25.t50.t7 t15.t25.t50.t8))
% 0.68/0.90  (step t15.t25.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t25.t50.t6 t15.t25.t50.t9))
% 0.68/0.90  (step t15.t25.t50.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t25.t50.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t25.t50.t10 t15.t25.t50.t11))
% 0.68/0.90  (step t15.t25.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t50.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t25.t50.t12 t15.t25.t50.t13))
% 0.68/0.90  (step t15.t25.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t50.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t25.t50.t14 t15.t25.t50.t15))
% 0.68/0.90  (step t15.t25.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t25.t50.t16 t15.t25.t50.t17))
% 0.68/0.90  (step t15.t25.t50 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t25.t51 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t25.t49 t15.t25.t50))
% 0.68/0.90  (step t15.t25.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t25.t48 t15.t25.t51))
% 0.68/0.90  (step t15.t25.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t25.t45 t15.t25.t52 a5))
% 0.68/0.90  (step t15.t25.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t25.t25 t15.t25.t30 t15.t25.t39 a7 t15.t25.t44 t15.t25.t53 a4 a3 a2))
% 0.68/0.90  (step t15.t25.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t25.t54))
% 0.68/0.90  (step t15.t25.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t25.t54))
% 0.68/0.90  (step t15.t25.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t25.t55 t15.t25.t56))
% 0.68/0.90  (step t15.t25.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t25.t24 t15.t25.t57))
% 0.68/0.90  (step t15.t25.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t25.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t25.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t25.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t15.t25.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t15.t25.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t25.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t15.t25.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t25.t61.t2.t2 t15.t25.t61.t2.t3))
% 0.68/0.90  (step t15.t25.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t25.t61.t2.t4 t15.t25.t61.t2.t5))
% 0.68/0.90  (step t15.t25.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t15.t25.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t25.t61.t2 t15.t25.t61.t3))
% 0.68/0.90  (step t15.t25.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t25.t61.t4))
% 0.68/0.90  (step t15.t25.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t25.t61.t5 t15.t25.t61.t6))
% 0.68/0.90  (step t15.t25.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t15.t25.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t15.t25.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t61 t15.t25.t62))
% 0.68/0.90  (step t15.t25.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t25.t60 t15.t25.t63))
% 0.68/0.90  (step t15.t25.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t25.t59 t15.t25.t64))
% 0.68/0.90  (step t15.t25.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t25.t58 t15.t25.t65))
% 0.68/0.90  (step t15.t25.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t25.t23 t15.t25.t66 a10))
% 0.68/0.90  (step t15.t25.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t25.t4 t15.t25.t13 t15.t25.t22 t15.t25.t67 t15.t25.t30 t15.t25.t39 a7 t15.t25.t44 t15.t25.t53 a4 a3 a2))
% 0.68/0.90  (step t15.t25.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t15.t25.t68))
% 0.68/0.90  (step t15.t25.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t25.t68))
% 0.68/0.90  (step t15.t25.t71 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t25.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t25.t70 t15.t25.t71))
% 0.68/0.90  (step t15.t25.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t25.t69 t15.t25.t72))
% 0.68/0.90  (step t15.t25.t74 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t25.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t25.t70 t15.t25.t74))
% 0.68/0.90  (step t15.t25.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t25.t73 t15.t25.t75))
% 0.68/0.90  (step t15.t25.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t25.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t25.t76 t15.t25.t77))
% 0.68/0.90  (step t15.t25 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t26 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t24 t15.t25))
% 0.68/0.90  (step t15.t27 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t28 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t28.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t28.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t28.t4 (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)
% 0.68/0.90  (step t15.t28.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t28.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t28.t4 t15.t28.t5))
% 0.68/0.90  (step t15.t28.t7 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t28.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t28.t8.t1 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t28.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t28.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t28.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t15.t28.t8.t3))
% 0.68/0.90  (step t15.t28.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.68/0.90  (step t15.t28.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t15.t28.t8.t4 t15.t28.t8.t5))
% 0.68/0.90  (step t15.t28.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t28.t9 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t28.t7 t15.t28.t8))
% 0.68/0.90  (step t15.t28.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t15.t28.t6 t15.t28.t9))
% 0.68/0.90  (step t15.t28.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t28.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t28.t10 t15.t28.t11))
% 0.68/0.90  (step t15.t28.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t28.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t28.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t28.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.68/0.90  (step t15.t28.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t28.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t15.t28.t14.t2 t15.t28.t14.t3))
% 0.68/0.90  (step t15.t28.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.90  (step t15.t28.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t28.t13 t15.t28.t14))
% 0.68/0.90  (step t15.t28.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t15.t28.t12 t15.t28.t15))
% 0.68/0.90  (step t15.t28.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t28.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t28.t16 t15.t28.t17))
% 0.68/0.90  (step t15.t28.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t28.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t28.t18 t15.t28.t19))
% 0.68/0.90  (step t15.t28 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.90  (step t15.t29 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t27 t15.t28))
% 0.68/0.90  (step t15.t30 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t26 t15.t29))
% 0.68/0.90  (step t15.t31 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t23 t15.t30 a13))
% 0.68/0.90  (step t15.t32 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t33 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t34.t7.t9 t15.t34.t7.t10))
% 0.68/0.90  (step t15.t34.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t34.t7.t8 t15.t34.t7.t11 a9))
% 0.68/0.90  (step t15.t34.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t34.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t34.t7.t15.t5 t15.t34.t7.t15.t6))
% 0.68/0.90  (step t15.t34.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t34.t7.t15.t4 t15.t34.t7.t15.t7 a6))
% 0.68/0.90  (step t15.t34.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t34.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t34.t7.t15.t11.t5))
% 0.68/0.90  (step t15.t34.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t34.t7.t15.t11.t5))
% 0.68/0.90  (step t15.t34.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t34.t7.t15.t11.t7 t15.t34.t7.t15.t11.t8))
% 0.68/0.90  (step t15.t34.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t34.t7.t15.t11.t6 t15.t34.t7.t15.t11.t9))
% 0.68/0.90  (step t15.t34.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t34.t7.t15.t11.t10 t15.t34.t7.t15.t11.t11))
% 0.68/0.90  (step t15.t34.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t34.t7.t15.t11.t12 t15.t34.t7.t15.t11.t13))
% 0.68/0.90  (step t15.t34.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t34.t7.t15.t10 t15.t34.t7.t15.t11))
% 0.68/0.90  (step t15.t34.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t34.t7.t15.t14.t4 t15.t34.t7.t15.t14.t5))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t15.t34.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t34.t7.t15.t14.t8.t3 t15.t34.t7.t15.t14.t8.t4))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t34.t7.t15.t14.t7 t15.t34.t7.t15.t14.t8))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t34.t7.t15.t14.t6 t15.t34.t7.t15.t14.t9))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t34.t7.t15.t14.t10 t15.t34.t7.t15.t14.t11))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t15.t14.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 (t15.t34.t7.t15.t14.t12 t15.t34.t7.t15.t14.t13))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t14.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 (t15.t34.t7.t15.t14.t14 t15.t34.t7.t15.t14.t15))
% 0.68/0.90  (step t15.t34.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t34.t7.t15.t14.t16 t15.t34.t7.t15.t14.t17))
% 0.68/0.90  (step t15.t34.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t34.t7.t15.t13 t15.t34.t7.t15.t14))
% 0.68/0.90  (step t15.t34.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t34.t7.t15.t12 t15.t34.t7.t15.t15))
% 0.68/0.90  (step t15.t34.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t34.t7.t15.t9 t15.t34.t7.t15.t16 a5))
% 0.68/0.90  (step t15.t34.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t34.t7.t15.t3 a7 t15.t34.t7.t15.t8 t15.t34.t7.t15.t17 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t34.t7.t15.t18))
% 0.68/0.90  (step t15.t34.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t34.t7.t15.t18))
% 0.68/0.90  (step t15.t34.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t34.t7.t15.t20 t15.t34.t7.t15.t21))
% 0.68/0.90  (step t15.t34.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t34.t7.t15.t19 t15.t34.t7.t15.t22))
% 0.68/0.90  (step t15.t34.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t34.t7.t15.t23 t15.t34.t7.t15.t24))
% 0.68/0.90  (step t15.t34.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t34.t7.t14 t15.t34.t7.t15))
% 0.68/0.90  (step t15.t34.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t34.t7.t18.t3 t15.t34.t7.t18.t4))
% 0.68/0.90  (step t15.t34.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t34.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t34.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t34.t7.t18.t7.t2))
% 0.68/0.90  (step t15.t34.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t34.t7.t18.t6 t15.t34.t7.t18.t7))
% 0.68/0.90  (step t15.t34.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t34.t7.t18.t5 t15.t34.t7.t18.t8))
% 0.68/0.90  (step t15.t34.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t34.t7.t18.t9 t15.t34.t7.t18.t10))
% 0.68/0.90  (step t15.t34.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t34.t7.t18.t11 t15.t34.t7.t18.t12))
% 0.68/0.90  (step t15.t34.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t34.t7.t17 t15.t34.t7.t18))
% 0.68/0.90  (step t15.t34.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t34.t7.t16 t15.t34.t7.t19))
% 0.68/0.90  (step t15.t34.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t34.t7.t13 t15.t34.t7.t20 a8))
% 0.68/0.90  (step t15.t34.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t34.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t34.t7.t23 t15.t34.t7.t24))
% 0.68/0.90  (step t15.t34.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t34.t7.t22 t15.t34.t7.t25 a6))
% 0.68/0.90  (step t15.t34.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t34.t7.t29.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t34.t7.t29.t5))
% 0.68/0.90  (step t15.t34.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t34.t7.t29.t5))
% 0.68/0.90  (step t15.t34.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t34.t7.t29.t7 t15.t34.t7.t29.t8))
% 0.68/0.90  (step t15.t34.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t34.t7.t29.t6 t15.t34.t7.t29.t9))
% 0.68/0.90  (step t15.t34.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t34.t7.t29.t10 t15.t34.t7.t29.t11))
% 0.68/0.90  (step t15.t34.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t34.t7.t29.t12 t15.t34.t7.t29.t13))
% 0.68/0.90  (step t15.t34.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t34.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t34.t7.t28 t15.t34.t7.t29))
% 0.68/0.90  (step t15.t34.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.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)
% 0.68/0.90  (step t15.t34.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t34.t7.t32.t4 t15.t34.t7.t32.t5))
% 0.68/0.90  (step t15.t34.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t34.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t34.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t34.t7.t32.t8.t3 t15.t34.t7.t32.t8.t4))
% 0.68/0.90  (step t15.t34.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t15.t34.t7.t32.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 (t15.t34.t7.t32.t7 t15.t34.t7.t32.t8))
% 0.68/0.90  (step t15.t34.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t34.t7.t32.t6 t15.t34.t7.t32.t9))
% 0.68/0.90  (step t15.t34.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t34.t7.t32.t10 t15.t34.t7.t32.t11))
% 0.68/0.90  (step t15.t34.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t34.t7.t32.t12 t15.t34.t7.t32.t13))
% 0.68/0.90  (step t15.t34.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t34.t7.t32.t14 t15.t34.t7.t32.t15))
% 0.68/0.90  (step t15.t34.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t34.t7.t32.t16 t15.t34.t7.t32.t17))
% 0.68/0.90  (step t15.t34.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t34.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t34.t7.t31 t15.t34.t7.t32))
% 0.68/0.90  (step t15.t34.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t34.t7.t30 t15.t34.t7.t33))
% 0.68/0.90  (step t15.t34.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t34.t7.t27 t15.t34.t7.t34 a5))
% 0.68/0.90  (step t15.t34.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t34.t7.t7 t15.t34.t7.t12 t15.t34.t7.t21 a7 t15.t34.t7.t26 t15.t34.t7.t35 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t34.t7.t36))
% 0.68/0.90  (step t15.t34.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t34.t7.t36))
% 0.68/0.90  (step t15.t34.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t34.t7.t37 t15.t34.t7.t38))
% 0.68/0.90  (step t15.t34.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t34.t7.t6 t15.t34.t7.t39))
% 0.68/0.90  (step t15.t34.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t34.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t15.t34.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t34.t7.t43.t2.t2 t15.t34.t7.t43.t2.t3))
% 0.68/0.90  (step t15.t34.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t34.t7.t43.t2.t4 t15.t34.t7.t43.t2.t5))
% 0.68/0.90  (step t15.t34.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t34.t7.t43.t2 t15.t34.t7.t43.t3))
% 0.68/0.90  (step t15.t34.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t34.t7.t43.t4))
% 0.68/0.90  (step t15.t34.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t34.t7.t43.t5 t15.t34.t7.t43.t6))
% 0.68/0.90  (step t15.t34.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t15.t34.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t34.t7.t43 t15.t34.t7.t44))
% 0.68/0.90  (step t15.t34.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t34.t7.t42 t15.t34.t7.t45))
% 0.68/0.90  (step t15.t34.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t34.t7.t41 t15.t34.t7.t46))
% 0.68/0.90  (step t15.t34.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t34.t7.t40 t15.t34.t7.t47))
% 0.68/0.90  (step t15.t34.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t34.t7.t5 t15.t34.t7.t48 a10))
% 0.68/0.90  (step t15.t34.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t34.t7.t4 t15.t34.t7.t49 t15.t34.t7.t12 t15.t34.t7.t21 a7 t15.t34.t7.t26 t15.t34.t7.t35 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t34.t7.t50))
% 0.68/0.90  (step t15.t34.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t34.t7.t51 t15.t34.t7.t52))
% 0.68/0.90  (step t15.t34.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t34.t7.t53 t15.t34.t7.t54))
% 0.68/0.90  (step t15.t34.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t34.t7.t55 t15.t34.t7.t56))
% 0.68/0.90  (step t15.t34.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t34.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t34.t6 t15.t34.t7))
% 0.68/0.90  (step t15.t34.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t34.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t34.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t34.t10.t4 t15.t34.t10.t5))
% 0.68/0.90  (step t15.t34.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t34.t10.t6 t15.t34.t10.t7))
% 0.68/0.90  (step t15.t34.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t34.t10.t8 t15.t34.t10.t9))
% 0.68/0.90  (step t15.t34.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t34.t10.t10 t15.t34.t10.t11))
% 0.68/0.90  (step t15.t34.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t34.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t34.t9 t15.t34.t10))
% 0.68/0.90  (step t15.t34.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t34.t8 t15.t34.t11))
% 0.68/0.90  (step t15.t34.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t34.t5 t15.t34.t12 a11))
% 0.68/0.90  (step t15.t34.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t34.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t15.t34.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t34.t18 t15.t34.t19))
% 0.68/0.90  (step t15.t34.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t34.t17 t15.t34.t20 a9))
% 0.68/0.90  (step t15.t34.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t34.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t34.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t34.t24.t5 t15.t34.t24.t6))
% 0.68/0.90  (step t15.t34.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t34.t24.t4 t15.t34.t24.t7 a6))
% 0.68/0.90  (step t15.t34.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t34.t24.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t34.t24.t11.t5))
% 0.68/0.90  (step t15.t34.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t34.t24.t11.t5))
% 0.68/0.90  (step t15.t34.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t34.t24.t11.t7 t15.t34.t24.t11.t8))
% 0.68/0.90  (step t15.t34.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t34.t24.t11.t6 t15.t34.t24.t11.t9))
% 0.68/0.90  (step t15.t34.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t34.t24.t11.t10 t15.t34.t24.t11.t11))
% 0.68/0.90  (step t15.t34.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t34.t24.t11.t12 t15.t34.t24.t11.t13))
% 0.68/0.90  (step t15.t34.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t34.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t34.t24.t10 t15.t34.t24.t11))
% 0.68/0.90  (step t15.t34.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.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)
% 0.68/0.90  (step t15.t34.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t34.t24.t14.t4 t15.t34.t24.t14.t5))
% 0.68/0.90  (step t15.t34.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t34.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t34.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t34.t24.t14.t8.t3 t15.t34.t24.t14.t8.t4))
% 0.68/0.90  (step t15.t34.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t15.t34.t24.t14.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 (t15.t34.t24.t14.t7 t15.t34.t24.t14.t8))
% 0.68/0.90  (step t15.t34.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t34.t24.t14.t6 t15.t34.t24.t14.t9))
% 0.68/0.90  (step t15.t34.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t34.t24.t14.t10 t15.t34.t24.t14.t11))
% 0.68/0.90  (step t15.t34.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t34.t24.t14.t12 t15.t34.t24.t14.t13))
% 0.68/0.90  (step t15.t34.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t34.t24.t14.t14 t15.t34.t24.t14.t15))
% 0.68/0.90  (step t15.t34.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t34.t24.t14.t16 t15.t34.t24.t14.t17))
% 0.68/0.90  (step t15.t34.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t34.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t34.t24.t13 t15.t34.t24.t14))
% 0.68/0.90  (step t15.t34.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t34.t24.t12 t15.t34.t24.t15))
% 0.68/0.90  (step t15.t34.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t34.t24.t9 t15.t34.t24.t16 a5))
% 0.68/0.90  (step t15.t34.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t34.t24.t3 a7 t15.t34.t24.t8 t15.t34.t24.t17 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t34.t24.t18))
% 0.68/0.90  (step t15.t34.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t34.t24.t18))
% 0.68/0.90  (step t15.t34.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t34.t24.t20 t15.t34.t24.t21))
% 0.68/0.90  (step t15.t34.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t34.t24.t19 t15.t34.t24.t22))
% 0.68/0.90  (step t15.t34.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t34.t24.t23 t15.t34.t24.t24))
% 0.68/0.90  (step t15.t34.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t34.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t34.t23 t15.t34.t24))
% 0.68/0.90  (step t15.t34.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t15.t34.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t34.t27.t3 t15.t34.t27.t4))
% 0.68/0.90  (step t15.t34.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t34.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t34.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t34.t27.t7.t2))
% 0.68/0.90  (step t15.t34.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t34.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t34.t27.t6 t15.t34.t27.t7))
% 0.68/0.90  (step t15.t34.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t34.t27.t5 t15.t34.t27.t8))
% 0.68/0.90  (step t15.t34.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t34.t27.t9 t15.t34.t27.t10))
% 0.68/0.90  (step t15.t34.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t34.t27.t11 t15.t34.t27.t12))
% 0.68/0.90  (step t15.t34.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t34.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t34.t26 t15.t34.t27))
% 0.68/0.90  (step t15.t34.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t34.t25 t15.t34.t28))
% 0.68/0.90  (step t15.t34.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t34.t22 t15.t34.t29 a8))
% 0.68/0.90  (step t15.t34.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t34.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t34.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t34.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t34.t32 t15.t34.t33))
% 0.68/0.90  (step t15.t34.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t34.t31 t15.t34.t34 a6))
% 0.68/0.90  (step t15.t34.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t34.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t38.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t34.t38.t5 (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)))))) :rule resolution :premises (t15.t34.t38.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t34.t38.t5))
% 0.68/0.90  (step t15.t34.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t34.t38.t5))
% 0.68/0.90  (step t15.t34.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t34.t38.t7 t15.t34.t38.t8))
% 0.68/0.90  (step t15.t34.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t34.t38.t6 t15.t34.t38.t9))
% 0.68/0.90  (step t15.t34.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t34.t38.t10 t15.t34.t38.t11))
% 0.68/0.90  (step t15.t34.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t34.t38.t12 t15.t34.t38.t13))
% 0.68/0.90  (step t15.t34.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t34.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t34.t37 t15.t34.t38))
% 0.68/0.90  (step t15.t34.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t15.t34.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t34.t41.t4 t15.t34.t41.t5))
% 0.68/0.90  (step t15.t34.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t15.t34.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t34.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t34.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t34.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t34.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t34.t41.t8.t3 t15.t34.t41.t8.t4))
% 0.68/0.90  (step t15.t34.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t15.t34.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t34.t41.t7 t15.t34.t41.t8))
% 0.68/0.90  (step t15.t34.t41.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t34.t41.t6 t15.t34.t41.t9))
% 0.68/0.90  (step t15.t34.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t34.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t34.t41.t10 t15.t34.t41.t11))
% 0.68/0.90  (step t15.t34.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t41.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 (t15.t34.t41.t12 t15.t34.t41.t13))
% 0.68/0.90  (step t15.t34.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t41.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 (t15.t34.t41.t14 t15.t34.t41.t15))
% 0.68/0.90  (step t15.t34.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t34.t41.t16 t15.t34.t41.t17))
% 0.68/0.90  (step t15.t34.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t34.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t34.t40 t15.t34.t41))
% 0.68/0.90  (step t15.t34.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t34.t39 t15.t34.t42))
% 0.68/0.90  (step t15.t34.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t34.t36 t15.t34.t43 a5))
% 0.68/0.90  (step t15.t34.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t34.t16 t15.t34.t21 t15.t34.t30 a7 t15.t34.t35 t15.t34.t44 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t34.t45))
% 0.68/0.90  (step t15.t34.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t34.t45))
% 0.68/0.90  (step t15.t34.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t34.t46 t15.t34.t47))
% 0.68/0.90  (step t15.t34.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t34.t15 t15.t34.t48))
% 0.68/0.90  (step t15.t34.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t34.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t34.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t34.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t15.t34.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t15.t34.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t34.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t15.t34.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t34.t52.t2.t2 t15.t34.t52.t2.t3))
% 0.68/0.90  (step t15.t34.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t34.t52.t2.t4 t15.t34.t52.t2.t5))
% 0.68/0.90  (step t15.t34.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t15.t34.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t34.t52.t2 t15.t34.t52.t3))
% 0.68/0.90  (step t15.t34.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t34.t52.t4))
% 0.68/0.90  (step t15.t34.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t34.t52.t5 t15.t34.t52.t6))
% 0.68/0.90  (step t15.t34.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t15.t34.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t15.t34.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t34.t52 t15.t34.t53))
% 0.68/0.90  (step t15.t34.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t34.t51 t15.t34.t54))
% 0.68/0.90  (step t15.t34.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t34.t50 t15.t34.t55))
% 0.68/0.90  (step t15.t34.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t34.t49 t15.t34.t56))
% 0.68/0.90  (step t15.t34.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t34.t14 t15.t34.t57 a10))
% 0.68/0.90  (step t15.t34.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t34.t4 t15.t34.t13 t15.t34.t58 t15.t34.t21 t15.t34.t30 a7 t15.t34.t35 t15.t34.t44 a4 a3 a2))
% 0.68/0.90  (step t15.t34.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t34.t59))
% 0.68/0.90  (step t15.t34.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t34.t59))
% 0.68/0.90  (step t15.t34.t62 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t34.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t34.t61 t15.t34.t62))
% 0.68/0.90  (step t15.t34.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t34.t60 t15.t34.t63))
% 0.68/0.90  (step t15.t34.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t34.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t15.t34.t61 t15.t34.t65))
% 0.68/0.90  (step t15.t34.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t15.t34.t64 t15.t34.t66))
% 0.68/0.90  (step t15.t34.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t34.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t15.t34.t67 t15.t34.t68))
% 0.68/0.90  (step t15.t34 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t35 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t15.t33 t15.t34))
% 0.68/0.90  (step t15.t36 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.90  (anchor :step t15.t37 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t37.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t37.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t37.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)
% 0.68/0.90  (step t15.t37.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t37.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t37.t4 t15.t37.t5))
% 0.68/0.90  (step t15.t37.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t37.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t37.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t37.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t37.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t37.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t37.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t15.t37.t8.t3 t15.t37.t8.t4))
% 0.68/0.90  (step t15.t37.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t15.t37.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t37.t7 t15.t37.t8))
% 0.68/0.90  (step t15.t37.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t15.t37.t6 t15.t37.t9))
% 0.68/0.90  (step t15.t37.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t37.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t15.t37.t10 t15.t37.t11))
% 0.68/0.90  (step t15.t37.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t37.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t37.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t37.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.90  (step t15.t37.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t37.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t15.t37.t14.t2 t15.t37.t14.t3))
% 0.68/0.90  (step t15.t37.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.90  (step t15.t37.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t37.t13 t15.t37.t14))
% 0.68/0.90  (step t15.t37.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t15.t37.t12 t15.t37.t15))
% 0.68/0.90  (step t15.t37.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t37.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t15.t37.t16 t15.t37.t17))
% 0.68/0.90  (step t15.t37.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t37.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t15.t37.t18 t15.t37.t19))
% 0.68/0.90  (step t15.t37 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.90  (step t15.t38 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t15.t36 t15.t37))
% 0.68/0.90  (step t15.t39 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t15.t35 t15.t38))
% 0.68/0.90  (step t15.t40 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t15.t32 t15.t39 a12))
% 0.68/0.90  (step t15.t41 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t42 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t43.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t43.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t43.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t43.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t43.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t43.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t43.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t15.t43.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t43.t9 t15.t43.t10))
% 0.68/0.90  (step t15.t43.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t43.t8 t15.t43.t11 a9))
% 0.68/0.90  (step t15.t43.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t43.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t43.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t43.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t43.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t43.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t43.t15.t5 t15.t43.t15.t6))
% 0.68/0.90  (step t15.t43.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t43.t15.t4 t15.t43.t15.t7 a6))
% 0.68/0.90  (step t15.t43.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t43.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t43.t15.t11.t5 (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)))))) :rule resolution :premises (t15.t43.t15.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t43.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t43.t15.t11.t5))
% 0.68/0.90  (step t15.t43.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t43.t15.t11.t5))
% 0.68/0.90  (step t15.t43.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t43.t15.t11.t7 t15.t43.t15.t11.t8))
% 0.68/0.90  (step t15.t43.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t43.t15.t11.t6 t15.t43.t15.t11.t9))
% 0.68/0.90  (step t15.t43.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t43.t15.t11.t10 t15.t43.t15.t11.t11))
% 0.68/0.90  (step t15.t43.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t43.t15.t11.t12 t15.t43.t15.t11.t13))
% 0.68/0.90  (step t15.t43.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t43.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t43.t15.t10 t15.t43.t15.t11))
% 0.68/0.90  (step t15.t43.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t43.t15.t14.t4 t15.t43.t15.t14.t5))
% 0.68/0.90  (step t15.t43.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t15.t43.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t43.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t43.t15.t14.t8.t3 t15.t43.t15.t14.t8.t4))
% 0.68/0.90  (step t15.t43.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t15.t43.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t43.t15.t14.t7 t15.t43.t15.t14.t8))
% 0.68/0.90  (step t15.t43.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t43.t15.t14.t6 t15.t43.t15.t14.t9))
% 0.68/0.90  (step t15.t43.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t43.t15.t14.t10 t15.t43.t15.t14.t11))
% 0.68/0.90  (step t15.t43.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t15.t14.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 (t15.t43.t15.t14.t12 t15.t43.t15.t14.t13))
% 0.68/0.90  (step t15.t43.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t14.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 (t15.t43.t15.t14.t14 t15.t43.t15.t14.t15))
% 0.68/0.90  (step t15.t43.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t43.t15.t14.t16 t15.t43.t15.t14.t17))
% 0.68/0.90  (step t15.t43.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t43.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t43.t15.t13 t15.t43.t15.t14))
% 0.68/0.90  (step t15.t43.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t43.t15.t12 t15.t43.t15.t15))
% 0.68/0.90  (step t15.t43.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t43.t15.t9 t15.t43.t15.t16 a5))
% 0.68/0.90  (step t15.t43.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t43.t15.t3 a7 t15.t43.t15.t8 t15.t43.t15.t17 a4 a3 a2))
% 0.68/0.90  (step t15.t43.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t43.t15.t18))
% 0.68/0.90  (step t15.t43.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t43.t15.t18))
% 0.68/0.90  (step t15.t43.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t43.t15.t20 t15.t43.t15.t21))
% 0.68/0.90  (step t15.t43.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t43.t15.t19 t15.t43.t15.t22))
% 0.68/0.90  (step t15.t43.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t43.t15.t23 t15.t43.t15.t24))
% 0.68/0.90  (step t15.t43.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t43.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t43.t14 t15.t43.t15))
% 0.68/0.90  (step t15.t43.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t43.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t15.t43.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t43.t18.t3 t15.t43.t18.t4))
% 0.68/0.90  (step t15.t43.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t43.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t43.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t43.t18.t7.t2))
% 0.68/0.90  (step t15.t43.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t43.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t43.t18.t6 t15.t43.t18.t7))
% 0.68/0.90  (step t15.t43.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t43.t18.t5 t15.t43.t18.t8))
% 0.68/0.90  (step t15.t43.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t43.t18.t9 t15.t43.t18.t10))
% 0.68/0.90  (step t15.t43.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t43.t18.t11 t15.t43.t18.t12))
% 0.68/0.90  (step t15.t43.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t43.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t43.t17 t15.t43.t18))
% 0.68/0.90  (step t15.t43.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t43.t16 t15.t43.t19))
% 0.68/0.90  (step t15.t43.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t43.t13 t15.t43.t20 a8))
% 0.68/0.90  (step t15.t43.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t43.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t43.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t43.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t43.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t43.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t43.t23 t15.t43.t24))
% 0.68/0.90  (step t15.t43.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t43.t22 t15.t43.t25 a6))
% 0.68/0.90  (step t15.t43.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t43.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t43.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t43.t29.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t43.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t43.t29.t5))
% 0.68/0.90  (step t15.t43.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t43.t29.t5))
% 0.68/0.90  (step t15.t43.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t43.t29.t7 t15.t43.t29.t8))
% 0.68/0.90  (step t15.t43.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t43.t29.t6 t15.t43.t29.t9))
% 0.68/0.90  (step t15.t43.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t43.t29.t10 t15.t43.t29.t11))
% 0.68/0.90  (step t15.t43.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t43.t29.t12 t15.t43.t29.t13))
% 0.68/0.90  (step t15.t43.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t43.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t43.t28 t15.t43.t29))
% 0.68/0.90  (step t15.t43.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t32.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)
% 0.68/0.90  (step t15.t43.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t43.t32.t4 t15.t43.t32.t5))
% 0.68/0.90  (step t15.t43.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t43.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t43.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t43.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t43.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t43.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t43.t32.t8.t3 t15.t43.t32.t8.t4))
% 0.68/0.90  (step t15.t43.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t15.t43.t32.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 (t15.t43.t32.t7 t15.t43.t32.t8))
% 0.68/0.90  (step t15.t43.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t43.t32.t6 t15.t43.t32.t9))
% 0.68/0.90  (step t15.t43.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t43.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t43.t32.t10 t15.t43.t32.t11))
% 0.68/0.90  (step t15.t43.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t43.t32.t12 t15.t43.t32.t13))
% 0.68/0.90  (step t15.t43.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t43.t32.t14 t15.t43.t32.t15))
% 0.68/0.90  (step t15.t43.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t43.t32.t16 t15.t43.t32.t17))
% 0.68/0.90  (step t15.t43.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t43.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t43.t31 t15.t43.t32))
% 0.68/0.90  (step t15.t43.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t43.t30 t15.t43.t33))
% 0.68/0.90  (step t15.t43.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t43.t27 t15.t43.t34 a5))
% 0.68/0.90  (step t15.t43.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t43.t7 t15.t43.t12 t15.t43.t21 a7 t15.t43.t26 t15.t43.t35 a4 a3 a2))
% 0.68/0.90  (step t15.t43.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t43.t36))
% 0.68/0.90  (step t15.t43.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t43.t36))
% 0.68/0.90  (step t15.t43.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t43.t37 t15.t43.t38))
% 0.68/0.90  (step t15.t43.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t43.t6 t15.t43.t39))
% 0.68/0.90  (step t15.t43.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t43.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t43.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t43.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t15.t43.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t15.t43.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t43.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t15.t43.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t43.t43.t2.t2 t15.t43.t43.t2.t3))
% 0.68/0.90  (step t15.t43.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t43.t43.t2.t4 t15.t43.t43.t2.t5))
% 0.68/0.90  (step t15.t43.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t15.t43.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t43.t43.t2 t15.t43.t43.t3))
% 0.68/0.90  (step t15.t43.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t43.t43.t4))
% 0.68/0.90  (step t15.t43.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t43.t43.t5 t15.t43.t43.t6))
% 0.68/0.90  (step t15.t43.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t15.t43.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t15.t43.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t43.t43 t15.t43.t44))
% 0.68/0.90  (step t15.t43.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t43.t42 t15.t43.t45))
% 0.68/0.90  (step t15.t43.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t43.t41 t15.t43.t46))
% 0.68/0.90  (step t15.t43.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t43.t40 t15.t43.t47))
% 0.68/0.90  (step t15.t43.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t43.t5 t15.t43.t48 a10))
% 0.68/0.90  (step t15.t43.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t43.t4 t15.t43.t49 t15.t43.t12 t15.t43.t21 a7 t15.t43.t26 t15.t43.t35 a4 a3 a2))
% 0.68/0.90  (step t15.t43.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t15.t43.t50))
% 0.68/0.90  (step t15.t43.t52 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t43.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t15.t43.t51 t15.t43.t52))
% 0.68/0.90  (step t15.t43.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t43.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t15.t43.t53 t15.t43.t54))
% 0.68/0.90  (step t15.t43.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t43.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t15.t43.t55 t15.t43.t56))
% 0.68/0.90  (step t15.t43 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t44 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t15.t42 t15.t43))
% 0.68/0.90  (step t15.t45 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t15.t46 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t46.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t46.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t46.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t46.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t46.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t46.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t15.t46.t4 t15.t46.t5))
% 0.68/0.90  (step t15.t46.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t46.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t15.t46.t6 t15.t46.t7))
% 0.68/0.90  (step t15.t46.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t46.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t15.t46.t8 t15.t46.t9))
% 0.68/0.90  (step t15.t46.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t46.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t15.t46.t10 t15.t46.t11))
% 0.68/0.90  (step t15.t46 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t47 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t15.t45 t15.t46))
% 0.68/0.90  (step t15.t48 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t15.t44 t15.t47))
% 0.68/0.90  (step t15.t49 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t15.t41 t15.t48 a11))
% 0.68/0.90  (step t15.t50 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t51 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t52 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t53 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t54 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t15.t55 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t15.t56 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t54 t15.t55))
% 0.68/0.90  (step t15.t57 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t15.t53 t15.t56 a9))
% 0.68/0.90  (step t15.t58 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t59 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t60 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t60.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t60.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t60.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t60.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t60.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t60.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t60.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t60.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t60.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t60.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t60.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t60.t5 t15.t60.t6))
% 0.68/0.90  (step t15.t60.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t60.t4 t15.t60.t7 a6))
% 0.68/0.90  (step t15.t60.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t60.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t60.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t60.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t60.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t60.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t60.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t15.t60.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t60.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t60.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t60.t11.t5))
% 0.68/0.90  (step t15.t60.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t60.t11.t5))
% 0.68/0.90  (step t15.t60.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t60.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t60.t11.t7 t15.t60.t11.t8))
% 0.68/0.90  (step t15.t60.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t15.t60.t11.t6 t15.t60.t11.t9))
% 0.68/0.90  (step t15.t60.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t60.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t15.t60.t11.t10 t15.t60.t11.t11))
% 0.68/0.90  (step t15.t60.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t60.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t15.t60.t11.t12 t15.t60.t11.t13))
% 0.68/0.90  (step t15.t60.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t60.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t15.t60.t10 t15.t60.t11))
% 0.68/0.90  (step t15.t60.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t60.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t60.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t60.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t60.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t60.t14.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)
% 0.68/0.90  (step t15.t60.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t60.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t15.t60.t14.t4 t15.t60.t14.t5))
% 0.68/0.90  (step t15.t60.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t60.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t60.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t60.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t60.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t60.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t60.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t60.t14.t8.t3 t15.t60.t14.t8.t4))
% 0.68/0.90  (step t15.t60.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t15.t60.t14.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 (t15.t60.t14.t7 t15.t60.t14.t8))
% 0.68/0.90  (step t15.t60.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t60.t14.t6 t15.t60.t14.t9))
% 0.68/0.90  (step t15.t60.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t60.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t15.t60.t14.t10 t15.t60.t14.t11))
% 0.68/0.90  (step t15.t60.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t60.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t15.t60.t14.t12 t15.t60.t14.t13))
% 0.68/0.90  (step t15.t60.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t60.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t15.t60.t14.t14 t15.t60.t14.t15))
% 0.68/0.90  (step t15.t60.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t60.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t15.t60.t14.t16 t15.t60.t14.t17))
% 0.68/0.90  (step t15.t60.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t15.t60.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t60.t13 t15.t60.t14))
% 0.68/0.90  (step t15.t60.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t60.t12 t15.t60.t15))
% 0.68/0.90  (step t15.t60.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t60.t9 t15.t60.t16 a5))
% 0.68/0.90  (step t15.t60.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t15.t60.t3 a7 t15.t60.t8 t15.t60.t17 a4 a3 a2))
% 0.68/0.90  (step t15.t60.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t60.t18))
% 0.68/0.90  (step t15.t60.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t15.t60.t18))
% 0.68/0.90  (step t15.t60.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t60.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t15.t60.t20 t15.t60.t21))
% 0.68/0.90  (step t15.t60.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t15.t60.t19 t15.t60.t22))
% 0.68/0.90  (step t15.t60.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t60.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t15.t60.t23 t15.t60.t24))
% 0.68/0.90  (step t15.t60 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t61 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t15.t59 t15.t60))
% 0.68/0.90  (step t15.t62 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t15.t63 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t63.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t63.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t63.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t15.t63.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t63.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t63.t3 t15.t63.t4))
% 0.68/0.90  (step t15.t63.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t63.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t63.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t63.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t63.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t15.t63.t7.t2))
% 0.68/0.90  (step t15.t63.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t63.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t63.t6 t15.t63.t7))
% 0.68/0.90  (step t15.t63.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t15.t63.t5 t15.t63.t8))
% 0.68/0.90  (step t15.t63.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t63.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t15.t63.t9 t15.t63.t10))
% 0.68/0.90  (step t15.t63.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t15.t63.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t15.t63.t11 t15.t63.t12))
% 0.68/0.90  (step t15.t63 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t15.t64 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t15.t62 t15.t63))
% 0.68/0.90  (step t15.t65 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t15.t61 t15.t64))
% 0.68/0.90  (step t15.t66 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t15.t58 t15.t65 a8))
% 0.68/0.90  (step t15.t67 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t68 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t15.t69 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t15.t69.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t69.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t15.t69.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t15.t69 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t15.t70 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t15.t68 t15.t69))
% 0.68/0.90  (step t15.t71 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t15.t67 t15.t70 a6))
% 0.68/0.90  (step t15.t72 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t15.t73 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t74 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t74.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t74.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t74.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t74.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t15.t74.t5 (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)))))) :rule resolution :premises (t15.t74.t4 a4 a3 a2))
% 0.68/0.90  (step t15.t74.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t15.t74.t5))
% 0.68/0.90  (step t15.t74.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t15.t74.t5))
% 0.68/0.90  (step t15.t74.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t74.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t15.t74.t7 t15.t74.t8))
% 0.68/0.90  (step t15.t74.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t15.t74.t6 t15.t74.t9))
% 0.68/0.90  (step t15.t74.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t74.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t15.t74.t10 t15.t74.t11))
% 0.68/0.90  (step t15.t74.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t74.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t15.t74.t12 t15.t74.t13))
% 0.68/0.90  (step t15.t74 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t15.t75 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t15.t73 t15.t74))
% 0.68/0.90  (step t15.t76 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t15.t77 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t77.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t77.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t77.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t77.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t15.t77.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t77.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t15.t77.t4 t15.t77.t5))
% 0.68/0.90  (step t15.t77.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t15.t77.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t15.t77.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t77.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t15.t77.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t15.t77.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t15.t77.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t15.t77.t8.t3 t15.t77.t8.t4))
% 0.68/0.90  (step t15.t77.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t15.t77.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t15.t77.t7 t15.t77.t8))
% 0.68/0.90  (step t15.t77.t10 (cl (= (@ (lambda ((X (-> $$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 (t15.t77.t6 t15.t77.t9))
% 0.68/0.90  (step t15.t77.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t15.t77.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t15.t77.t10 t15.t77.t11))
% 0.68/0.90  (step t15.t77.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t15.t77.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 (t15.t77.t12 t15.t77.t13))
% 0.68/0.90  (step t15.t77.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t77.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 (t15.t77.t14 t15.t77.t15))
% 0.68/0.90  (step t15.t77.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t15.t77.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t15.t77.t16 t15.t77.t17))
% 0.68/0.90  (step t15.t77 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t15.t78 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t15.t76 t15.t77))
% 0.68/0.90  (step t15.t79 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t15.t75 t15.t78))
% 0.68/0.90  (step t15.t80 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t15.t72 t15.t79 a5))
% 0.68/0.90  (step t15.t81 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t52 t15.t57 t15.t66 a7 t15.t71 t15.t80 a4 a3 a2))
% 0.68/0.90  (step t15.t82 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t81))
% 0.68/0.90  (step t15.t83 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t15.t81))
% 0.68/0.90  (step t15.t84 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t15.t82 t15.t83))
% 0.68/0.90  (step t15.t85 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t15.t51 t15.t84))
% 0.68/0.90  (step t15.t86 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t15.t87 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t15.t88 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t15.t88.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t15.t88.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t15.t88.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t15.t88.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t15.t88.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t88.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t15.t88.t2.t2 t15.t88.t2.t3))
% 0.68/0.90  (step t15.t88.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t88.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t15.t88.t2.t4 t15.t88.t2.t5))
% 0.68/0.90  (step t15.t88.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t15.t88.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t15.t88.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t15.t88.t2 t15.t88.t3))
% 0.68/0.90  (step t15.t88.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t15.t88.t4))
% 0.68/0.90  (step t15.t88.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t15.t88.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t15.t88.t5 t15.t88.t6))
% 0.68/0.90  (step t15.t88 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t15.t89 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t15.t90 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t88 t15.t89))
% 0.68/0.90  (step t15.t91 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t15.t87 t15.t90))
% 0.68/0.90  (step t15.t92 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t15.t86 t15.t91))
% 0.68/0.90  (step t15.t93 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t15.t85 t15.t92))
% 0.68/0.90  (step t15.t94 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t15.t50 t15.t93 a10))
% 0.68/0.90  (step t15.t95 (cl (and (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t15.t4 t15.t13 t15.t22 t15.t31 t15.t40 t15.t49 t15.t94 t15.t57 t15.t66 a7 t15.t71 t15.t80 a4 a3 a2))
% 0.68/0.90  (step t15.t96 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t15.t95))
% 0.68/0.90  (step t15.t97 (cl (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule and :premises (t15.t95))
% 0.68/0.90  (step t15.t98 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t15.t99 (cl (= (@ tptp.iequiv P) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P))) :rule cong :premises (t15.t97 t15.t98))
% 0.68/0.90  (step t15.t100 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t15.t101 (cl (= (@ (@ tptp.iequiv P) Q) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q))) :rule cong :premises (t15.t99 t15.t100))
% 0.68/0.90  (step t15.t102 (cl (= (@ tptp.inot (@ (@ tptp.iequiv P) Q)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)))) :rule cong :premises (t15.t96 t15.t101))
% 0.68/0.90  (step t15.t103 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t15.t104 (cl (= (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) __flatten_var_0))) :rule cong :premises (t15.t102 t15.t103))
% 0.68/0.90  (step t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t16 (cl (= (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))) (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) __flatten_var_0))))) :rule cong :premises (t14 t15))
% 0.68/0.90  (step t17 (cl (= tptp.ixor tptp.ixor)) :rule refl)
% 0.68/0.90  (anchor :step t18 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t18.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t18.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t18.t4 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule refl)
% 0.68/0.90  (step t18.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule all_simplify)
% 0.68/0.90  (step t18.t6 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t18.t7 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Q))) :rule cong :premises (t18.t5 t18.t6))
% 0.68/0.90  (step t18.t8 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Q) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule all_simplify)
% 0.68/0.90  (step t18.t9 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t18.t7 t18.t8))
% 0.68/0.90  (step t18.t10 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))))) :rule cong :premises (t18.t4 t18.t9))
% 0.68/0.90  (step t18.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t18.t12 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t18.t12.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t18.t12.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t18.t12.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t18.t12.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t18.t12.t2.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Y) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.90  (step t18.t12.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y)))))))) :rule cong :premises (t18.t12.t2.t2 t18.t12.t2.t3))
% 0.68/0.90  (step t18.t12.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y))))))))) :rule bind)
% 0.68/0.90  (step t18.t12.t3 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y))))))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))))))) :rule all_simplify)
% 0.68/0.90  (step t18.t12.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))))) (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))) :rule all_simplify)
% 0.68/0.90  (step t18.t12.t5 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel Y) Y)) (@ P Y))))))) (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))) :rule trans :premises (t18.t12.t3 t18.t12.t4))
% 0.68/0.90  (step t18.t12.t6 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Y))) (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))) :rule trans :premises (t18.t12.t2 t18.t12.t5))
% 0.68/0.90  (step t18.t12.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Y)))) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))) :rule cong :premises (t18.t12.t6))
% 0.68/0.90  (step t18.t12 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) Y))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))))) :rule bind)
% 0.68/0.90  (step t18.t13 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (lambda ((__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))))) :rule trans :premises (t18.t11 t18.t12))
% 0.68/0.90  (step t18.t14 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) (lambda ((__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))))) :rule trans :premises (t18.t10 t18.t13))
% 0.68/0.90  (step t18.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t18.t16 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))) __flatten_var_0))) :rule cong :premises (t18.t14 t18.t15))
% 0.68/0.90  (step t18.t17 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))) __flatten_var_0) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))) :rule all_simplify)
% 0.68/0.90  (step t18.t18 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) __flatten_var_0) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))) :rule trans :premises (t18.t16 t18.t17))
% 0.68/0.90  (step t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))))) :rule bind)
% 0.68/0.90  (step t19 (cl (= (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) P) Q)) __flatten_var_0))) (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))))) :rule cong :premises (t17 t18))
% 0.68/0.90  (step t20 (cl (= (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))) (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))))) :rule trans :premises (t16 t19))
% 0.68/0.90  (step t21 (cl (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y)))))))) :rule resolution :premises (t13 t20 a16))
% 0.68/0.90  (step t22 (cl (not (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))))) (not (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0)))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule equiv_pos2)
% 0.68/0.90  (step t23 (cl (= tptp.iequiv tptp.iequiv)) :rule refl)
% 0.68/0.90  (anchor :step t24 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t4 (cl (and (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t5 (cl (not (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t6 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t4 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t5 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t6 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t7.t7.t9 t24.t7.t7.t7.t7.t10))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t7.t7.t7.t8 t24.t7.t7.t7.t7.t11 a9))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t5 t24.t7.t7.t7.t7.t15.t6))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t7.t7.t15.t4 t24.t7.t7.t7.t7.t15.t7 a6))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t7.t7.t15.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t7.t7.t15.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t11.t7 t24.t7.t7.t7.t7.t15.t11.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t11.t6 t24.t7.t7.t7.t7.t15.t11.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t7.t15.t11.t10 t24.t7.t7.t7.t7.t15.t11.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t11.t12 t24.t7.t7.t7.t7.t15.t11.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t10 t24.t7.t7.t7.t7.t15.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.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)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t7.t15.t14.t4 t24.t7.t7.t7.t7.t15.t14.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t14.t8.t3 t24.t7.t7.t7.t7.t15.t14.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.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 (t24.t7.t7.t7.t7.t15.t14.t7 t24.t7.t7.t7.t7.t15.t14.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t7.t7.t15.t14.t6 t24.t7.t7.t7.t7.t15.t14.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t7.t15.t14.t10 t24.t7.t7.t7.t7.t15.t14.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t7.t7.t7.t15.t14.t12 t24.t7.t7.t7.t7.t15.t14.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t14.t14 t24.t7.t7.t7.t7.t15.t14.t15))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t7.t7.t7.t15.t14.t16 t24.t7.t7.t7.t7.t15.t14.t17))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t13 t24.t7.t7.t7.t7.t15.t14))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t7.t7.t15.t12 t24.t7.t7.t7.t7.t15.t15))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t7.t7.t15.t9 t24.t7.t7.t7.t7.t15.t16 a5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t7.t7.t7.t15.t3 a7 t24.t7.t7.t7.t7.t15.t8 t24.t7.t7.t7.t7.t15.t17 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t7.t7.t15.t18))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t7.t7.t7.t15.t18))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t20 t24.t7.t7.t7.t7.t15.t21))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t19 t24.t7.t7.t7.t7.t15.t22))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t7.t15.t23 t24.t7.t7.t7.t7.t15.t24))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t7.t7.t14 t24.t7.t7.t7.t7.t15))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t7.t7.t18.t3 t24.t7.t7.t7.t7.t18.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t7.t7.t7.t18.t7.t2))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t7.t7.t18.t6 t24.t7.t7.t7.t7.t18.t7))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t7.t7.t18.t5 t24.t7.t7.t7.t7.t18.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t7.t18.t9 t24.t7.t7.t7.t7.t18.t10))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t7.t7.t7.t18.t11 t24.t7.t7.t7.t7.t18.t12))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t7.t7.t7.t17 t24.t7.t7.t7.t7.t18))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t7.t7.t7.t16 t24.t7.t7.t7.t7.t19))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t7.t7.t7.t13 t24.t7.t7.t7.t7.t20 a8))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t7.t7.t23 t24.t7.t7.t7.t7.t24))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t7.t7.t22 t24.t7.t7.t7.t7.t25 a6))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t5 (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)))))) :rule resolution :premises (t24.t7.t7.t7.t7.t29.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t7.t7.t29.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t7.t7.t29.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t7.t7.t29.t7 t24.t7.t7.t7.t7.t29.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t7.t29.t6 t24.t7.t7.t7.t7.t29.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t7.t7.t7.t29.t10 t24.t7.t7.t7.t7.t29.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t7.t29.t12 t24.t7.t7.t7.t7.t29.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t7.t7.t7.t28 t24.t7.t7.t7.t7.t29))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t7.t7.t7.t32.t4 t24.t7.t7.t7.t7.t32.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t7.t7.t32.t8.t3 t24.t7.t7.t7.t7.t32.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t7.t7.t32.t7 t24.t7.t7.t7.t7.t32.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t7.t32.t6 t24.t7.t7.t7.t7.t32.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t7.t7.t7.t32.t10 t24.t7.t7.t7.t7.t32.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.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 (t24.t7.t7.t7.t7.t32.t12 t24.t7.t7.t7.t7.t32.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.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 (t24.t7.t7.t7.t7.t32.t14 t24.t7.t7.t7.t7.t32.t15))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t7.t32.t16 t24.t7.t7.t7.t7.t32.t17))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t7.t7.t31 t24.t7.t7.t7.t7.t32))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t7.t7.t30 t24.t7.t7.t7.t7.t33))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t7.t7.t27 t24.t7.t7.t7.t7.t34 a5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t7.t7.t7 t24.t7.t7.t7.t7.t12 t24.t7.t7.t7.t7.t21 a7 t24.t7.t7.t7.t7.t26 t24.t7.t7.t7.t7.t35 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t7.t7.t7.t36))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t7.t7.t7.t36))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t7.t7.t37 t24.t7.t7.t7.t7.t38))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t7.t7.t7.t6 t24.t7.t7.t7.t7.t39))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t7.t7.t7.t43.t2.t2 t24.t7.t7.t7.t7.t43.t2.t3))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t7.t7.t7.t43.t2.t4 t24.t7.t7.t7.t7.t43.t2.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t7.t7.t7.t43.t2 t24.t7.t7.t7.t7.t43.t3))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t7.t7.t7.t43.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t7.t7.t7.t43.t5 t24.t7.t7.t7.t7.t43.t6))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t7.t7.t43 t24.t7.t7.t7.t7.t44))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t7.t7.t42 t24.t7.t7.t7.t7.t45))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t7.t7.t7.t41 t24.t7.t7.t7.t7.t46))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t7.t7.t7.t40 t24.t7.t7.t7.t7.t47))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t7.t7.t7.t5 t24.t7.t7.t7.t7.t48 a10))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t7.t7.t7.t4 t24.t7.t7.t7.t7.t49 t24.t7.t7.t7.t7.t12 t24.t7.t7.t7.t7.t21 a7 t24.t7.t7.t7.t7.t26 t24.t7.t7.t7.t7.t35 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t7.t7.t50))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t7.t7.t7.t7.t51 t24.t7.t7.t7.t7.t52))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t7.t7.t7.t7.t53 t24.t7.t7.t7.t7.t54))
% 0.68/0.90  (step t24.t7.t7.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t7.t55 t24.t7.t7.t7.t7.t56))
% 0.68/0.90  (step t24.t7.t7.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t7.t6 t24.t7.t7.t7.t7))
% 0.68/0.90  (step t24.t7.t7.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t7.t7.t7.t10.t4 t24.t7.t7.t7.t10.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t7.t7.t7.t10.t6 t24.t7.t7.t7.t10.t7))
% 0.68/0.90  (step t24.t7.t7.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t10.t8 t24.t7.t7.t7.t10.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t7.t7.t7.t10.t10 t24.t7.t7.t7.t10.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t7.t9 t24.t7.t7.t7.t10))
% 0.68/0.90  (step t24.t7.t7.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t7.t8 t24.t7.t7.t7.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t7.t5 t24.t7.t7.t7.t12 a11))
% 0.68/0.90  (step t24.t7.t7.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t7.t18 t24.t7.t7.t7.t19))
% 0.68/0.90  (step t24.t7.t7.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t7.t7.t17 t24.t7.t7.t7.t20 a9))
% 0.68/0.90  (step t24.t7.t7.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t7.t24.t5 t24.t7.t7.t7.t24.t6))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t7.t24.t4 t24.t7.t7.t7.t24.t7 a6))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t5 (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)))))) :rule resolution :premises (t24.t7.t7.t7.t24.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t7.t24.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t7.t24.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t7.t24.t11.t7 t24.t7.t7.t7.t24.t11.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t24.t11.t6 t24.t7.t7.t7.t24.t11.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t7.t7.t24.t11.t10 t24.t7.t7.t7.t24.t11.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t24.t11.t12 t24.t7.t7.t7.t24.t11.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t7.t7.t24.t10 t24.t7.t7.t7.t24.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t7.t7.t24.t14.t4 t24.t7.t7.t7.t24.t14.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t7.t24.t14.t8.t3 t24.t7.t7.t7.t24.t14.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t7.t24.t14.t7 t24.t7.t7.t7.t24.t14.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t24.t14.t6 t24.t7.t7.t7.t24.t14.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t7.t7.t24.t14.t10 t24.t7.t7.t7.t24.t14.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.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 (t24.t7.t7.t7.t24.t14.t12 t24.t7.t7.t7.t24.t14.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.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 (t24.t7.t7.t7.t24.t14.t14 t24.t7.t7.t7.t24.t14.t15))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t24.t14.t16 t24.t7.t7.t7.t24.t14.t17))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t7.t24.t13 t24.t7.t7.t7.t24.t14))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t7.t24.t12 t24.t7.t7.t7.t24.t15))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t7.t24.t9 t24.t7.t7.t7.t24.t16 a5))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t7.t24.t3 a7 t24.t7.t7.t7.t24.t8 t24.t7.t7.t7.t24.t17 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t7.t24.t18))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t7.t7.t24.t18))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t7.t7.t24.t20 t24.t7.t7.t7.t24.t21))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t7.t7.t24.t19 t24.t7.t7.t7.t24.t22))
% 0.68/0.90  (step t24.t7.t7.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t24.t23 t24.t7.t7.t7.t24.t24))
% 0.68/0.90  (step t24.t7.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t7.t23 t24.t7.t7.t7.t24))
% 0.68/0.90  (step t24.t7.t7.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t7.t27.t3 t24.t7.t7.t7.t27.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t7.t7.t27.t7.t2))
% 0.68/0.90  (step t24.t7.t7.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t7.t27.t6 t24.t7.t7.t7.t27.t7))
% 0.68/0.90  (step t24.t7.t7.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t7.t27.t5 t24.t7.t7.t7.t27.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t27.t9 t24.t7.t7.t7.t27.t10))
% 0.68/0.90  (step t24.t7.t7.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t7.t7.t27.t11 t24.t7.t7.t7.t27.t12))
% 0.68/0.90  (step t24.t7.t7.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t7.t7.t26 t24.t7.t7.t7.t27))
% 0.68/0.90  (step t24.t7.t7.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t7.t7.t25 t24.t7.t7.t7.t28))
% 0.68/0.90  (step t24.t7.t7.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t7.t7.t22 t24.t7.t7.t7.t29 a8))
% 0.68/0.90  (step t24.t7.t7.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t7.t32 t24.t7.t7.t7.t33))
% 0.68/0.90  (step t24.t7.t7.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t7.t31 t24.t7.t7.t7.t34 a6))
% 0.68/0.90  (step t24.t7.t7.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t7.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t7.t38.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t7.t38.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t7.t38.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t7.t38.t7 t24.t7.t7.t7.t38.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t7.t7.t38.t6 t24.t7.t7.t7.t38.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t38.t10 t24.t7.t7.t7.t38.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t38.t12 t24.t7.t7.t7.t38.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t38 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t7.t37 t24.t7.t7.t7.t38))
% 0.68/0.90  (step t24.t7.t7.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.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)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t41.t4 t24.t7.t7.t7.t41.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t7.t41.t8.t3 t24.t7.t7.t7.t41.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t7.t41.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 (t24.t7.t7.t7.t41.t7 t24.t7.t7.t7.t41.t8))
% 0.68/0.90  (step t24.t7.t7.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t7.t41.t6 t24.t7.t7.t7.t41.t9))
% 0.68/0.90  (step t24.t7.t7.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t7.t41.t10 t24.t7.t7.t7.t41.t11))
% 0.68/0.90  (step t24.t7.t7.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t7.t7.t41.t12 t24.t7.t7.t7.t41.t13))
% 0.68/0.90  (step t24.t7.t7.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t41.t14 t24.t7.t7.t7.t41.t15))
% 0.68/0.90  (step t24.t7.t7.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t7.t7.t41.t16 t24.t7.t7.t7.t41.t17))
% 0.68/0.90  (step t24.t7.t7.t7.t41 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t7.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t7.t40 t24.t7.t7.t7.t41))
% 0.68/0.90  (step t24.t7.t7.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t7.t39 t24.t7.t7.t7.t42))
% 0.68/0.90  (step t24.t7.t7.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t7.t36 t24.t7.t7.t7.t43 a5))
% 0.68/0.90  (step t24.t7.t7.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t7.t7.t16 t24.t7.t7.t7.t21 t24.t7.t7.t7.t30 a7 t24.t7.t7.t7.t35 t24.t7.t7.t7.t44 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t7.t7.t45))
% 0.68/0.90  (step t24.t7.t7.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t7.t7.t45))
% 0.68/0.90  (step t24.t7.t7.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t7.t46 t24.t7.t7.t7.t47))
% 0.68/0.90  (step t24.t7.t7.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t7.t7.t15 t24.t7.t7.t7.t48))
% 0.68/0.90  (step t24.t7.t7.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t24.t7.t7.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t7.t7.t52.t2.t2 t24.t7.t7.t7.t52.t2.t3))
% 0.68/0.90  (step t24.t7.t7.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t7.t7.t52.t2.t4 t24.t7.t7.t7.t52.t2.t5))
% 0.68/0.90  (step t24.t7.t7.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t7.t7.t52.t2 t24.t7.t7.t7.t52.t3))
% 0.68/0.90  (step t24.t7.t7.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t7.t7.t52.t4))
% 0.68/0.90  (step t24.t7.t7.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t7.t7.t52.t5 t24.t7.t7.t7.t52.t6))
% 0.68/0.90  (step t24.t7.t7.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t7.t52 t24.t7.t7.t7.t53))
% 0.68/0.90  (step t24.t7.t7.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t7.t51 t24.t7.t7.t7.t54))
% 0.68/0.90  (step t24.t7.t7.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t7.t7.t50 t24.t7.t7.t7.t55))
% 0.68/0.90  (step t24.t7.t7.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t7.t7.t49 t24.t7.t7.t7.t56))
% 0.68/0.90  (step t24.t7.t7.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t7.t7.t14 t24.t7.t7.t7.t57 a10))
% 0.68/0.90  (step t24.t7.t7.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t7.t7.t4 t24.t7.t7.t7.t13 t24.t7.t7.t7.t58 t24.t7.t7.t7.t21 t24.t7.t7.t7.t30 a7 t24.t7.t7.t7.t35 t24.t7.t7.t7.t44 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t7.t59))
% 0.68/0.90  (step t24.t7.t7.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t7.t7.t59))
% 0.68/0.90  (step t24.t7.t7.t7.t62 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t7.t7.t61 t24.t7.t7.t7.t62))
% 0.68/0.90  (step t24.t7.t7.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t7.t7.t60 t24.t7.t7.t7.t63))
% 0.68/0.90  (step t24.t7.t7.t7.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t24.t7.t7.t7.t61 t24.t7.t7.t7.t65))
% 0.68/0.90  (step t24.t7.t7.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t24.t7.t7.t7.t64 t24.t7.t7.t7.t66))
% 0.68/0.90  (step t24.t7.t7.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t7.t67 t24.t7.t7.t7.t68))
% 0.68/0.90  (step t24.t7.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t6 t24.t7.t7.t7))
% 0.68/0.90  (step t24.t7.t7.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t10.t4 t24.t7.t7.t10.t5))
% 0.68/0.90  (step t24.t7.t7.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t24.t7.t7.t10.t8.t3 t24.t7.t7.t10.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t7.t7.t10.t7 t24.t7.t7.t10.t8))
% 0.68/0.90  (step t24.t7.t7.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t7.t7.t10.t6 t24.t7.t7.t10.t9))
% 0.68/0.90  (step t24.t7.t7.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t24.t7.t7.t10.t10 t24.t7.t7.t10.t11))
% 0.68/0.90  (step t24.t7.t7.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t24.t7.t7.t10.t14.t2 t24.t7.t7.t10.t14.t3))
% 0.68/0.90  (step t24.t7.t7.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t7.t7.t10.t13 t24.t7.t7.t10.t14))
% 0.68/0.90  (step t24.t7.t7.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t7.t7.t10.t12 t24.t7.t7.t10.t15))
% 0.68/0.90  (step t24.t7.t7.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t10.t16 t24.t7.t7.t10.t17))
% 0.68/0.90  (step t24.t7.t7.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t24.t7.t7.t10.t18 t24.t7.t7.t10.t19))
% 0.68/0.90  (step t24.t7.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t24.t7.t7.t9 t24.t7.t7.t10))
% 0.68/0.90  (step t24.t7.t7.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t24.t7.t7.t8 t24.t7.t7.t11))
% 0.68/0.90  (step t24.t7.t7.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t24.t7.t7.t5 t24.t7.t7.t12 a12))
% 0.68/0.90  (step t24.t7.t7.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t16.t9 t24.t7.t7.t16.t10))
% 0.68/0.90  (step t24.t7.t7.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t7.t16.t8 t24.t7.t7.t16.t11 a9))
% 0.68/0.90  (step t24.t7.t7.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t16.t15.t5 t24.t7.t7.t16.t15.t6))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t16.t15.t4 t24.t7.t7.t16.t15.t7 a6))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t16.t15.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t16.t15.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t16.t15.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t16.t15.t11.t7 t24.t7.t7.t16.t15.t11.t8))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t7.t16.t15.t11.t6 t24.t7.t7.t16.t15.t11.t9))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t16.t15.t11.t10 t24.t7.t7.t16.t15.t11.t11))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t16.t15.t11.t12 t24.t7.t7.t16.t15.t11.t13))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t16.t15.t10 t24.t7.t7.t16.t15.t11))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.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)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t16.t15.t14.t4 t24.t7.t7.t16.t15.t14.t5))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t16.t15.t14.t8.t3 t24.t7.t7.t16.t15.t14.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.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 (t24.t7.t7.t16.t15.t14.t7 t24.t7.t7.t16.t15.t14.t8))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t16.t15.t14.t6 t24.t7.t7.t16.t15.t14.t9))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t16.t15.t14.t10 t24.t7.t7.t16.t15.t14.t11))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t7.t16.t15.t14.t12 t24.t7.t7.t16.t15.t14.t13))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t16.t15.t14.t14 t24.t7.t7.t16.t15.t14.t15))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t7.t16.t15.t14.t16 t24.t7.t7.t16.t15.t14.t17))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t16.t15.t13 t24.t7.t7.t16.t15.t14))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t16.t15.t12 t24.t7.t7.t16.t15.t15))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t16.t15.t9 t24.t7.t7.t16.t15.t16 a5))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t7.t16.t15.t3 a7 t24.t7.t7.t16.t15.t8 t24.t7.t7.t16.t15.t17 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t16.t15.t18))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t7.t16.t15.t18))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t7.t16.t15.t20 t24.t7.t7.t16.t15.t21))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t7.t16.t15.t19 t24.t7.t7.t16.t15.t22))
% 0.68/0.90  (step t24.t7.t7.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t16.t15.t23 t24.t7.t7.t16.t15.t24))
% 0.68/0.90  (step t24.t7.t7.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t16.t14 t24.t7.t7.t16.t15))
% 0.68/0.90  (step t24.t7.t7.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t16.t18.t3 t24.t7.t7.t16.t18.t4))
% 0.68/0.90  (step t24.t7.t7.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t7.t16.t18.t7.t2))
% 0.68/0.90  (step t24.t7.t7.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t16.t18.t6 t24.t7.t7.t16.t18.t7))
% 0.68/0.90  (step t24.t7.t7.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t16.t18.t5 t24.t7.t7.t16.t18.t8))
% 0.68/0.90  (step t24.t7.t7.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t16.t18.t9 t24.t7.t7.t16.t18.t10))
% 0.68/0.90  (step t24.t7.t7.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t7.t16.t18.t11 t24.t7.t7.t16.t18.t12))
% 0.68/0.90  (step t24.t7.t7.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t7.t16.t17 t24.t7.t7.t16.t18))
% 0.68/0.90  (step t24.t7.t7.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t7.t16.t16 t24.t7.t7.t16.t19))
% 0.68/0.90  (step t24.t7.t7.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t7.t16.t13 t24.t7.t7.t16.t20 a8))
% 0.68/0.90  (step t24.t7.t7.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t16.t23 t24.t7.t7.t16.t24))
% 0.68/0.90  (step t24.t7.t7.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t16.t22 t24.t7.t7.t16.t25 a6))
% 0.68/0.90  (step t24.t7.t7.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t16.t29.t5 (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)))))) :rule resolution :premises (t24.t7.t7.t16.t29.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t16.t29.t5))
% 0.68/0.90  (step t24.t7.t7.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t16.t29.t5))
% 0.68/0.90  (step t24.t7.t7.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t16.t29.t7 t24.t7.t7.t16.t29.t8))
% 0.68/0.90  (step t24.t7.t7.t16.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t7.t16.t29.t6 t24.t7.t7.t16.t29.t9))
% 0.68/0.90  (step t24.t7.t7.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t7.t16.t29.t10 t24.t7.t7.t16.t29.t11))
% 0.68/0.90  (step t24.t7.t7.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t16.t29.t12 t24.t7.t7.t16.t29.t13))
% 0.68/0.90  (step t24.t7.t7.t16.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t7.t16.t28 t24.t7.t7.t16.t29))
% 0.68/0.90  (step t24.t7.t7.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t7.t16.t32.t4 t24.t7.t7.t16.t32.t5))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t16.t32.t8.t3 t24.t7.t7.t16.t32.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t16.t32.t7 t24.t7.t7.t16.t32.t8))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t16.t32.t6 t24.t7.t7.t16.t32.t9))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t7.t16.t32.t10 t24.t7.t7.t16.t32.t11))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t32.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 (t24.t7.t7.t16.t32.t12 t24.t7.t7.t16.t32.t13))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t32.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 (t24.t7.t7.t16.t32.t14 t24.t7.t7.t16.t32.t15))
% 0.68/0.90  (step t24.t7.t7.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t16.t32.t16 t24.t7.t7.t16.t32.t17))
% 0.68/0.90  (step t24.t7.t7.t16.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t16.t31 t24.t7.t7.t16.t32))
% 0.68/0.90  (step t24.t7.t7.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t16.t30 t24.t7.t7.t16.t33))
% 0.68/0.90  (step t24.t7.t7.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t16.t27 t24.t7.t7.t16.t34 a5))
% 0.68/0.90  (step t24.t7.t7.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t16.t7 t24.t7.t7.t16.t12 t24.t7.t7.t16.t21 a7 t24.t7.t7.t16.t26 t24.t7.t7.t16.t35 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t7.t16.t36))
% 0.68/0.90  (step t24.t7.t7.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t7.t16.t36))
% 0.68/0.90  (step t24.t7.t7.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t16.t37 t24.t7.t7.t16.t38))
% 0.68/0.90  (step t24.t7.t7.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t7.t16.t6 t24.t7.t7.t16.t39))
% 0.68/0.90  (step t24.t7.t7.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t24.t7.t7.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t7.t16.t43.t2.t2 t24.t7.t7.t16.t43.t2.t3))
% 0.68/0.90  (step t24.t7.t7.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t7.t16.t43.t2.t4 t24.t7.t7.t16.t43.t2.t5))
% 0.68/0.90  (step t24.t7.t7.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t7.t16.t43.t2 t24.t7.t7.t16.t43.t3))
% 0.68/0.90  (step t24.t7.t7.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t7.t16.t43.t4))
% 0.68/0.90  (step t24.t7.t7.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t7.t16.t43.t5 t24.t7.t7.t16.t43.t6))
% 0.68/0.90  (step t24.t7.t7.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t16.t43 t24.t7.t7.t16.t44))
% 0.68/0.90  (step t24.t7.t7.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t16.t42 t24.t7.t7.t16.t45))
% 0.68/0.90  (step t24.t7.t7.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t7.t16.t41 t24.t7.t7.t16.t46))
% 0.68/0.90  (step t24.t7.t7.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t7.t16.t40 t24.t7.t7.t16.t47))
% 0.68/0.90  (step t24.t7.t7.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t7.t16.t5 t24.t7.t7.t16.t48 a10))
% 0.68/0.90  (step t24.t7.t7.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t7.t16.t4 t24.t7.t7.t16.t49 t24.t7.t7.t16.t12 t24.t7.t7.t16.t21 a7 t24.t7.t7.t16.t26 t24.t7.t7.t16.t35 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t16.t50))
% 0.68/0.90  (step t24.t7.t7.t16.t52 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t7.t7.t16.t51 t24.t7.t7.t16.t52))
% 0.68/0.90  (step t24.t7.t7.t16.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t7.t7.t16.t53 t24.t7.t7.t16.t54))
% 0.68/0.90  (step t24.t7.t7.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t16.t55 t24.t7.t7.t16.t56))
% 0.68/0.90  (step t24.t7.t7.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t15 t24.t7.t7.t16))
% 0.68/0.90  (step t24.t7.t7.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t19.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t7.t7.t19.t4 t24.t7.t7.t19.t5))
% 0.68/0.90  (step t24.t7.t7.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t7.t7.t19.t6 t24.t7.t7.t19.t7))
% 0.68/0.90  (step t24.t7.t7.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t19.t8 t24.t7.t7.t19.t9))
% 0.68/0.90  (step t24.t7.t7.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t7.t7.t19.t10 t24.t7.t7.t19.t11))
% 0.68/0.90  (step t24.t7.t7.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t18 t24.t7.t7.t19))
% 0.68/0.90  (step t24.t7.t7.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t17 t24.t7.t7.t20))
% 0.68/0.90  (step t24.t7.t7.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t14 t24.t7.t7.t21 a11))
% 0.68/0.90  (step t24.t7.t7.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t27 t24.t7.t7.t28))
% 0.68/0.90  (step t24.t7.t7.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t7.t26 t24.t7.t7.t29 a9))
% 0.68/0.90  (step t24.t7.t7.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t33.t5 t24.t7.t7.t33.t6))
% 0.68/0.90  (step t24.t7.t7.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t33.t4 t24.t7.t7.t33.t7 a6))
% 0.68/0.90  (step t24.t7.t7.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t33.t11.t5 (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)))))) :rule resolution :premises (t24.t7.t7.t33.t11.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t33.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t33.t11.t5))
% 0.68/0.90  (step t24.t7.t7.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t33.t11.t7 t24.t7.t7.t33.t11.t8))
% 0.68/0.90  (step t24.t7.t7.t33.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t7.t33.t11.t6 t24.t7.t7.t33.t11.t9))
% 0.68/0.90  (step t24.t7.t7.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t7.t33.t11.t10 t24.t7.t7.t33.t11.t11))
% 0.68/0.90  (step t24.t7.t7.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t33.t11.t12 t24.t7.t7.t33.t11.t13))
% 0.68/0.90  (step t24.t7.t7.t33.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t7.t33.t10 t24.t7.t7.t33.t11))
% 0.68/0.90  (step t24.t7.t7.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t33.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t7.t33.t14.t4 t24.t7.t7.t33.t14.t5))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.90  (anchor :step t24.t7.t7.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t33.t14.t8.t3 t24.t7.t7.t33.t14.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t33.t14.t7 t24.t7.t7.t33.t14.t8))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t33.t14.t6 t24.t7.t7.t33.t14.t9))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t7.t33.t14.t10 t24.t7.t7.t33.t14.t11))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t33.t14.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 (t24.t7.t7.t33.t14.t12 t24.t7.t7.t33.t14.t13))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t14.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 (t24.t7.t7.t33.t14.t14 t24.t7.t7.t33.t14.t15))
% 0.68/0.90  (step t24.t7.t7.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t33.t14.t16 t24.t7.t7.t33.t14.t17))
% 0.68/0.90  (step t24.t7.t7.t33.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t33.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t33.t13 t24.t7.t7.t33.t14))
% 0.68/0.90  (step t24.t7.t7.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t33.t12 t24.t7.t7.t33.t15))
% 0.68/0.90  (step t24.t7.t7.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t33.t9 t24.t7.t7.t33.t16 a5))
% 0.68/0.90  (step t24.t7.t7.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t33.t3 a7 t24.t7.t7.t33.t8 t24.t7.t7.t33.t17 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t33.t18))
% 0.68/0.90  (step t24.t7.t7.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t7.t33.t18))
% 0.68/0.90  (step t24.t7.t7.t33.t21 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t7.t33.t20 t24.t7.t7.t33.t21))
% 0.68/0.90  (step t24.t7.t7.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t7.t33.t19 t24.t7.t7.t33.t22))
% 0.68/0.90  (step t24.t7.t7.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t33.t23 t24.t7.t7.t33.t24))
% 0.68/0.90  (step t24.t7.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t32 t24.t7.t7.t33))
% 0.68/0.90  (step t24.t7.t7.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t36.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t36.t3 t24.t7.t7.t36.t4))
% 0.68/0.90  (step t24.t7.t7.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t7.t36.t7.t2))
% 0.68/0.90  (step t24.t7.t7.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t36.t6 t24.t7.t7.t36.t7))
% 0.68/0.90  (step t24.t7.t7.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t7.t36.t5 t24.t7.t7.t36.t8))
% 0.68/0.90  (step t24.t7.t7.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t36.t9 t24.t7.t7.t36.t10))
% 0.68/0.90  (step t24.t7.t7.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t7.t36.t11 t24.t7.t7.t36.t12))
% 0.68/0.90  (step t24.t7.t7.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t7.t35 t24.t7.t7.t36))
% 0.68/0.90  (step t24.t7.t7.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t7.t34 t24.t7.t7.t37))
% 0.68/0.90  (step t24.t7.t7.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t7.t31 t24.t7.t7.t38 a8))
% 0.68/0.90  (step t24.t7.t7.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.90  (step t24.t7.t7.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t42.t2 (cl (= X X)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t7.t41 t24.t7.t7.t42))
% 0.68/0.90  (step t24.t7.t7.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t7.t40 t24.t7.t7.t43 a6))
% 0.68/0.90  (step t24.t7.t7.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.90  (step t24.t7.t7.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t47.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t47.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t47.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.90  (step t24.t7.t7.t47.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t47.t4 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t7.t47.t5))
% 0.68/0.90  (step t24.t7.t7.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t7.t47.t5))
% 0.68/0.90  (step t24.t7.t7.t47.t8 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t7.t47.t7 t24.t7.t7.t47.t8))
% 0.68/0.90  (step t24.t7.t7.t47.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t7.t47.t6 t24.t7.t7.t47.t9))
% 0.68/0.90  (step t24.t7.t7.t47.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t47.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t47.t10 t24.t7.t7.t47.t11))
% 0.68/0.90  (step t24.t7.t7.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t47.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t47.t12 t24.t7.t7.t47.t13))
% 0.68/0.90  (step t24.t7.t7.t47 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t7.t46 t24.t7.t7.t47))
% 0.68/0.90  (step t24.t7.t7.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t50.t1 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.t2 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.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)
% 0.68/0.90  (step t24.t7.t7.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t50.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t7.t50.t4 t24.t7.t7.t50.t5))
% 0.68/0.90  (step t24.t7.t7.t50.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.90  (step t24.t7.t7.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t7.t50.t8.t3 t24.t7.t7.t50.t8.t4))
% 0.68/0.90  (step t24.t7.t7.t50.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t50.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 (t24.t7.t7.t50.t7 t24.t7.t7.t50.t8))
% 0.68/0.90  (step t24.t7.t7.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t7.t50.t6 t24.t7.t7.t50.t9))
% 0.68/0.90  (step t24.t7.t7.t50.t11 (cl (= V V)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t7.t50.t10 t24.t7.t7.t50.t11))
% 0.68/0.90  (step t24.t7.t7.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t50.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t7.t50.t12 t24.t7.t7.t50.t13))
% 0.68/0.90  (step t24.t7.t7.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t50.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t50.t14 t24.t7.t7.t50.t15))
% 0.68/0.90  (step t24.t7.t7.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t7.t50.t16 t24.t7.t7.t50.t17))
% 0.68/0.90  (step t24.t7.t7.t50 (cl (= (lambda ((U (-> $$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)
% 0.68/0.90  (step t24.t7.t7.t51 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t7.t49 t24.t7.t7.t50))
% 0.68/0.90  (step t24.t7.t7.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t7.t48 t24.t7.t7.t51))
% 0.68/0.90  (step t24.t7.t7.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t7.t45 t24.t7.t7.t52 a5))
% 0.68/0.90  (step t24.t7.t7.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t7.t25 t24.t7.t7.t30 t24.t7.t7.t39 a7 t24.t7.t7.t44 t24.t7.t7.t53 a4 a3 a2))
% 0.68/0.90  (step t24.t7.t7.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t7.t54))
% 0.68/0.90  (step t24.t7.t7.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t7.t54))
% 0.68/0.90  (step t24.t7.t7.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t7.t55 t24.t7.t7.t56))
% 0.68/0.90  (step t24.t7.t7.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t7.t24 t24.t7.t7.t57))
% 0.68/0.90  (step t24.t7.t7.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.90  (anchor :step t24.t7.t7.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.90  (step t24.t7.t7.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.90  (anchor :step t24.t7.t7.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.90  (step t24.t7.t7.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.90  (step t24.t7.t7.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t7.t61.t2.t2 t24.t7.t7.t61.t2.t3))
% 0.68/0.90  (step t24.t7.t7.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t7.t61.t2.t4 t24.t7.t7.t61.t2.t5))
% 0.68/0.90  (step t24.t7.t7.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t7.t61.t2 t24.t7.t7.t61.t3))
% 0.68/0.90  (step t24.t7.t7.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t7.t61.t4))
% 0.68/0.90  (step t24.t7.t7.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t7.t61.t5 t24.t7.t7.t61.t6))
% 0.68/0.90  (step t24.t7.t7.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.90  (step t24.t7.t7.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.90  (step t24.t7.t7.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t61 t24.t7.t7.t62))
% 0.68/0.90  (step t24.t7.t7.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t7.t60 t24.t7.t7.t63))
% 0.68/0.90  (step t24.t7.t7.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t7.t59 t24.t7.t7.t64))
% 0.68/0.91  (step t24.t7.t7.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t7.t58 t24.t7.t7.t65))
% 0.68/0.91  (step t24.t7.t7.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t7.t23 t24.t7.t7.t66 a10))
% 0.68/0.91  (step t24.t7.t7.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t7.t4 t24.t7.t7.t13 t24.t7.t7.t22 t24.t7.t7.t67 t24.t7.t7.t30 t24.t7.t7.t39 a7 t24.t7.t7.t44 t24.t7.t7.t53 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t7.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t24.t7.t7.t68))
% 0.68/0.91  (step t24.t7.t7.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t7.t68))
% 0.68/0.91  (step t24.t7.t7.t71 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t7.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t7.t70 t24.t7.t7.t71))
% 0.68/0.91  (step t24.t7.t7.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t7.t69 t24.t7.t7.t72))
% 0.68/0.91  (step t24.t7.t7.t74 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t7.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t24.t7.t7.t70 t24.t7.t7.t74))
% 0.68/0.91  (step t24.t7.t7.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t24.t7.t7.t73 t24.t7.t7.t75))
% 0.68/0.91  (step t24.t7.t7.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t7.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t24.t7.t7.t76 t24.t7.t7.t77))
% 0.68/0.91  (step t24.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t8 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t24.t7.t6 t24.t7.t7))
% 0.68/0.91  (step t24.t7.t9 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t4 (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)
% 0.68/0.91  (step t24.t7.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t10.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t10.t4 t24.t7.t10.t5))
% 0.68/0.91  (step t24.t7.t10.t7 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t10.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t10.t8.t1 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t10.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t10.t8.t3))
% 0.68/0.91  (step t24.t7.t10.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t24.t7.t10.t8.t4 t24.t7.t10.t8.t5))
% 0.68/0.91  (step t24.t7.t10.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t7.t10.t9 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t24.t7.t10.t7 t24.t7.t10.t8))
% 0.68/0.91  (step t24.t7.t10.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t24.t7.t10.t6 t24.t7.t10.t9))
% 0.68/0.91  (step t24.t7.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t10.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t24.t7.t10.t10 t24.t7.t10.t11))
% 0.68/0.91  (step t24.t7.t10.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t10.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t10.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t10.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t24.t7.t10.t14.t2 t24.t7.t10.t14.t3))
% 0.68/0.91  (step t24.t7.t10.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t10.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t24.t7.t10.t13 t24.t7.t10.t14))
% 0.68/0.91  (step t24.t7.t10.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t24.t7.t10.t12 t24.t7.t10.t15))
% 0.68/0.91  (step t24.t7.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t10.t16 t24.t7.t10.t17))
% 0.68/0.91  (step t24.t7.t10.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t10.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t24.t7.t10.t18 t24.t7.t10.t19))
% 0.68/0.91  (step t24.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t11 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t24.t7.t9 t24.t7.t10))
% 0.68/0.91  (step t24.t7.t12 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t24.t7.t8 t24.t7.t11))
% 0.68/0.91  (step t24.t7.t13 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t24.t7.t5 t24.t7.t12 a13))
% 0.68/0.91  (step t24.t7.t14 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t15 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t16.t7.t9 t24.t7.t16.t7.t10))
% 0.68/0.91  (step t24.t7.t16.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t16.t7.t8 t24.t7.t16.t7.t11 a9))
% 0.68/0.91  (step t24.t7.t16.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t16.t7.t15.t5 t24.t7.t16.t7.t15.t6))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t16.t7.t15.t4 t24.t7.t16.t7.t15.t7 a6))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t24.t7.t16.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t16.t7.t15.t11.t5))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t16.t7.t15.t11.t5))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t16.t7.t15.t11.t7 t24.t7.t16.t7.t15.t11.t8))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t16.t7.t15.t11.t6 t24.t7.t16.t7.t15.t11.t9))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t16.t7.t15.t11.t10 t24.t7.t16.t7.t15.t11.t11))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t7.t15.t11.t12 t24.t7.t16.t7.t15.t11.t13))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t16.t7.t15.t10 t24.t7.t16.t7.t15.t11))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t16.t7.t15.t14.t4 t24.t7.t16.t7.t15.t14.t5))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t16.t7.t15.t14.t8.t3 t24.t7.t16.t7.t15.t14.t8.t4))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t16.t7.t15.t14.t7 t24.t7.t16.t7.t15.t14.t8))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t16.t7.t15.t14.t6 t24.t7.t16.t7.t15.t14.t9))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t16.t7.t15.t14.t10 t24.t7.t16.t7.t15.t14.t11))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.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 (t24.t7.t16.t7.t15.t14.t12 t24.t7.t16.t7.t15.t14.t13))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.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 (t24.t7.t16.t7.t15.t14.t14 t24.t7.t16.t7.t15.t14.t15))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t7.t15.t14.t16 t24.t7.t16.t7.t15.t14.t17))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t16.t7.t15.t13 t24.t7.t16.t7.t15.t14))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t16.t7.t15.t12 t24.t7.t16.t7.t15.t15))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t16.t7.t15.t9 t24.t7.t16.t7.t15.t16 a5))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t16.t7.t15.t3 a7 t24.t7.t16.t7.t15.t8 t24.t7.t16.t7.t15.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t16.t7.t15.t18))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t16.t7.t15.t18))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t16.t7.t15.t20 t24.t7.t16.t7.t15.t21))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t16.t7.t15.t19 t24.t7.t16.t7.t15.t22))
% 0.68/0.91  (step t24.t7.t16.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t7.t15.t23 t24.t7.t16.t7.t15.t24))
% 0.68/0.91  (step t24.t7.t16.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t16.t7.t14 t24.t7.t16.t7.t15))
% 0.68/0.91  (step t24.t7.t16.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t16.t7.t18.t3 t24.t7.t16.t7.t18.t4))
% 0.68/0.91  (step t24.t7.t16.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t16.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t16.t7.t18.t7.t2))
% 0.68/0.91  (step t24.t7.t16.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t16.t7.t18.t6 t24.t7.t16.t7.t18.t7))
% 0.68/0.91  (step t24.t7.t16.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t16.t7.t18.t5 t24.t7.t16.t7.t18.t8))
% 0.68/0.91  (step t24.t7.t16.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t7.t18.t9 t24.t7.t16.t7.t18.t10))
% 0.68/0.91  (step t24.t7.t16.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t16.t7.t18.t11 t24.t7.t16.t7.t18.t12))
% 0.68/0.91  (step t24.t7.t16.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t16.t7.t17 t24.t7.t16.t7.t18))
% 0.68/0.91  (step t24.t7.t16.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t16.t7.t16 t24.t7.t16.t7.t19))
% 0.68/0.91  (step t24.t7.t16.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t16.t7.t13 t24.t7.t16.t7.t20 a8))
% 0.68/0.91  (step t24.t7.t16.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t16.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t16.t7.t23 t24.t7.t16.t7.t24))
% 0.68/0.91  (step t24.t7.t16.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t16.t7.t22 t24.t7.t16.t7.t25 a6))
% 0.68/0.91  (step t24.t7.t16.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t16.t7.t29.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t16.t7.t29.t5))
% 0.68/0.91  (step t24.t7.t16.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t16.t7.t29.t5))
% 0.68/0.91  (step t24.t7.t16.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t16.t7.t29.t7 t24.t7.t16.t7.t29.t8))
% 0.68/0.91  (step t24.t7.t16.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t16.t7.t29.t6 t24.t7.t16.t7.t29.t9))
% 0.68/0.91  (step t24.t7.t16.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t7.t29.t10 t24.t7.t16.t7.t29.t11))
% 0.68/0.91  (step t24.t7.t16.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t7.t29.t12 t24.t7.t16.t7.t29.t13))
% 0.68/0.91  (step t24.t7.t16.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t16.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t16.t7.t28 t24.t7.t16.t7.t29))
% 0.68/0.91  (step t24.t7.t16.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.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)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t16.t7.t32.t4 t24.t7.t16.t7.t32.t5))
% 0.68/0.91  (step t24.t7.t16.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t16.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t16.t7.t32.t8.t3 t24.t7.t16.t7.t32.t8.t4))
% 0.68/0.91  (step t24.t7.t16.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t7.t16.t7.t32.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 (t24.t7.t16.t7.t32.t7 t24.t7.t16.t7.t32.t8))
% 0.68/0.91  (step t24.t7.t16.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t16.t7.t32.t6 t24.t7.t16.t7.t32.t9))
% 0.68/0.91  (step t24.t7.t16.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t7.t32.t10 t24.t7.t16.t7.t32.t11))
% 0.68/0.91  (step t24.t7.t16.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t16.t7.t32.t12 t24.t7.t16.t7.t32.t13))
% 0.68/0.91  (step t24.t7.t16.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t7.t32.t14 t24.t7.t16.t7.t32.t15))
% 0.68/0.91  (step t24.t7.t16.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t16.t7.t32.t16 t24.t7.t16.t7.t32.t17))
% 0.68/0.91  (step t24.t7.t16.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t16.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t16.t7.t31 t24.t7.t16.t7.t32))
% 0.68/0.91  (step t24.t7.t16.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t16.t7.t30 t24.t7.t16.t7.t33))
% 0.68/0.91  (step t24.t7.t16.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t16.t7.t27 t24.t7.t16.t7.t34 a5))
% 0.68/0.91  (step t24.t7.t16.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t16.t7.t7 t24.t7.t16.t7.t12 t24.t7.t16.t7.t21 a7 t24.t7.t16.t7.t26 t24.t7.t16.t7.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t16.t7.t36))
% 0.68/0.91  (step t24.t7.t16.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t16.t7.t36))
% 0.68/0.91  (step t24.t7.t16.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t16.t7.t37 t24.t7.t16.t7.t38))
% 0.68/0.91  (step t24.t7.t16.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t16.t7.t6 t24.t7.t16.t7.t39))
% 0.68/0.91  (step t24.t7.t16.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t7.t16.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t16.t7.t43.t2.t2 t24.t7.t16.t7.t43.t2.t3))
% 0.68/0.91  (step t24.t7.t16.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t16.t7.t43.t2.t4 t24.t7.t16.t7.t43.t2.t5))
% 0.68/0.91  (step t24.t7.t16.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t16.t7.t43.t2 t24.t7.t16.t7.t43.t3))
% 0.68/0.91  (step t24.t7.t16.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t16.t7.t43.t4))
% 0.68/0.91  (step t24.t7.t16.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t16.t7.t43.t5 t24.t7.t16.t7.t43.t6))
% 0.68/0.91  (step t24.t7.t16.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t16.t7.t43 t24.t7.t16.t7.t44))
% 0.68/0.91  (step t24.t7.t16.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t16.t7.t42 t24.t7.t16.t7.t45))
% 0.68/0.91  (step t24.t7.t16.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t16.t7.t41 t24.t7.t16.t7.t46))
% 0.68/0.91  (step t24.t7.t16.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t16.t7.t40 t24.t7.t16.t7.t47))
% 0.68/0.91  (step t24.t7.t16.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t16.t7.t5 t24.t7.t16.t7.t48 a10))
% 0.68/0.91  (step t24.t7.t16.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t16.t7.t4 t24.t7.t16.t7.t49 t24.t7.t16.t7.t12 t24.t7.t16.t7.t21 a7 t24.t7.t16.t7.t26 t24.t7.t16.t7.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t16.t7.t50))
% 0.68/0.91  (step t24.t7.t16.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t7.t16.t7.t51 t24.t7.t16.t7.t52))
% 0.68/0.91  (step t24.t7.t16.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t7.t16.t7.t53 t24.t7.t16.t7.t54))
% 0.68/0.91  (step t24.t7.t16.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t7.t55 t24.t7.t16.t7.t56))
% 0.68/0.91  (step t24.t7.t16.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t7.t16.t6 t24.t7.t16.t7))
% 0.68/0.91  (step t24.t7.t16.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t7.t16.t10.t4 t24.t7.t16.t10.t5))
% 0.68/0.91  (step t24.t7.t16.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t7.t16.t10.t6 t24.t7.t16.t10.t7))
% 0.68/0.91  (step t24.t7.t16.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t10.t8 t24.t7.t16.t10.t9))
% 0.68/0.91  (step t24.t7.t16.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t7.t16.t10.t10 t24.t7.t16.t10.t11))
% 0.68/0.91  (step t24.t7.t16.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t7.t16.t9 t24.t7.t16.t10))
% 0.68/0.91  (step t24.t7.t16.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t7.t16.t8 t24.t7.t16.t11))
% 0.68/0.91  (step t24.t7.t16.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t7.t16.t5 t24.t7.t16.t12 a11))
% 0.68/0.91  (step t24.t7.t16.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t16.t18 t24.t7.t16.t19))
% 0.68/0.91  (step t24.t7.t16.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t16.t17 t24.t7.t16.t20 a9))
% 0.68/0.91  (step t24.t7.t16.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t16.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t16.t24.t5 t24.t7.t16.t24.t6))
% 0.68/0.91  (step t24.t7.t16.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t16.t24.t4 t24.t7.t16.t24.t7 a6))
% 0.68/0.91  (step t24.t7.t16.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t16.t24.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t16.t24.t11.t5))
% 0.68/0.91  (step t24.t7.t16.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t16.t24.t11.t5))
% 0.68/0.91  (step t24.t7.t16.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t16.t24.t11.t7 t24.t7.t16.t24.t11.t8))
% 0.68/0.91  (step t24.t7.t16.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t16.t24.t11.t6 t24.t7.t16.t24.t11.t9))
% 0.68/0.91  (step t24.t7.t16.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t24.t11.t10 t24.t7.t16.t24.t11.t11))
% 0.68/0.91  (step t24.t7.t16.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t24.t11.t12 t24.t7.t16.t24.t11.t13))
% 0.68/0.91  (step t24.t7.t16.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t16.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t16.t24.t10 t24.t7.t16.t24.t11))
% 0.68/0.91  (step t24.t7.t16.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.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)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t16.t24.t14.t4 t24.t7.t16.t24.t14.t5))
% 0.68/0.91  (step t24.t7.t16.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t16.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t16.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t16.t24.t14.t8.t3 t24.t7.t16.t24.t14.t8.t4))
% 0.68/0.91  (step t24.t7.t16.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t7.t16.t24.t14.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 (t24.t7.t16.t24.t14.t7 t24.t7.t16.t24.t14.t8))
% 0.68/0.91  (step t24.t7.t16.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t16.t24.t14.t6 t24.t7.t16.t24.t14.t9))
% 0.68/0.91  (step t24.t7.t16.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t24.t14.t10 t24.t7.t16.t24.t14.t11))
% 0.68/0.91  (step t24.t7.t16.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t16.t24.t14.t12 t24.t7.t16.t24.t14.t13))
% 0.68/0.91  (step t24.t7.t16.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t24.t14.t14 t24.t7.t16.t24.t14.t15))
% 0.68/0.91  (step t24.t7.t16.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t16.t24.t14.t16 t24.t7.t16.t24.t14.t17))
% 0.68/0.91  (step t24.t7.t16.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t16.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t16.t24.t13 t24.t7.t16.t24.t14))
% 0.68/0.91  (step t24.t7.t16.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t16.t24.t12 t24.t7.t16.t24.t15))
% 0.68/0.91  (step t24.t7.t16.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t16.t24.t9 t24.t7.t16.t24.t16 a5))
% 0.68/0.91  (step t24.t7.t16.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t16.t24.t3 a7 t24.t7.t16.t24.t8 t24.t7.t16.t24.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t16.t24.t18))
% 0.68/0.91  (step t24.t7.t16.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t16.t24.t18))
% 0.68/0.91  (step t24.t7.t16.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t16.t24.t20 t24.t7.t16.t24.t21))
% 0.68/0.91  (step t24.t7.t16.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t16.t24.t19 t24.t7.t16.t24.t22))
% 0.68/0.91  (step t24.t7.t16.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t24.t23 t24.t7.t16.t24.t24))
% 0.68/0.91  (step t24.t7.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t16.t23 t24.t7.t16.t24))
% 0.68/0.91  (step t24.t7.t16.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t16.t27.t3 t24.t7.t16.t27.t4))
% 0.68/0.91  (step t24.t7.t16.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t16.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t16.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t16.t27.t7.t2))
% 0.68/0.91  (step t24.t7.t16.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t16.t27.t6 t24.t7.t16.t27.t7))
% 0.68/0.91  (step t24.t7.t16.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t16.t27.t5 t24.t7.t16.t27.t8))
% 0.68/0.91  (step t24.t7.t16.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t27.t9 t24.t7.t16.t27.t10))
% 0.68/0.91  (step t24.t7.t16.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t16.t27.t11 t24.t7.t16.t27.t12))
% 0.68/0.91  (step t24.t7.t16.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t16.t26 t24.t7.t16.t27))
% 0.68/0.91  (step t24.t7.t16.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t16.t25 t24.t7.t16.t28))
% 0.68/0.91  (step t24.t7.t16.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t16.t22 t24.t7.t16.t29 a8))
% 0.68/0.91  (step t24.t7.t16.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t16.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t16.t32 t24.t7.t16.t33))
% 0.68/0.91  (step t24.t7.t16.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t16.t31 t24.t7.t16.t34 a6))
% 0.68/0.91  (step t24.t7.t16.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t16.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t38.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t16.t38.t5 (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)))))) :rule resolution :premises (t24.t7.t16.t38.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t16.t38.t5))
% 0.68/0.91  (step t24.t7.t16.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t16.t38.t5))
% 0.68/0.91  (step t24.t7.t16.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t16.t38.t7 t24.t7.t16.t38.t8))
% 0.68/0.91  (step t24.t7.t16.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t16.t38.t6 t24.t7.t16.t38.t9))
% 0.68/0.91  (step t24.t7.t16.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t16.t38.t10 t24.t7.t16.t38.t11))
% 0.68/0.91  (step t24.t7.t16.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t38.t12 t24.t7.t16.t38.t13))
% 0.68/0.91  (step t24.t7.t16.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t16.t37 t24.t7.t16.t38))
% 0.68/0.91  (step t24.t7.t16.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t16.t41.t4 t24.t7.t16.t41.t5))
% 0.68/0.91  (step t24.t7.t16.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t7.t16.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t16.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t16.t41.t8.t3 t24.t7.t16.t41.t8.t4))
% 0.68/0.91  (step t24.t7.t16.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t16.t41.t7 t24.t7.t16.t41.t8))
% 0.68/0.91  (step t24.t7.t16.t41.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t16.t41.t6 t24.t7.t16.t41.t9))
% 0.68/0.91  (step t24.t7.t16.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t16.t41.t10 t24.t7.t16.t41.t11))
% 0.68/0.91  (step t24.t7.t16.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t41.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 (t24.t7.t16.t41.t12 t24.t7.t16.t41.t13))
% 0.68/0.91  (step t24.t7.t16.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t41.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 (t24.t7.t16.t41.t14 t24.t7.t16.t41.t15))
% 0.68/0.91  (step t24.t7.t16.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t16.t41.t16 t24.t7.t16.t41.t17))
% 0.68/0.91  (step t24.t7.t16.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t16.t40 t24.t7.t16.t41))
% 0.68/0.91  (step t24.t7.t16.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t16.t39 t24.t7.t16.t42))
% 0.68/0.91  (step t24.t7.t16.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t16.t36 t24.t7.t16.t43 a5))
% 0.68/0.91  (step t24.t7.t16.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t16.t16 t24.t7.t16.t21 t24.t7.t16.t30 a7 t24.t7.t16.t35 t24.t7.t16.t44 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t16.t45))
% 0.68/0.91  (step t24.t7.t16.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t16.t45))
% 0.68/0.91  (step t24.t7.t16.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t16.t46 t24.t7.t16.t47))
% 0.68/0.91  (step t24.t7.t16.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t16.t15 t24.t7.t16.t48))
% 0.68/0.91  (step t24.t7.t16.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t16.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t16.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t16.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t7.t16.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t16.t52.t2.t2 t24.t7.t16.t52.t2.t3))
% 0.68/0.91  (step t24.t7.t16.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t16.t52.t2.t4 t24.t7.t16.t52.t2.t5))
% 0.68/0.91  (step t24.t7.t16.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t16.t52.t2 t24.t7.t16.t52.t3))
% 0.68/0.91  (step t24.t7.t16.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t16.t52.t4))
% 0.68/0.91  (step t24.t7.t16.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t16.t52.t5 t24.t7.t16.t52.t6))
% 0.68/0.91  (step t24.t7.t16.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t7.t16.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t16.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t16.t52 t24.t7.t16.t53))
% 0.68/0.91  (step t24.t7.t16.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t16.t51 t24.t7.t16.t54))
% 0.68/0.91  (step t24.t7.t16.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t16.t50 t24.t7.t16.t55))
% 0.68/0.91  (step t24.t7.t16.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t16.t49 t24.t7.t16.t56))
% 0.68/0.91  (step t24.t7.t16.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t16.t14 t24.t7.t16.t57 a10))
% 0.68/0.91  (step t24.t7.t16.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t16.t4 t24.t7.t16.t13 t24.t7.t16.t58 t24.t7.t16.t21 t24.t7.t16.t30 a7 t24.t7.t16.t35 t24.t7.t16.t44 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t16.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t16.t59))
% 0.68/0.91  (step t24.t7.t16.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t16.t59))
% 0.68/0.91  (step t24.t7.t16.t62 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t16.t61 t24.t7.t16.t62))
% 0.68/0.91  (step t24.t7.t16.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t16.t60 t24.t7.t16.t63))
% 0.68/0.91  (step t24.t7.t16.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t24.t7.t16.t61 t24.t7.t16.t65))
% 0.68/0.91  (step t24.t7.t16.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t24.t7.t16.t64 t24.t7.t16.t66))
% 0.68/0.91  (step t24.t7.t16.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t16.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t24.t7.t16.t67 t24.t7.t16.t68))
% 0.68/0.91  (step t24.t7.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t17 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t24.t7.t15 t24.t7.t16))
% 0.68/0.91  (step t24.t7.t18 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t19.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)
% 0.68/0.91  (step t24.t7.t19.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t19.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t19.t4 t24.t7.t19.t5))
% 0.68/0.91  (step t24.t7.t19.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t19.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t19.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t19.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t24.t7.t19.t8.t3 t24.t7.t19.t8.t4))
% 0.68/0.91  (step t24.t7.t19.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t7.t19.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t7.t19.t7 t24.t7.t19.t8))
% 0.68/0.91  (step t24.t7.t19.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t7.t19.t6 t24.t7.t19.t9))
% 0.68/0.91  (step t24.t7.t19.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t19.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t24.t7.t19.t10 t24.t7.t19.t11))
% 0.68/0.91  (step t24.t7.t19.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t19.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t19.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t19.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t24.t7.t19.t14.t2 t24.t7.t19.t14.t3))
% 0.68/0.91  (step t24.t7.t19.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t19.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t7.t19.t13 t24.t7.t19.t14))
% 0.68/0.91  (step t24.t7.t19.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t7.t19.t12 t24.t7.t19.t15))
% 0.68/0.91  (step t24.t7.t19.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t19.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t19.t16 t24.t7.t19.t17))
% 0.68/0.91  (step t24.t7.t19.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t19.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t24.t7.t19.t18 t24.t7.t19.t19))
% 0.68/0.91  (step t24.t7.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t20 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t24.t7.t18 t24.t7.t19))
% 0.68/0.91  (step t24.t7.t21 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t24.t7.t17 t24.t7.t20))
% 0.68/0.91  (step t24.t7.t22 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t24.t7.t14 t24.t7.t21 a12))
% 0.68/0.91  (step t24.t7.t23 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t24 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t25.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t25.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t25.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t25.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t25.t9 t24.t7.t25.t10))
% 0.68/0.91  (step t24.t7.t25.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t25.t8 t24.t7.t25.t11 a9))
% 0.68/0.91  (step t24.t7.t25.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t25.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t25.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t25.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t25.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t25.t15.t5 t24.t7.t25.t15.t6))
% 0.68/0.91  (step t24.t7.t25.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t25.t15.t4 t24.t7.t25.t15.t7 a6))
% 0.68/0.91  (step t24.t7.t25.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t25.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t25.t15.t11.t5 (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)))))) :rule resolution :premises (t24.t7.t25.t15.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t25.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t25.t15.t11.t5))
% 0.68/0.91  (step t24.t7.t25.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t25.t15.t11.t5))
% 0.68/0.91  (step t24.t7.t25.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t25.t15.t11.t7 t24.t7.t25.t15.t11.t8))
% 0.68/0.91  (step t24.t7.t25.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t25.t15.t11.t6 t24.t7.t25.t15.t11.t9))
% 0.68/0.91  (step t24.t7.t25.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t25.t15.t11.t10 t24.t7.t25.t15.t11.t11))
% 0.68/0.91  (step t24.t7.t25.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t25.t15.t11.t12 t24.t7.t25.t15.t11.t13))
% 0.68/0.91  (step t24.t7.t25.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t25.t15.t10 t24.t7.t25.t15.t11))
% 0.68/0.91  (step t24.t7.t25.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t25.t15.t14.t4 t24.t7.t25.t15.t14.t5))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t7.t25.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t25.t15.t14.t8.t3 t24.t7.t25.t15.t14.t8.t4))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t25.t15.t14.t7 t24.t7.t25.t15.t14.t8))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t25.t15.t14.t6 t24.t7.t25.t15.t14.t9))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t25.t15.t14.t10 t24.t7.t25.t15.t14.t11))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t15.t14.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 (t24.t7.t25.t15.t14.t12 t24.t7.t25.t15.t14.t13))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t14.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 (t24.t7.t25.t15.t14.t14 t24.t7.t25.t15.t14.t15))
% 0.68/0.91  (step t24.t7.t25.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t25.t15.t14.t16 t24.t7.t25.t15.t14.t17))
% 0.68/0.91  (step t24.t7.t25.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t25.t15.t13 t24.t7.t25.t15.t14))
% 0.68/0.91  (step t24.t7.t25.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t25.t15.t12 t24.t7.t25.t15.t15))
% 0.68/0.91  (step t24.t7.t25.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t25.t15.t9 t24.t7.t25.t15.t16 a5))
% 0.68/0.91  (step t24.t7.t25.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t25.t15.t3 a7 t24.t7.t25.t15.t8 t24.t7.t25.t15.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t25.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t25.t15.t18))
% 0.68/0.91  (step t24.t7.t25.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t25.t15.t18))
% 0.68/0.91  (step t24.t7.t25.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t25.t15.t20 t24.t7.t25.t15.t21))
% 0.68/0.91  (step t24.t7.t25.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t25.t15.t19 t24.t7.t25.t15.t22))
% 0.68/0.91  (step t24.t7.t25.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t25.t15.t23 t24.t7.t25.t15.t24))
% 0.68/0.91  (step t24.t7.t25.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t25.t14 t24.t7.t25.t15))
% 0.68/0.91  (step t24.t7.t25.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t25.t18.t3 t24.t7.t25.t18.t4))
% 0.68/0.91  (step t24.t7.t25.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t25.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t25.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t25.t18.t7.t2))
% 0.68/0.91  (step t24.t7.t25.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t25.t18.t6 t24.t7.t25.t18.t7))
% 0.68/0.91  (step t24.t7.t25.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t25.t18.t5 t24.t7.t25.t18.t8))
% 0.68/0.91  (step t24.t7.t25.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t25.t18.t9 t24.t7.t25.t18.t10))
% 0.68/0.91  (step t24.t7.t25.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t25.t18.t11 t24.t7.t25.t18.t12))
% 0.68/0.91  (step t24.t7.t25.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t25.t17 t24.t7.t25.t18))
% 0.68/0.91  (step t24.t7.t25.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t25.t16 t24.t7.t25.t19))
% 0.68/0.91  (step t24.t7.t25.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t25.t13 t24.t7.t25.t20 a8))
% 0.68/0.91  (step t24.t7.t25.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t25.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t25.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t25.t23 t24.t7.t25.t24))
% 0.68/0.91  (step t24.t7.t25.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t25.t22 t24.t7.t25.t25 a6))
% 0.68/0.91  (step t24.t7.t25.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t25.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t25.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t25.t29.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t25.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t25.t29.t5))
% 0.68/0.91  (step t24.t7.t25.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t25.t29.t5))
% 0.68/0.91  (step t24.t7.t25.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t25.t29.t7 t24.t7.t25.t29.t8))
% 0.68/0.91  (step t24.t7.t25.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t25.t29.t6 t24.t7.t25.t29.t9))
% 0.68/0.91  (step t24.t7.t25.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t25.t29.t10 t24.t7.t25.t29.t11))
% 0.68/0.91  (step t24.t7.t25.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t25.t29.t12 t24.t7.t25.t29.t13))
% 0.68/0.91  (step t24.t7.t25.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t25.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t25.t28 t24.t7.t25.t29))
% 0.68/0.91  (step t24.t7.t25.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.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)
% 0.68/0.91  (step t24.t7.t25.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t25.t32.t4 t24.t7.t25.t32.t5))
% 0.68/0.91  (step t24.t7.t25.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t25.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t25.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t25.t32.t8.t3 t24.t7.t25.t32.t8.t4))
% 0.68/0.91  (step t24.t7.t25.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t7.t25.t32.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 (t24.t7.t25.t32.t7 t24.t7.t25.t32.t8))
% 0.68/0.91  (step t24.t7.t25.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t25.t32.t6 t24.t7.t25.t32.t9))
% 0.68/0.91  (step t24.t7.t25.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t25.t32.t10 t24.t7.t25.t32.t11))
% 0.68/0.91  (step t24.t7.t25.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t25.t32.t12 t24.t7.t25.t32.t13))
% 0.68/0.91  (step t24.t7.t25.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t25.t32.t14 t24.t7.t25.t32.t15))
% 0.68/0.91  (step t24.t7.t25.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t25.t32.t16 t24.t7.t25.t32.t17))
% 0.68/0.91  (step t24.t7.t25.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t25.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t25.t31 t24.t7.t25.t32))
% 0.68/0.91  (step t24.t7.t25.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t25.t30 t24.t7.t25.t33))
% 0.68/0.91  (step t24.t7.t25.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t25.t27 t24.t7.t25.t34 a5))
% 0.68/0.91  (step t24.t7.t25.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t25.t7 t24.t7.t25.t12 t24.t7.t25.t21 a7 t24.t7.t25.t26 t24.t7.t25.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t25.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t25.t36))
% 0.68/0.91  (step t24.t7.t25.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t25.t36))
% 0.68/0.91  (step t24.t7.t25.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t25.t37 t24.t7.t25.t38))
% 0.68/0.91  (step t24.t7.t25.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t25.t6 t24.t7.t25.t39))
% 0.68/0.91  (step t24.t7.t25.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t25.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t25.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t25.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t7.t25.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t25.t43.t2.t2 t24.t7.t25.t43.t2.t3))
% 0.68/0.91  (step t24.t7.t25.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t25.t43.t2.t4 t24.t7.t25.t43.t2.t5))
% 0.68/0.91  (step t24.t7.t25.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t25.t43.t2 t24.t7.t25.t43.t3))
% 0.68/0.91  (step t24.t7.t25.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t25.t43.t4))
% 0.68/0.91  (step t24.t7.t25.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t25.t43.t5 t24.t7.t25.t43.t6))
% 0.68/0.91  (step t24.t7.t25.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t7.t25.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t25.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t25.t43 t24.t7.t25.t44))
% 0.68/0.91  (step t24.t7.t25.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t25.t42 t24.t7.t25.t45))
% 0.68/0.91  (step t24.t7.t25.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t25.t41 t24.t7.t25.t46))
% 0.68/0.91  (step t24.t7.t25.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t25.t40 t24.t7.t25.t47))
% 0.68/0.91  (step t24.t7.t25.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t25.t5 t24.t7.t25.t48 a10))
% 0.68/0.91  (step t24.t7.t25.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t25.t4 t24.t7.t25.t49 t24.t7.t25.t12 t24.t7.t25.t21 a7 t24.t7.t25.t26 t24.t7.t25.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t25.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t25.t50))
% 0.68/0.91  (step t24.t7.t25.t52 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t7.t25.t51 t24.t7.t25.t52))
% 0.68/0.91  (step t24.t7.t25.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t7.t25.t53 t24.t7.t25.t54))
% 0.68/0.91  (step t24.t7.t25.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t25.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t7.t25.t55 t24.t7.t25.t56))
% 0.68/0.91  (step t24.t7.t25 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t26 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t7.t24 t24.t7.t25))
% 0.68/0.91  (step t24.t7.t27 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t28 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t28.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t28.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t28.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t28.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t28.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t7.t28.t4 t24.t7.t28.t5))
% 0.68/0.91  (step t24.t7.t28.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t28.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t7.t28.t6 t24.t7.t28.t7))
% 0.68/0.91  (step t24.t7.t28.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t28.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t7.t28.t8 t24.t7.t28.t9))
% 0.68/0.91  (step t24.t7.t28.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t28.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t7.t28.t10 t24.t7.t28.t11))
% 0.68/0.91  (step t24.t7.t28 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t7.t29 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t7.t27 t24.t7.t28))
% 0.68/0.91  (step t24.t7.t30 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t7.t26 t24.t7.t29))
% 0.68/0.91  (step t24.t7.t31 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t7.t23 t24.t7.t30 a11))
% 0.68/0.91  (step t24.t7.t32 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t33 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t34 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t35 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t36 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t7.t37 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t38 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t36 t24.t7.t37))
% 0.68/0.91  (step t24.t7.t39 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t7.t35 t24.t7.t38 a9))
% 0.68/0.91  (step t24.t7.t40 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t41 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t42.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t42.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t42.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t42.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t42.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t42.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t42.t5 t24.t7.t42.t6))
% 0.68/0.91  (step t24.t7.t42.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t42.t4 t24.t7.t42.t7 a6))
% 0.68/0.91  (step t24.t7.t42.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t42.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t42.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t42.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t42.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t42.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t42.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t42.t11.t5))
% 0.68/0.91  (step t24.t7.t42.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t42.t11.t5))
% 0.68/0.91  (step t24.t7.t42.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t42.t11.t7 t24.t7.t42.t11.t8))
% 0.68/0.91  (step t24.t7.t42.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t7.t42.t11.t6 t24.t7.t42.t11.t9))
% 0.68/0.91  (step t24.t7.t42.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t7.t42.t11.t10 t24.t7.t42.t11.t11))
% 0.68/0.91  (step t24.t7.t42.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t7.t42.t11.t12 t24.t7.t42.t11.t13))
% 0.68/0.91  (step t24.t7.t42.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t42.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t7.t42.t10 t24.t7.t42.t11))
% 0.68/0.91  (step t24.t7.t42.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t42.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t42.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.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)
% 0.68/0.91  (step t24.t7.t42.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t42.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t42.t14.t4 t24.t7.t42.t14.t5))
% 0.68/0.91  (step t24.t7.t42.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t42.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t42.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t42.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t42.t14.t8.t3 t24.t7.t42.t14.t8.t4))
% 0.68/0.91  (step t24.t7.t42.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t7.t42.t14.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 (t24.t7.t42.t14.t7 t24.t7.t42.t14.t8))
% 0.68/0.91  (step t24.t7.t42.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t42.t14.t6 t24.t7.t42.t14.t9))
% 0.68/0.91  (step t24.t7.t42.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t7.t42.t14.t10 t24.t7.t42.t14.t11))
% 0.68/0.91  (step t24.t7.t42.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t42.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t7.t42.t14.t12 t24.t7.t42.t14.t13))
% 0.68/0.91  (step t24.t7.t42.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t7.t42.t14.t14 t24.t7.t42.t14.t15))
% 0.68/0.91  (step t24.t7.t42.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t42.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t7.t42.t14.t16 t24.t7.t42.t14.t17))
% 0.68/0.91  (step t24.t7.t42.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t7.t42.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t42.t13 t24.t7.t42.t14))
% 0.68/0.91  (step t24.t7.t42.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t42.t12 t24.t7.t42.t15))
% 0.68/0.91  (step t24.t7.t42.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t42.t9 t24.t7.t42.t16 a5))
% 0.68/0.91  (step t24.t7.t42.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t7.t42.t3 a7 t24.t7.t42.t8 t24.t7.t42.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t42.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t42.t18))
% 0.68/0.91  (step t24.t7.t42.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t7.t42.t18))
% 0.68/0.91  (step t24.t7.t42.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t7.t42.t20 t24.t7.t42.t21))
% 0.68/0.91  (step t24.t7.t42.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t7.t42.t19 t24.t7.t42.t22))
% 0.68/0.91  (step t24.t7.t42.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t42.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t7.t42.t23 t24.t7.t42.t24))
% 0.68/0.91  (step t24.t7.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t43 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t7.t41 t24.t7.t42))
% 0.68/0.91  (step t24.t7.t44 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t45 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t45.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t45.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t45.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t45.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t45.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t45.t3 t24.t7.t45.t4))
% 0.68/0.91  (step t24.t7.t45.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t45.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t45.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t45.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t45.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t7.t45.t7.t2))
% 0.68/0.91  (step t24.t7.t45.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t45.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t45.t6 t24.t7.t45.t7))
% 0.68/0.91  (step t24.t7.t45.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t7.t45.t5 t24.t7.t45.t8))
% 0.68/0.91  (step t24.t7.t45.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t45.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t7.t45.t9 t24.t7.t45.t10))
% 0.68/0.91  (step t24.t7.t45.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t45.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t7.t45.t11 t24.t7.t45.t12))
% 0.68/0.91  (step t24.t7.t45 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t7.t46 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t7.t44 t24.t7.t45))
% 0.68/0.91  (step t24.t7.t47 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t7.t43 t24.t7.t46))
% 0.68/0.91  (step t24.t7.t48 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t7.t40 t24.t7.t47 a8))
% 0.68/0.91  (step t24.t7.t49 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t50 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t51 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t7.t51.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t51.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t7.t51.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t51 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t7.t52 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t7.t50 t24.t7.t51))
% 0.68/0.91  (step t24.t7.t53 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t7.t49 t24.t7.t52 a6))
% 0.68/0.91  (step t24.t7.t54 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t7.t55 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t56 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t56.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t56.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t56.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t56.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t7.t56.t5 (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)))))) :rule resolution :premises (t24.t7.t56.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t56.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t7.t56.t5))
% 0.68/0.91  (step t24.t7.t56.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t7.t56.t5))
% 0.68/0.91  (step t24.t7.t56.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t56.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t7.t56.t7 t24.t7.t56.t8))
% 0.68/0.91  (step t24.t7.t56.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t7.t56.t6 t24.t7.t56.t9))
% 0.68/0.91  (step t24.t7.t56.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t56.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t7.t56.t10 t24.t7.t56.t11))
% 0.68/0.91  (step t24.t7.t56.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t56.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t56.t12 t24.t7.t56.t13))
% 0.68/0.91  (step t24.t7.t56 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t7.t57 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t7.t55 t24.t7.t56))
% 0.68/0.91  (step t24.t7.t58 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t59 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t59.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t59.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t59.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t59.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t7.t59.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t59.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t7.t59.t4 t24.t7.t59.t5))
% 0.68/0.91  (step t24.t7.t59.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t7.t59.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t7.t59.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t59.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t7.t59.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t59.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t7.t59.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t7.t59.t8.t3 t24.t7.t59.t8.t4))
% 0.68/0.91  (step t24.t7.t59.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t7.t59.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t7.t59.t7 t24.t7.t59.t8))
% 0.68/0.91  (step t24.t7.t59.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t7.t59.t6 t24.t7.t59.t9))
% 0.68/0.91  (step t24.t7.t59.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t7.t59.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t7.t59.t10 t24.t7.t59.t11))
% 0.68/0.91  (step t24.t7.t59.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t59.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 (t24.t7.t59.t12 t24.t7.t59.t13))
% 0.68/0.91  (step t24.t7.t59.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t59.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 (t24.t7.t59.t14 t24.t7.t59.t15))
% 0.68/0.91  (step t24.t7.t59.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t59.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t7.t59.t16 t24.t7.t59.t17))
% 0.68/0.91  (step t24.t7.t59 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t7.t60 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t7.t58 t24.t7.t59))
% 0.68/0.91  (step t24.t7.t61 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t7.t57 t24.t7.t60))
% 0.68/0.91  (step t24.t7.t62 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t7.t54 t24.t7.t61 a5))
% 0.68/0.91  (step t24.t7.t63 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t34 t24.t7.t39 t24.t7.t48 a7 t24.t7.t53 t24.t7.t62 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t64 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t7.t63))
% 0.68/0.91  (step t24.t7.t65 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t7.t63))
% 0.68/0.91  (step t24.t7.t66 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t7.t64 t24.t7.t65))
% 0.68/0.91  (step t24.t7.t67 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t7.t33 t24.t7.t66))
% 0.68/0.91  (step t24.t7.t68 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t7.t69 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t7.t70 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t7.t70.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t7.t70.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t7.t70.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t7.t70.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t7.t70.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t70.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t7.t70.t2.t2 t24.t7.t70.t2.t3))
% 0.68/0.91  (step t24.t7.t70.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t70.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t7.t70.t2.t4 t24.t7.t70.t2.t5))
% 0.68/0.91  (step t24.t7.t70.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t7.t70.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t70.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t7.t70.t2 t24.t7.t70.t3))
% 0.68/0.91  (step t24.t7.t70.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t7.t70.t4))
% 0.68/0.91  (step t24.t7.t70.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t70.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t7.t70.t5 t24.t7.t70.t6))
% 0.68/0.91  (step t24.t7.t70 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t7.t71 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t7.t72 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t70 t24.t7.t71))
% 0.68/0.91  (step t24.t7.t73 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t7.t69 t24.t7.t72))
% 0.68/0.91  (step t24.t7.t74 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t7.t68 t24.t7.t73))
% 0.68/0.91  (step t24.t7.t75 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t7.t67 t24.t7.t74))
% 0.68/0.91  (step t24.t7.t76 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t7.t32 t24.t7.t75 a10))
% 0.68/0.91  (step t24.t7.t77 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t7.t4 t24.t7.t13 t24.t7.t22 t24.t7.t31 t24.t7.t76 t24.t7.t39 t24.t7.t48 a7 t24.t7.t53 t24.t7.t62 a4 a3 a2))
% 0.68/0.91  (step t24.t7.t78 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule and :premises (t24.t7.t77))
% 0.68/0.91  (step t24.t7.t79 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t7.t80 (cl (= (@ tptp.iimplies Q) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t24.t7.t78 t24.t7.t79))
% 0.68/0.91  (step t24.t7.t81 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t7.t82 (cl (= (@ (@ tptp.iimplies Q) P) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P))) :rule cong :premises (t24.t7.t80 t24.t7.t81))
% 0.68/0.91  (step t24.t7.t83 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t7.t84 (cl (= (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) :rule cong :premises (t24.t7.t82 t24.t7.t83))
% 0.68/0.91  (step t24.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t8 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))))) :rule cong :premises (t24.t6 t24.t7))
% 0.68/0.91  (step t24.t9 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.68/0.91  (anchor :step t24.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t10.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.91  (step t24.t10.t5 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t10.t6 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t24.t10.t4 t24.t10.t5))
% 0.68/0.91  (step t24.t10.t7 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.91  (step t24.t10.t8 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t24.t10.t6 t24.t10.t7))
% 0.68/0.91  (step t24.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t10.t10 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t10.t8 t24.t10.t9))
% 0.68/0.91  (step t24.t10.t11 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t10.t12 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t10.t10 t24.t10.t11))
% 0.68/0.91  (step t24.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t11 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t9 t24.t10))
% 0.68/0.91  (step t24.t12 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t8 t24.t11))
% 0.68/0.91  (step t24.t13 (cl (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t5 t24.t12 a14))
% 0.68/0.91  (step t24.t14 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t15 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t7.t7.t9 t24.t16.t7.t7.t10))
% 0.68/0.91  (step t24.t16.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t16.t7.t7.t8 t24.t16.t7.t7.t11 a9))
% 0.68/0.91  (step t24.t16.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t7.t7.t15.t5 t24.t16.t7.t7.t15.t6))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t7.t7.t15.t4 t24.t16.t7.t7.t15.t7 a6))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t24.t16.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t7.t7.t15.t11.t5))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t7.t7.t15.t11.t5))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t7.t7.t15.t11.t7 t24.t16.t7.t7.t15.t11.t8))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t16.t7.t7.t15.t11.t6 t24.t16.t7.t7.t15.t11.t9))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t16.t7.t7.t15.t11.t10 t24.t16.t7.t7.t15.t11.t11))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t7.t15.t11.t12 t24.t16.t7.t7.t15.t11.t13))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t16.t7.t7.t15.t10 t24.t16.t7.t7.t15.t11))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t16.t7.t7.t15.t14.t4 t24.t16.t7.t7.t15.t14.t5))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t7.t7.t15.t14.t8.t3 t24.t16.t7.t7.t15.t14.t8.t4))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t7.t7.t15.t14.t7 t24.t16.t7.t7.t15.t14.t8))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t7.t7.t15.t14.t6 t24.t16.t7.t7.t15.t14.t9))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t16.t7.t7.t15.t14.t10 t24.t16.t7.t7.t15.t14.t11))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.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 (t24.t16.t7.t7.t15.t14.t12 t24.t16.t7.t7.t15.t14.t13))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.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 (t24.t16.t7.t7.t15.t14.t14 t24.t16.t7.t7.t15.t14.t15))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t7.t15.t14.t16 t24.t16.t7.t7.t15.t14.t17))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t7.t7.t15.t13 t24.t16.t7.t7.t15.t14))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t7.t7.t15.t12 t24.t16.t7.t7.t15.t15))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t7.t7.t15.t9 t24.t16.t7.t7.t15.t16 a5))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t7.t7.t15.t3 a7 t24.t16.t7.t7.t15.t8 t24.t16.t7.t7.t15.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t7.t7.t15.t18))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t16.t7.t7.t15.t18))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t16.t7.t7.t15.t20 t24.t16.t7.t7.t15.t21))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t16.t7.t7.t15.t19 t24.t16.t7.t7.t15.t22))
% 0.68/0.91  (step t24.t16.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t7.t15.t23 t24.t16.t7.t7.t15.t24))
% 0.68/0.91  (step t24.t16.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t16.t7.t7.t14 t24.t16.t7.t7.t15))
% 0.68/0.91  (step t24.t16.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t7.t7.t18.t3 t24.t16.t7.t7.t18.t4))
% 0.68/0.91  (step t24.t16.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t16.t7.t7.t18.t7.t2))
% 0.68/0.91  (step t24.t16.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t7.t7.t18.t6 t24.t16.t7.t7.t18.t7))
% 0.68/0.91  (step t24.t16.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t7.t7.t18.t5 t24.t16.t7.t7.t18.t8))
% 0.68/0.91  (step t24.t16.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t7.t18.t9 t24.t16.t7.t7.t18.t10))
% 0.68/0.91  (step t24.t16.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t16.t7.t7.t18.t11 t24.t16.t7.t7.t18.t12))
% 0.68/0.91  (step t24.t16.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t16.t7.t7.t17 t24.t16.t7.t7.t18))
% 0.68/0.91  (step t24.t16.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t16.t7.t7.t16 t24.t16.t7.t7.t19))
% 0.68/0.91  (step t24.t16.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t16.t7.t7.t13 t24.t16.t7.t7.t20 a8))
% 0.68/0.91  (step t24.t16.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t7.t7.t23 t24.t16.t7.t7.t24))
% 0.68/0.91  (step t24.t16.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t7.t7.t22 t24.t16.t7.t7.t25 a6))
% 0.68/0.91  (step t24.t16.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t7.t7.t29.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t7.t7.t29.t5))
% 0.68/0.91  (step t24.t16.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t7.t7.t29.t5))
% 0.68/0.91  (step t24.t16.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t7.t7.t29.t7 t24.t16.t7.t7.t29.t8))
% 0.68/0.91  (step t24.t16.t7.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t16.t7.t7.t29.t6 t24.t16.t7.t7.t29.t9))
% 0.68/0.91  (step t24.t16.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t7.t29.t10 t24.t16.t7.t7.t29.t11))
% 0.68/0.91  (step t24.t16.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t7.t29.t12 t24.t16.t7.t7.t29.t13))
% 0.68/0.91  (step t24.t16.t7.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t16.t7.t7.t28 t24.t16.t7.t7.t29))
% 0.68/0.91  (step t24.t16.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.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)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t7.t7.t32.t4 t24.t16.t7.t7.t32.t5))
% 0.68/0.91  (step t24.t16.t7.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t7.t7.t32.t8.t3 t24.t16.t7.t7.t32.t8.t4))
% 0.68/0.91  (step t24.t16.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t16.t7.t7.t32.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 (t24.t16.t7.t7.t32.t7 t24.t16.t7.t7.t32.t8))
% 0.68/0.91  (step t24.t16.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t7.t7.t32.t6 t24.t16.t7.t7.t32.t9))
% 0.68/0.91  (step t24.t16.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t7.t32.t10 t24.t16.t7.t7.t32.t11))
% 0.68/0.91  (step t24.t16.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t16.t7.t7.t32.t12 t24.t16.t7.t7.t32.t13))
% 0.68/0.91  (step t24.t16.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t7.t32.t14 t24.t16.t7.t7.t32.t15))
% 0.68/0.91  (step t24.t16.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t16.t7.t7.t32.t16 t24.t16.t7.t7.t32.t17))
% 0.68/0.91  (step t24.t16.t7.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t7.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t7.t7.t31 t24.t16.t7.t7.t32))
% 0.68/0.91  (step t24.t16.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t7.t7.t30 t24.t16.t7.t7.t33))
% 0.68/0.91  (step t24.t16.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t7.t7.t27 t24.t16.t7.t7.t34 a5))
% 0.68/0.91  (step t24.t16.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t16.t7.t7.t7 t24.t16.t7.t7.t12 t24.t16.t7.t7.t21 a7 t24.t16.t7.t7.t26 t24.t16.t7.t7.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t16.t7.t7.t36))
% 0.68/0.91  (step t24.t16.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t16.t7.t7.t36))
% 0.68/0.91  (step t24.t16.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t7.t7.t37 t24.t16.t7.t7.t38))
% 0.68/0.91  (step t24.t16.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t16.t7.t7.t6 t24.t16.t7.t7.t39))
% 0.68/0.91  (step t24.t16.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t16.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t16.t7.t7.t43.t2.t2 t24.t16.t7.t7.t43.t2.t3))
% 0.68/0.91  (step t24.t16.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t16.t7.t7.t43.t2.t4 t24.t16.t7.t7.t43.t2.t5))
% 0.68/0.91  (step t24.t16.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t16.t7.t7.t43.t2 t24.t16.t7.t7.t43.t3))
% 0.68/0.91  (step t24.t16.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t16.t7.t7.t43.t4))
% 0.68/0.91  (step t24.t16.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t16.t7.t7.t43.t5 t24.t16.t7.t7.t43.t6))
% 0.68/0.91  (step t24.t16.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t7.t7.t43 t24.t16.t7.t7.t44))
% 0.68/0.91  (step t24.t16.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t7.t7.t42 t24.t16.t7.t7.t45))
% 0.68/0.91  (step t24.t16.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t16.t7.t7.t41 t24.t16.t7.t7.t46))
% 0.68/0.91  (step t24.t16.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t16.t7.t7.t40 t24.t16.t7.t7.t47))
% 0.68/0.91  (step t24.t16.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t16.t7.t7.t5 t24.t16.t7.t7.t48 a10))
% 0.68/0.91  (step t24.t16.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t7.t7.t4 t24.t16.t7.t7.t49 t24.t16.t7.t7.t12 t24.t16.t7.t7.t21 a7 t24.t16.t7.t7.t26 t24.t16.t7.t7.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t7.t7.t50))
% 0.68/0.91  (step t24.t16.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t16.t7.t7.t51 t24.t16.t7.t7.t52))
% 0.68/0.91  (step t24.t16.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t16.t7.t7.t53 t24.t16.t7.t7.t54))
% 0.68/0.91  (step t24.t16.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t7.t55 t24.t16.t7.t7.t56))
% 0.68/0.91  (step t24.t16.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t16.t7.t6 t24.t16.t7.t7))
% 0.68/0.91  (step t24.t16.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t16.t7.t10.t4 t24.t16.t7.t10.t5))
% 0.68/0.91  (step t24.t16.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t16.t7.t10.t6 t24.t16.t7.t10.t7))
% 0.68/0.91  (step t24.t16.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t10.t8 t24.t16.t7.t10.t9))
% 0.68/0.91  (step t24.t16.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t16.t7.t10.t10 t24.t16.t7.t10.t11))
% 0.68/0.91  (step t24.t16.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t16.t7.t9 t24.t16.t7.t10))
% 0.68/0.91  (step t24.t16.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t16.t7.t8 t24.t16.t7.t11))
% 0.68/0.91  (step t24.t16.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t16.t7.t5 t24.t16.t7.t12 a11))
% 0.68/0.91  (step t24.t16.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t7.t18 t24.t16.t7.t19))
% 0.68/0.91  (step t24.t16.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t16.t7.t17 t24.t16.t7.t20 a9))
% 0.68/0.91  (step t24.t16.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t7.t24.t5 t24.t16.t7.t24.t6))
% 0.68/0.91  (step t24.t16.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t7.t24.t4 t24.t16.t7.t24.t7 a6))
% 0.68/0.91  (step t24.t16.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t7.t24.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t7.t24.t11.t5))
% 0.68/0.91  (step t24.t16.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t7.t24.t11.t5))
% 0.68/0.91  (step t24.t16.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t7.t24.t11.t7 t24.t16.t7.t24.t11.t8))
% 0.68/0.91  (step t24.t16.t7.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t16.t7.t24.t11.t6 t24.t16.t7.t24.t11.t9))
% 0.68/0.91  (step t24.t16.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t24.t11.t10 t24.t16.t7.t24.t11.t11))
% 0.68/0.91  (step t24.t16.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t24.t11.t12 t24.t16.t7.t24.t11.t13))
% 0.68/0.91  (step t24.t16.t7.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t16.t7.t24.t10 t24.t16.t7.t24.t11))
% 0.68/0.91  (step t24.t16.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.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)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t7.t24.t14.t4 t24.t16.t7.t24.t14.t5))
% 0.68/0.91  (step t24.t16.t7.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t7.t24.t14.t8.t3 t24.t16.t7.t24.t14.t8.t4))
% 0.68/0.91  (step t24.t16.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t16.t7.t24.t14.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 (t24.t16.t7.t24.t14.t7 t24.t16.t7.t24.t14.t8))
% 0.68/0.91  (step t24.t16.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t7.t24.t14.t6 t24.t16.t7.t24.t14.t9))
% 0.68/0.91  (step t24.t16.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t24.t14.t10 t24.t16.t7.t24.t14.t11))
% 0.68/0.91  (step t24.t16.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t16.t7.t24.t14.t12 t24.t16.t7.t24.t14.t13))
% 0.68/0.91  (step t24.t16.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t24.t14.t14 t24.t16.t7.t24.t14.t15))
% 0.68/0.91  (step t24.t16.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t16.t7.t24.t14.t16 t24.t16.t7.t24.t14.t17))
% 0.68/0.91  (step t24.t16.t7.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t7.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t7.t24.t13 t24.t16.t7.t24.t14))
% 0.68/0.91  (step t24.t16.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t7.t24.t12 t24.t16.t7.t24.t15))
% 0.68/0.91  (step t24.t16.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t7.t24.t9 t24.t16.t7.t24.t16 a5))
% 0.68/0.91  (step t24.t16.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t16.t7.t24.t3 a7 t24.t16.t7.t24.t8 t24.t16.t7.t24.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t7.t24.t18))
% 0.68/0.91  (step t24.t16.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t16.t7.t24.t18))
% 0.68/0.91  (step t24.t16.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t16.t7.t24.t20 t24.t16.t7.t24.t21))
% 0.68/0.91  (step t24.t16.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t16.t7.t24.t19 t24.t16.t7.t24.t22))
% 0.68/0.91  (step t24.t16.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t24.t23 t24.t16.t7.t24.t24))
% 0.68/0.91  (step t24.t16.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t16.t7.t23 t24.t16.t7.t24))
% 0.68/0.91  (step t24.t16.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t7.t27.t3 t24.t16.t7.t27.t4))
% 0.68/0.91  (step t24.t16.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t16.t7.t27.t7.t2))
% 0.68/0.91  (step t24.t16.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t7.t27.t6 t24.t16.t7.t27.t7))
% 0.68/0.91  (step t24.t16.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t7.t27.t5 t24.t16.t7.t27.t8))
% 0.68/0.91  (step t24.t16.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t27.t9 t24.t16.t7.t27.t10))
% 0.68/0.91  (step t24.t16.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t16.t7.t27.t11 t24.t16.t7.t27.t12))
% 0.68/0.91  (step t24.t16.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t16.t7.t26 t24.t16.t7.t27))
% 0.68/0.91  (step t24.t16.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t16.t7.t25 t24.t16.t7.t28))
% 0.68/0.91  (step t24.t16.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t16.t7.t22 t24.t16.t7.t29 a8))
% 0.68/0.91  (step t24.t16.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t7.t32 t24.t16.t7.t33))
% 0.68/0.91  (step t24.t16.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t7.t31 t24.t16.t7.t34 a6))
% 0.68/0.91  (step t24.t16.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t38.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t7.t38.t5 (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)))))) :rule resolution :premises (t24.t16.t7.t38.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t7.t38.t5))
% 0.68/0.91  (step t24.t16.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t7.t38.t5))
% 0.68/0.91  (step t24.t16.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t7.t38.t7 t24.t16.t7.t38.t8))
% 0.68/0.91  (step t24.t16.t7.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t16.t7.t38.t6 t24.t16.t7.t38.t9))
% 0.68/0.91  (step t24.t16.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t16.t7.t38.t10 t24.t16.t7.t38.t11))
% 0.68/0.91  (step t24.t16.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t38.t12 t24.t16.t7.t38.t13))
% 0.68/0.91  (step t24.t16.t7.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t16.t7.t37 t24.t16.t7.t38))
% 0.68/0.91  (step t24.t16.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t16.t7.t41.t4 t24.t16.t7.t41.t5))
% 0.68/0.91  (step t24.t16.t7.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t16.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t7.t41.t8.t3 t24.t16.t7.t41.t8.t4))
% 0.68/0.91  (step t24.t16.t7.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t7.t41.t7 t24.t16.t7.t41.t8))
% 0.68/0.91  (step t24.t16.t7.t41.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t7.t41.t6 t24.t16.t7.t41.t9))
% 0.68/0.91  (step t24.t16.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t16.t7.t41.t10 t24.t16.t7.t41.t11))
% 0.68/0.91  (step t24.t16.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t41.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 (t24.t16.t7.t41.t12 t24.t16.t7.t41.t13))
% 0.68/0.91  (step t24.t16.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t41.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 (t24.t16.t7.t41.t14 t24.t16.t7.t41.t15))
% 0.68/0.91  (step t24.t16.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t7.t41.t16 t24.t16.t7.t41.t17))
% 0.68/0.91  (step t24.t16.t7.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t7.t40 t24.t16.t7.t41))
% 0.68/0.91  (step t24.t16.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t7.t39 t24.t16.t7.t42))
% 0.68/0.91  (step t24.t16.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t7.t36 t24.t16.t7.t43 a5))
% 0.68/0.91  (step t24.t16.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t7.t16 t24.t16.t7.t21 t24.t16.t7.t30 a7 t24.t16.t7.t35 t24.t16.t7.t44 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t16.t7.t45))
% 0.68/0.91  (step t24.t16.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t16.t7.t45))
% 0.68/0.91  (step t24.t16.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t7.t46 t24.t16.t7.t47))
% 0.68/0.91  (step t24.t16.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t16.t7.t15 t24.t16.t7.t48))
% 0.68/0.91  (step t24.t16.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t16.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t16.t7.t52.t2.t2 t24.t16.t7.t52.t2.t3))
% 0.68/0.91  (step t24.t16.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t16.t7.t52.t2.t4 t24.t16.t7.t52.t2.t5))
% 0.68/0.91  (step t24.t16.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t16.t7.t52.t2 t24.t16.t7.t52.t3))
% 0.68/0.91  (step t24.t16.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t16.t7.t52.t4))
% 0.68/0.91  (step t24.t16.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t16.t7.t52.t5 t24.t16.t7.t52.t6))
% 0.68/0.91  (step t24.t16.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t16.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t7.t52 t24.t16.t7.t53))
% 0.68/0.91  (step t24.t16.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t7.t51 t24.t16.t7.t54))
% 0.68/0.91  (step t24.t16.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t16.t7.t50 t24.t16.t7.t55))
% 0.68/0.91  (step t24.t16.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t16.t7.t49 t24.t16.t7.t56))
% 0.68/0.91  (step t24.t16.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t16.t7.t14 t24.t16.t7.t57 a10))
% 0.68/0.91  (step t24.t16.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t7.t4 t24.t16.t7.t13 t24.t16.t7.t58 t24.t16.t7.t21 t24.t16.t7.t30 a7 t24.t16.t7.t35 t24.t16.t7.t44 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t7.t59))
% 0.68/0.91  (step t24.t16.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t16.t7.t59))
% 0.68/0.91  (step t24.t16.t7.t62 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t16.t7.t61 t24.t16.t7.t62))
% 0.68/0.91  (step t24.t16.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t16.t7.t60 t24.t16.t7.t63))
% 0.68/0.91  (step t24.t16.t7.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t24.t16.t7.t61 t24.t16.t7.t65))
% 0.68/0.91  (step t24.t16.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t24.t16.t7.t64 t24.t16.t7.t66))
% 0.68/0.91  (step t24.t16.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t24.t16.t7.t67 t24.t16.t7.t68))
% 0.68/0.91  (step t24.t16.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t24.t16.t6 t24.t16.t7))
% 0.68/0.91  (step t24.t16.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.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)
% 0.68/0.91  (step t24.t16.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t10.t4 t24.t16.t10.t5))
% 0.68/0.91  (step t24.t16.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t24.t16.t10.t8.t3 t24.t16.t10.t8.t4))
% 0.68/0.91  (step t24.t16.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t16.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t16.t10.t7 t24.t16.t10.t8))
% 0.68/0.91  (step t24.t16.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t16.t10.t6 t24.t16.t10.t9))
% 0.68/0.91  (step t24.t16.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t24.t16.t10.t10 t24.t16.t10.t11))
% 0.68/0.91  (step t24.t16.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t24.t16.t10.t14.t2 t24.t16.t10.t14.t3))
% 0.68/0.91  (step t24.t16.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t16.t10.t13 t24.t16.t10.t14))
% 0.68/0.91  (step t24.t16.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t16.t10.t12 t24.t16.t10.t15))
% 0.68/0.91  (step t24.t16.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t24.t16.t10.t16 t24.t16.t10.t17))
% 0.68/0.91  (step t24.t16.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t24.t16.t10.t18 t24.t16.t10.t19))
% 0.68/0.91  (step t24.t16.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t24.t16.t9 t24.t16.t10))
% 0.68/0.91  (step t24.t16.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t24.t16.t8 t24.t16.t11))
% 0.68/0.91  (step t24.t16.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t24.t16.t5 t24.t16.t12 a12))
% 0.68/0.91  (step t24.t16.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t16.t9 t24.t16.t16.t10))
% 0.68/0.91  (step t24.t16.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t16.t16.t8 t24.t16.t16.t11 a9))
% 0.68/0.91  (step t24.t16.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t16.t15.t5 t24.t16.t16.t15.t6))
% 0.68/0.91  (step t24.t16.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t16.t15.t4 t24.t16.t16.t15.t7 a6))
% 0.68/0.91  (step t24.t16.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t16.t15.t11.t5 (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)))))) :rule resolution :premises (t24.t16.t16.t15.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t16.t15.t11.t5))
% 0.68/0.91  (step t24.t16.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t16.t15.t11.t5))
% 0.68/0.91  (step t24.t16.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t16.t15.t11.t7 t24.t16.t16.t15.t11.t8))
% 0.68/0.91  (step t24.t16.t16.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t16.t16.t15.t11.t6 t24.t16.t16.t15.t11.t9))
% 0.68/0.91  (step t24.t16.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t16.t16.t15.t11.t10 t24.t16.t16.t15.t11.t11))
% 0.68/0.91  (step t24.t16.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t16.t15.t11.t12 t24.t16.t16.t15.t11.t13))
% 0.68/0.91  (step t24.t16.t16.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t16.t16.t15.t10 t24.t16.t16.t15.t11))
% 0.68/0.91  (step t24.t16.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t16.t16.t15.t14.t4 t24.t16.t16.t15.t14.t5))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t16.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t16.t15.t14.t8.t3 t24.t16.t16.t15.t14.t8.t4))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t16.t15.t14.t7 t24.t16.t16.t15.t14.t8))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t16.t15.t14.t6 t24.t16.t16.t15.t14.t9))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t16.t16.t15.t14.t10 t24.t16.t16.t15.t14.t11))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t15.t14.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 (t24.t16.t16.t15.t14.t12 t24.t16.t16.t15.t14.t13))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t14.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 (t24.t16.t16.t15.t14.t14 t24.t16.t16.t15.t14.t15))
% 0.68/0.91  (step t24.t16.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t16.t15.t14.t16 t24.t16.t16.t15.t14.t17))
% 0.68/0.91  (step t24.t16.t16.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t16.t15.t13 t24.t16.t16.t15.t14))
% 0.68/0.91  (step t24.t16.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t16.t15.t12 t24.t16.t16.t15.t15))
% 0.68/0.91  (step t24.t16.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t16.t15.t9 t24.t16.t16.t15.t16 a5))
% 0.68/0.91  (step t24.t16.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t16.t15.t3 a7 t24.t16.t16.t15.t8 t24.t16.t16.t15.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t16.t15.t18))
% 0.68/0.91  (step t24.t16.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t16.t16.t15.t18))
% 0.68/0.91  (step t24.t16.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t16.t16.t15.t20 t24.t16.t16.t15.t21))
% 0.68/0.91  (step t24.t16.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t16.t16.t15.t19 t24.t16.t16.t15.t22))
% 0.68/0.91  (step t24.t16.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t16.t16.t15.t23 t24.t16.t16.t15.t24))
% 0.68/0.91  (step t24.t16.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t16.t16.t14 t24.t16.t16.t15))
% 0.68/0.91  (step t24.t16.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t16.t18.t3 t24.t16.t16.t18.t4))
% 0.68/0.91  (step t24.t16.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t16.t16.t18.t7.t2))
% 0.68/0.91  (step t24.t16.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t16.t18.t6 t24.t16.t16.t18.t7))
% 0.68/0.91  (step t24.t16.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t16.t18.t5 t24.t16.t16.t18.t8))
% 0.68/0.91  (step t24.t16.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t16.t16.t18.t9 t24.t16.t16.t18.t10))
% 0.68/0.91  (step t24.t16.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t16.t16.t18.t11 t24.t16.t16.t18.t12))
% 0.68/0.91  (step t24.t16.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t16.t16.t17 t24.t16.t16.t18))
% 0.68/0.91  (step t24.t16.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t16.t16.t16 t24.t16.t16.t19))
% 0.68/0.91  (step t24.t16.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t16.t16.t13 t24.t16.t16.t20 a8))
% 0.68/0.91  (step t24.t16.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t16.t23 t24.t16.t16.t24))
% 0.68/0.91  (step t24.t16.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t16.t22 t24.t16.t16.t25 a6))
% 0.68/0.91  (step t24.t16.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t16.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t16.t29.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t16.t29.t5))
% 0.68/0.91  (step t24.t16.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t16.t29.t5))
% 0.68/0.91  (step t24.t16.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t16.t29.t7 t24.t16.t16.t29.t8))
% 0.68/0.91  (step t24.t16.t16.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t16.t16.t29.t6 t24.t16.t16.t29.t9))
% 0.68/0.91  (step t24.t16.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t16.t16.t29.t10 t24.t16.t16.t29.t11))
% 0.68/0.91  (step t24.t16.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t16.t16.t29.t12 t24.t16.t16.t29.t13))
% 0.68/0.91  (step t24.t16.t16.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t16.t16.t28 t24.t16.t16.t29))
% 0.68/0.91  (step t24.t16.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.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)
% 0.68/0.91  (step t24.t16.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t16.t32.t4 t24.t16.t16.t32.t5))
% 0.68/0.91  (step t24.t16.t16.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t16.t32.t8.t3 t24.t16.t16.t32.t8.t4))
% 0.68/0.91  (step t24.t16.t16.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t16.t16.t32.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 (t24.t16.t16.t32.t7 t24.t16.t16.t32.t8))
% 0.68/0.91  (step t24.t16.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t16.t32.t6 t24.t16.t16.t32.t9))
% 0.68/0.91  (step t24.t16.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t16.t16.t32.t10 t24.t16.t16.t32.t11))
% 0.68/0.91  (step t24.t16.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t16.t16.t32.t12 t24.t16.t16.t32.t13))
% 0.68/0.91  (step t24.t16.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t16.t16.t32.t14 t24.t16.t16.t32.t15))
% 0.68/0.91  (step t24.t16.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t16.t16.t32.t16 t24.t16.t16.t32.t17))
% 0.68/0.91  (step t24.t16.t16.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t16.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t16.t31 t24.t16.t16.t32))
% 0.68/0.91  (step t24.t16.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t16.t30 t24.t16.t16.t33))
% 0.68/0.91  (step t24.t16.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t16.t27 t24.t16.t16.t34 a5))
% 0.68/0.91  (step t24.t16.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t16.t16.t7 t24.t16.t16.t12 t24.t16.t16.t21 a7 t24.t16.t16.t26 t24.t16.t16.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t16.t16.t36))
% 0.68/0.91  (step t24.t16.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t16.t16.t36))
% 0.68/0.91  (step t24.t16.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t16.t37 t24.t16.t16.t38))
% 0.68/0.91  (step t24.t16.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t16.t16.t6 t24.t16.t16.t39))
% 0.68/0.91  (step t24.t16.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t16.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t16.t16.t43.t2.t2 t24.t16.t16.t43.t2.t3))
% 0.68/0.91  (step t24.t16.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t16.t16.t43.t2.t4 t24.t16.t16.t43.t2.t5))
% 0.68/0.91  (step t24.t16.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t16.t16.t43.t2 t24.t16.t16.t43.t3))
% 0.68/0.91  (step t24.t16.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t16.t16.t43.t4))
% 0.68/0.91  (step t24.t16.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t16.t16.t43.t5 t24.t16.t16.t43.t6))
% 0.68/0.91  (step t24.t16.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t16.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t16.t43 t24.t16.t16.t44))
% 0.68/0.91  (step t24.t16.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t16.t42 t24.t16.t16.t45))
% 0.68/0.91  (step t24.t16.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t16.t16.t41 t24.t16.t16.t46))
% 0.68/0.91  (step t24.t16.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t16.t16.t40 t24.t16.t16.t47))
% 0.68/0.91  (step t24.t16.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t16.t16.t5 t24.t16.t16.t48 a10))
% 0.68/0.91  (step t24.t16.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t16.t4 t24.t16.t16.t49 t24.t16.t16.t12 t24.t16.t16.t21 a7 t24.t16.t16.t26 t24.t16.t16.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t16.t50))
% 0.68/0.91  (step t24.t16.t16.t52 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t16.t16.t51 t24.t16.t16.t52))
% 0.68/0.91  (step t24.t16.t16.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t16.t16.t53 t24.t16.t16.t54))
% 0.68/0.91  (step t24.t16.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t16.t16.t55 t24.t16.t16.t56))
% 0.68/0.91  (step t24.t16.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t16.t15 t24.t16.t16))
% 0.68/0.91  (step t24.t16.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t19.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t16.t19.t4 t24.t16.t19.t5))
% 0.68/0.91  (step t24.t16.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t16.t19.t6 t24.t16.t19.t7))
% 0.68/0.91  (step t24.t16.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t16.t19.t8 t24.t16.t19.t9))
% 0.68/0.91  (step t24.t16.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t16.t19.t10 t24.t16.t19.t11))
% 0.68/0.91  (step t24.t16.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t16.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t16.t18 t24.t16.t19))
% 0.68/0.91  (step t24.t16.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t16.t17 t24.t16.t20))
% 0.68/0.91  (step t24.t16.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t16.t14 t24.t16.t21 a11))
% 0.68/0.91  (step t24.t16.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t16.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t27 t24.t16.t28))
% 0.68/0.91  (step t24.t16.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t16.t26 t24.t16.t29 a9))
% 0.68/0.91  (step t24.t16.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t33.t5 t24.t16.t33.t6))
% 0.68/0.91  (step t24.t16.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t33.t4 t24.t16.t33.t7 a6))
% 0.68/0.91  (step t24.t16.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t33.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t33.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t33.t11.t5))
% 0.68/0.91  (step t24.t16.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t33.t11.t5))
% 0.68/0.91  (step t24.t16.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t33.t11.t7 t24.t16.t33.t11.t8))
% 0.68/0.91  (step t24.t16.t33.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t16.t33.t11.t6 t24.t16.t33.t11.t9))
% 0.68/0.91  (step t24.t16.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t16.t33.t11.t10 t24.t16.t33.t11.t11))
% 0.68/0.91  (step t24.t16.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t16.t33.t11.t12 t24.t16.t33.t11.t13))
% 0.68/0.91  (step t24.t16.t33.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t16.t33.t10 t24.t16.t33.t11))
% 0.68/0.91  (step t24.t16.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.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)
% 0.68/0.91  (step t24.t16.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t33.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t33.t14.t4 t24.t16.t33.t14.t5))
% 0.68/0.91  (step t24.t16.t33.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t33.t14.t8.t3 t24.t16.t33.t14.t8.t4))
% 0.68/0.91  (step t24.t16.t33.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t16.t33.t14.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 (t24.t16.t33.t14.t7 t24.t16.t33.t14.t8))
% 0.68/0.91  (step t24.t16.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t33.t14.t6 t24.t16.t33.t14.t9))
% 0.68/0.91  (step t24.t16.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t16.t33.t14.t10 t24.t16.t33.t14.t11))
% 0.68/0.91  (step t24.t16.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t33.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t16.t33.t14.t12 t24.t16.t33.t14.t13))
% 0.68/0.91  (step t24.t16.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t16.t33.t14.t14 t24.t16.t33.t14.t15))
% 0.68/0.91  (step t24.t16.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t16.t33.t14.t16 t24.t16.t33.t14.t17))
% 0.68/0.91  (step t24.t16.t33.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t16.t33.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t33.t13 t24.t16.t33.t14))
% 0.68/0.91  (step t24.t16.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t33.t12 t24.t16.t33.t15))
% 0.68/0.91  (step t24.t16.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t33.t9 t24.t16.t33.t16 a5))
% 0.68/0.91  (step t24.t16.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t16.t33.t3 a7 t24.t16.t33.t8 t24.t16.t33.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t33.t18))
% 0.68/0.91  (step t24.t16.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t16.t33.t18))
% 0.68/0.91  (step t24.t16.t33.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t16.t33.t20 t24.t16.t33.t21))
% 0.68/0.91  (step t24.t16.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t16.t33.t19 t24.t16.t33.t22))
% 0.68/0.91  (step t24.t16.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t16.t33.t23 t24.t16.t33.t24))
% 0.68/0.91  (step t24.t16.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t16.t32 t24.t16.t33))
% 0.68/0.91  (step t24.t16.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t36.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t36.t3 t24.t16.t36.t4))
% 0.68/0.91  (step t24.t16.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t16.t36.t7.t2))
% 0.68/0.91  (step t24.t16.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t36.t6 t24.t16.t36.t7))
% 0.68/0.91  (step t24.t16.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t16.t36.t5 t24.t16.t36.t8))
% 0.68/0.91  (step t24.t16.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t16.t36.t9 t24.t16.t36.t10))
% 0.68/0.91  (step t24.t16.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t16.t36.t11 t24.t16.t36.t12))
% 0.68/0.91  (step t24.t16.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t16.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t16.t35 t24.t16.t36))
% 0.68/0.91  (step t24.t16.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t16.t34 t24.t16.t37))
% 0.68/0.91  (step t24.t16.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t16.t31 t24.t16.t38 a8))
% 0.68/0.91  (step t24.t16.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t16.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t42.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t16.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t16.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t16.t41 t24.t16.t42))
% 0.68/0.91  (step t24.t16.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t16.t40 t24.t16.t43 a6))
% 0.68/0.91  (step t24.t16.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t16.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t47.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t47.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t47.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t16.t47.t5 (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)))))) :rule resolution :premises (t24.t16.t47.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t16.t47.t5))
% 0.68/0.91  (step t24.t16.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t16.t47.t5))
% 0.68/0.91  (step t24.t16.t47.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t16.t47.t7 t24.t16.t47.t8))
% 0.68/0.91  (step t24.t16.t47.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t16.t47.t6 t24.t16.t47.t9))
% 0.68/0.91  (step t24.t16.t47.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t47.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t16.t47.t10 t24.t16.t47.t11))
% 0.68/0.91  (step t24.t16.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t47.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t47.t12 t24.t16.t47.t13))
% 0.68/0.91  (step t24.t16.t47 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t16.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t16.t46 t24.t16.t47))
% 0.68/0.91  (step t24.t16.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t50.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t50.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t50.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t16.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t50.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t16.t50.t4 t24.t16.t50.t5))
% 0.68/0.91  (step t24.t16.t50.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t16.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t16.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t16.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t16.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t16.t50.t8.t3 t24.t16.t50.t8.t4))
% 0.68/0.91  (step t24.t16.t50.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t16.t50.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t16.t50.t7 t24.t16.t50.t8))
% 0.68/0.91  (step t24.t16.t50.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t16.t50.t6 t24.t16.t50.t9))
% 0.68/0.91  (step t24.t16.t50.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t16.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t16.t50.t10 t24.t16.t50.t11))
% 0.68/0.91  (step t24.t16.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t50.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 (t24.t16.t50.t12 t24.t16.t50.t13))
% 0.68/0.91  (step t24.t16.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t50.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 (t24.t16.t50.t14 t24.t16.t50.t15))
% 0.68/0.91  (step t24.t16.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t16.t50.t16 t24.t16.t50.t17))
% 0.68/0.91  (step t24.t16.t50 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t16.t51 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t16.t49 t24.t16.t50))
% 0.68/0.91  (step t24.t16.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t16.t48 t24.t16.t51))
% 0.68/0.91  (step t24.t16.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t16.t45 t24.t16.t52 a5))
% 0.68/0.91  (step t24.t16.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t16.t25 t24.t16.t30 t24.t16.t39 a7 t24.t16.t44 t24.t16.t53 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t16.t54))
% 0.68/0.91  (step t24.t16.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t16.t54))
% 0.68/0.91  (step t24.t16.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t16.t55 t24.t16.t56))
% 0.68/0.91  (step t24.t16.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t16.t24 t24.t16.t57))
% 0.68/0.91  (step t24.t16.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t16.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t16.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t16.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t16.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t16.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t16.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t16.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t16.t61.t2.t2 t24.t16.t61.t2.t3))
% 0.68/0.91  (step t24.t16.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t16.t61.t2.t4 t24.t16.t61.t2.t5))
% 0.68/0.91  (step t24.t16.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t16.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t16.t61.t2 t24.t16.t61.t3))
% 0.68/0.91  (step t24.t16.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t16.t61.t4))
% 0.68/0.91  (step t24.t16.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t16.t61.t5 t24.t16.t61.t6))
% 0.68/0.91  (step t24.t16.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t16.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t16.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t61 t24.t16.t62))
% 0.68/0.91  (step t24.t16.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t16.t60 t24.t16.t63))
% 0.68/0.91  (step t24.t16.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t16.t59 t24.t16.t64))
% 0.68/0.91  (step t24.t16.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t16.t58 t24.t16.t65))
% 0.68/0.91  (step t24.t16.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t16.t23 t24.t16.t66 a10))
% 0.68/0.91  (step t24.t16.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t16.t4 t24.t16.t13 t24.t16.t22 t24.t16.t67 t24.t16.t30 t24.t16.t39 a7 t24.t16.t44 t24.t16.t53 a4 a3 a2))
% 0.68/0.91  (step t24.t16.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t24.t16.t68))
% 0.68/0.91  (step t24.t16.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t16.t68))
% 0.68/0.91  (step t24.t16.t71 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t16.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t16.t70 t24.t16.t71))
% 0.68/0.91  (step t24.t16.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t16.t69 t24.t16.t72))
% 0.68/0.91  (step t24.t16.t74 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t16.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t24.t16.t70 t24.t16.t74))
% 0.68/0.91  (step t24.t16.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t24.t16.t73 t24.t16.t75))
% 0.68/0.91  (step t24.t16.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t16.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t24.t16.t76 t24.t16.t77))
% 0.68/0.91  (step t24.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t17 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t24.t15 t24.t16))
% 0.68/0.91  (step t24.t18 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t19.t4 (cl (= (lambda ((U (-> $$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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule refl)
% 0.68/0.91  (step t24.t19.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t19.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t19.t4 t24.t19.t5))
% 0.68/0.91  (step t24.t19.t7 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t19.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t19.t8.t1 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t19.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t19.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t19.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t24.t19.t8.t3))
% 0.68/0.91  (step t24.t19.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.68/0.91  (step t24.t19.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t24.t19.t8.t4 t24.t19.t8.t5))
% 0.68/0.91  (step t24.t19.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t19.t9 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t24.t19.t7 t24.t19.t8))
% 0.68/0.91  (step t24.t19.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t24.t19.t6 t24.t19.t9))
% 0.68/0.91  (step t24.t19.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t19.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t24.t19.t10 t24.t19.t11))
% 0.68/0.91  (step t24.t19.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t19.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t19.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t19.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.68/0.91  (step t24.t19.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t19.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t24.t19.t14.t2 t24.t19.t14.t3))
% 0.68/0.91  (step t24.t19.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t19.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t24.t19.t13 t24.t19.t14))
% 0.68/0.91  (step t24.t19.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t24.t19.t12 t24.t19.t15))
% 0.68/0.91  (step t24.t19.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t19.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t24.t19.t16 t24.t19.t17))
% 0.68/0.91  (step t24.t19.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t19.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t24.t19.t18 t24.t19.t19))
% 0.68/0.91  (step t24.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.91  (step t24.t20 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t24.t18 t24.t19))
% 0.68/0.91  (step t24.t21 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t24.t17 t24.t20))
% 0.68/0.91  (step t24.t22 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t24.t14 t24.t21 a13))
% 0.68/0.91  (step t24.t23 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t24 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t25.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t25.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t25.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t25.t7.t9 t24.t25.t7.t10))
% 0.68/0.91  (step t24.t25.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t25.t7.t8 t24.t25.t7.t11 a9))
% 0.68/0.91  (step t24.t25.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t25.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t25.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t25.t7.t15.t5 t24.t25.t7.t15.t6))
% 0.68/0.91  (step t24.t25.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t25.t7.t15.t4 t24.t25.t7.t15.t7 a6))
% 0.68/0.91  (step t24.t25.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.91  (step t24.t25.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t25.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t25.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t25.t7.t15.t11.t5))
% 0.68/0.91  (step t24.t25.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t25.t7.t15.t11.t5))
% 0.68/0.91  (step t24.t25.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t25.t7.t15.t11.t7 t24.t25.t7.t15.t11.t8))
% 0.68/0.91  (step t24.t25.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t25.t7.t15.t11.t6 t24.t25.t7.t15.t11.t9))
% 0.68/0.91  (step t24.t25.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t25.t7.t15.t11.t10 t24.t25.t7.t15.t11.t11))
% 0.68/0.91  (step t24.t25.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t25.t7.t15.t11.t12 t24.t25.t7.t15.t11.t13))
% 0.68/0.91  (step t24.t25.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t25.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t25.t7.t15.t10 t24.t25.t7.t15.t11))
% 0.68/0.91  (step t24.t25.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.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)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t25.t7.t15.t14.t4 t24.t25.t7.t15.t14.t5))
% 0.68/0.91  (step t24.t25.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t25.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t25.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t25.t7.t15.t14.t8.t3 t24.t25.t7.t15.t14.t8.t4))
% 0.68/0.91  (step t24.t25.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.91  (step t24.t25.t7.t15.t14.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 (t24.t25.t7.t15.t14.t7 t24.t25.t7.t15.t14.t8))
% 0.68/0.91  (step t24.t25.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t25.t7.t15.t14.t6 t24.t25.t7.t15.t14.t9))
% 0.68/0.91  (step t24.t25.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t25.t7.t15.t14.t10 t24.t25.t7.t15.t14.t11))
% 0.68/0.91  (step t24.t25.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t25.t7.t15.t14.t12 t24.t25.t7.t15.t14.t13))
% 0.68/0.91  (step t24.t25.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t25.t7.t15.t14.t14 t24.t25.t7.t15.t14.t15))
% 0.68/0.91  (step t24.t25.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t25.t7.t15.t14.t16 t24.t25.t7.t15.t14.t17))
% 0.68/0.91  (step t24.t25.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.91  (step t24.t25.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t25.t7.t15.t13 t24.t25.t7.t15.t14))
% 0.68/0.91  (step t24.t25.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t25.t7.t15.t12 t24.t25.t7.t15.t15))
% 0.68/0.91  (step t24.t25.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t25.t7.t15.t9 t24.t25.t7.t15.t16 a5))
% 0.68/0.91  (step t24.t25.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t25.t7.t15.t3 a7 t24.t25.t7.t15.t8 t24.t25.t7.t15.t17 a4 a3 a2))
% 0.68/0.91  (step t24.t25.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t25.t7.t15.t18))
% 0.68/0.91  (step t24.t25.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t25.t7.t15.t18))
% 0.68/0.91  (step t24.t25.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t25.t7.t15.t20 t24.t25.t7.t15.t21))
% 0.68/0.91  (step t24.t25.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t25.t7.t15.t19 t24.t25.t7.t15.t22))
% 0.68/0.91  (step t24.t25.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t25.t7.t15.t23 t24.t25.t7.t15.t24))
% 0.68/0.91  (step t24.t25.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t25.t7.t14 t24.t25.t7.t15))
% 0.68/0.91  (step t24.t25.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t25.t7.t18.t3 t24.t25.t7.t18.t4))
% 0.68/0.91  (step t24.t25.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t25.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t25.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t25.t7.t18.t7.t2))
% 0.68/0.91  (step t24.t25.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t25.t7.t18.t6 t24.t25.t7.t18.t7))
% 0.68/0.91  (step t24.t25.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t25.t7.t18.t5 t24.t25.t7.t18.t8))
% 0.68/0.91  (step t24.t25.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t25.t7.t18.t9 t24.t25.t7.t18.t10))
% 0.68/0.91  (step t24.t25.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t25.t7.t18.t11 t24.t25.t7.t18.t12))
% 0.68/0.91  (step t24.t25.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t25.t7.t17 t24.t25.t7.t18))
% 0.68/0.91  (step t24.t25.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t25.t7.t16 t24.t25.t7.t19))
% 0.68/0.91  (step t24.t25.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t25.t7.t13 t24.t25.t7.t20 a8))
% 0.68/0.91  (step t24.t25.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.91  (step t24.t25.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t25.t7.t23 t24.t25.t7.t24))
% 0.68/0.91  (step t24.t25.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t25.t7.t22 t24.t25.t7.t25 a6))
% 0.68/0.91  (step t24.t25.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.91  (step t24.t25.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.91  (step t24.t25.t7.t29.t5 (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)))))) :rule resolution :premises (t24.t25.t7.t29.t4 a4 a3 a2))
% 0.68/0.91  (step t24.t25.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t25.t7.t29.t5))
% 0.68/0.91  (step t24.t25.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t25.t7.t29.t5))
% 0.68/0.91  (step t24.t25.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t25.t7.t29.t7 t24.t25.t7.t29.t8))
% 0.68/0.91  (step t24.t25.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t25.t7.t29.t6 t24.t25.t7.t29.t9))
% 0.68/0.91  (step t24.t25.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t25.t7.t29.t10 t24.t25.t7.t29.t11))
% 0.68/0.91  (step t24.t25.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t25.t7.t29.t12 t24.t25.t7.t29.t13))
% 0.68/0.91  (step t24.t25.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t25.t7.t28 t24.t25.t7.t29))
% 0.68/0.91  (step t24.t25.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t25.t7.t32.t4 t24.t25.t7.t32.t5))
% 0.68/0.91  (step t24.t25.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.91  (anchor :step t24.t25.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.91  (step t24.t25.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t25.t7.t32.t8.t3 t24.t25.t7.t32.t8.t4))
% 0.68/0.91  (step t24.t25.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t25.t7.t32.t7 t24.t25.t7.t32.t8))
% 0.68/0.91  (step t24.t25.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t25.t7.t32.t6 t24.t25.t7.t32.t9))
% 0.68/0.91  (step t24.t25.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t25.t7.t32.t10 t24.t25.t7.t32.t11))
% 0.68/0.91  (step t24.t25.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t32.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 (t24.t25.t7.t32.t12 t24.t25.t7.t32.t13))
% 0.68/0.91  (step t24.t25.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t32.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 (t24.t25.t7.t32.t14 t24.t25.t7.t32.t15))
% 0.68/0.91  (step t24.t25.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t25.t7.t32.t16 t24.t25.t7.t32.t17))
% 0.68/0.91  (step t24.t25.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t25.t7.t31 t24.t25.t7.t32))
% 0.68/0.91  (step t24.t25.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t25.t7.t30 t24.t25.t7.t33))
% 0.68/0.91  (step t24.t25.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t25.t7.t27 t24.t25.t7.t34 a5))
% 0.68/0.91  (step t24.t25.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t25.t7.t7 t24.t25.t7.t12 t24.t25.t7.t21 a7 t24.t25.t7.t26 t24.t25.t7.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t25.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t25.t7.t36))
% 0.68/0.91  (step t24.t25.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t25.t7.t36))
% 0.68/0.91  (step t24.t25.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t25.t7.t37 t24.t25.t7.t38))
% 0.68/0.91  (step t24.t25.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t25.t7.t6 t24.t25.t7.t39))
% 0.68/0.91  (step t24.t25.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.91  (anchor :step t24.t25.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.91  (step t24.t25.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t25.t7.t43.t2.t2 t24.t25.t7.t43.t2.t3))
% 0.68/0.91  (step t24.t25.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t25.t7.t43.t2.t4 t24.t25.t7.t43.t2.t5))
% 0.68/0.91  (step t24.t25.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t25.t7.t43.t2 t24.t25.t7.t43.t3))
% 0.68/0.91  (step t24.t25.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t25.t7.t43.t4))
% 0.68/0.91  (step t24.t25.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t25.t7.t43.t5 t24.t25.t7.t43.t6))
% 0.68/0.91  (step t24.t25.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.91  (step t24.t25.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t25.t7.t43 t24.t25.t7.t44))
% 0.68/0.91  (step t24.t25.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t25.t7.t42 t24.t25.t7.t45))
% 0.68/0.91  (step t24.t25.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t25.t7.t41 t24.t25.t7.t46))
% 0.68/0.91  (step t24.t25.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t25.t7.t40 t24.t25.t7.t47))
% 0.68/0.91  (step t24.t25.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t25.t7.t5 t24.t25.t7.t48 a10))
% 0.68/0.91  (step t24.t25.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t25.t7.t4 t24.t25.t7.t49 t24.t25.t7.t12 t24.t25.t7.t21 a7 t24.t25.t7.t26 t24.t25.t7.t35 a4 a3 a2))
% 0.68/0.91  (step t24.t25.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t25.t7.t50))
% 0.68/0.91  (step t24.t25.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t25.t7.t51 t24.t25.t7.t52))
% 0.68/0.91  (step t24.t25.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t25.t7.t53 t24.t25.t7.t54))
% 0.68/0.91  (step t24.t25.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t25.t7.t55 t24.t25.t7.t56))
% 0.68/0.91  (step t24.t25.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.91  (step t24.t25.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t25.t6 t24.t25.t7))
% 0.68/0.91  (step t24.t25.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.91  (anchor :step t24.t25.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.91  (step t24.t25.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.91  (step t24.t25.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t25.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.91  (step t24.t25.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t25.t10.t4 t24.t25.t10.t5))
% 0.68/0.91  (step t24.t25.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t25.t10.t6 t24.t25.t10.t7))
% 0.68/0.91  (step t24.t25.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.91  (step t24.t25.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t25.t10.t8 t24.t25.t10.t9))
% 0.68/0.91  (step t24.t25.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.91  (step t24.t25.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t25.t10.t10 t24.t25.t10.t11))
% 0.68/0.91  (step t24.t25.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.91  (step t24.t25.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t25.t9 t24.t25.t10))
% 0.68/0.92  (step t24.t25.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t25.t8 t24.t25.t11))
% 0.68/0.92  (step t24.t25.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t25.t5 t24.t25.t12 a11))
% 0.68/0.92  (step t24.t25.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t25.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t24.t25.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t24.t25.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t25.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t24.t25.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t25.t18 t24.t25.t19))
% 0.68/0.92  (step t24.t25.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t25.t17 t24.t25.t20 a9))
% 0.68/0.92  (step t24.t25.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t25.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t25.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t24.t25.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t25.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t24.t25.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t24.t25.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t25.t24.t5 t24.t25.t24.t6))
% 0.68/0.92  (step t24.t25.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t25.t24.t4 t24.t25.t24.t7 a6))
% 0.68/0.92  (step t24.t25.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t25.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t25.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t24.t25.t24.t11.t5 (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)))))) :rule resolution :premises (t24.t25.t24.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t24.t25.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t25.t24.t11.t5))
% 0.68/0.92  (step t24.t25.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t25.t24.t11.t5))
% 0.68/0.92  (step t24.t25.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t25.t24.t11.t7 t24.t25.t24.t11.t8))
% 0.68/0.92  (step t24.t25.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t25.t24.t11.t6 t24.t25.t24.t11.t9))
% 0.68/0.92  (step t24.t25.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t25.t24.t11.t10 t24.t25.t24.t11.t11))
% 0.68/0.92  (step t24.t25.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t25.t24.t11.t12 t24.t25.t24.t11.t13))
% 0.68/0.92  (step t24.t25.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t25.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t25.t24.t10 t24.t25.t24.t11))
% 0.68/0.92  (step t24.t25.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t25.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t25.t24.t14.t4 t24.t25.t24.t14.t5))
% 0.68/0.92  (step t24.t25.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t24.t25.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t25.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t25.t24.t14.t8.t3 t24.t25.t24.t14.t8.t4))
% 0.68/0.92  (step t24.t25.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t24.t25.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t25.t24.t14.t7 t24.t25.t24.t14.t8))
% 0.68/0.92  (step t24.t25.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t25.t24.t14.t6 t24.t25.t24.t14.t9))
% 0.68/0.92  (step t24.t25.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t25.t24.t14.t10 t24.t25.t24.t14.t11))
% 0.68/0.92  (step t24.t25.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t24.t14.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 (t24.t25.t24.t14.t12 t24.t25.t24.t14.t13))
% 0.68/0.92  (step t24.t25.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t14.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 (t24.t25.t24.t14.t14 t24.t25.t24.t14.t15))
% 0.68/0.92  (step t24.t25.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t25.t24.t14.t16 t24.t25.t24.t14.t17))
% 0.68/0.92  (step t24.t25.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t24.t25.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t25.t24.t13 t24.t25.t24.t14))
% 0.68/0.92  (step t24.t25.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t25.t24.t12 t24.t25.t24.t15))
% 0.68/0.92  (step t24.t25.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t25.t24.t9 t24.t25.t24.t16 a5))
% 0.68/0.92  (step t24.t25.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t25.t24.t3 a7 t24.t25.t24.t8 t24.t25.t24.t17 a4 a3 a2))
% 0.68/0.92  (step t24.t25.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t25.t24.t18))
% 0.68/0.92  (step t24.t25.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t25.t24.t18))
% 0.68/0.92  (step t24.t25.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t25.t24.t20 t24.t25.t24.t21))
% 0.68/0.92  (step t24.t25.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t25.t24.t19 t24.t25.t24.t22))
% 0.68/0.92  (step t24.t25.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t25.t24.t23 t24.t25.t24.t24))
% 0.68/0.92  (step t24.t25.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t25.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t25.t23 t24.t25.t24))
% 0.68/0.92  (step t24.t25.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t25.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t25.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t24.t25.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t25.t27.t3 t24.t25.t27.t4))
% 0.68/0.92  (step t24.t25.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t25.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t25.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t25.t27.t7.t2))
% 0.68/0.92  (step t24.t25.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t24.t25.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t25.t27.t6 t24.t25.t27.t7))
% 0.68/0.92  (step t24.t25.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t25.t27.t5 t24.t25.t27.t8))
% 0.68/0.92  (step t24.t25.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t25.t27.t9 t24.t25.t27.t10))
% 0.68/0.92  (step t24.t25.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t25.t27.t11 t24.t25.t27.t12))
% 0.68/0.92  (step t24.t25.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t24.t25.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t25.t26 t24.t25.t27))
% 0.68/0.92  (step t24.t25.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t25.t25 t24.t25.t28))
% 0.68/0.92  (step t24.t25.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t25.t22 t24.t25.t29 a8))
% 0.68/0.92  (step t24.t25.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t25.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t24.t25.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t25.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t24.t25.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t24.t25.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t25.t32 t24.t25.t33))
% 0.68/0.92  (step t24.t25.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t25.t31 t24.t25.t34 a6))
% 0.68/0.92  (step t24.t25.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t25.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t25.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t24.t25.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t25.t38.t4 a4 a3 a2))
% 0.68/0.92  (step t24.t25.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t25.t38.t5))
% 0.68/0.92  (step t24.t25.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t25.t38.t5))
% 0.68/0.92  (step t24.t25.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t25.t38.t7 t24.t25.t38.t8))
% 0.68/0.92  (step t24.t25.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t25.t38.t6 t24.t25.t38.t9))
% 0.68/0.92  (step t24.t25.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t25.t38.t10 t24.t25.t38.t11))
% 0.68/0.92  (step t24.t25.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t25.t38.t12 t24.t25.t38.t13))
% 0.68/0.92  (step t24.t25.t38 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t24.t25.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t25.t37 t24.t25.t38))
% 0.68/0.92  (step t24.t25.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t25.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t41.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)
% 0.68/0.92  (step t24.t25.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t25.t41.t4 t24.t25.t41.t5))
% 0.68/0.92  (step t24.t25.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t25.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t25.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t25.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t25.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t24.t25.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t25.t41.t8.t3 t24.t25.t41.t8.t4))
% 0.68/0.92  (step t24.t25.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t24.t25.t41.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 (t24.t25.t41.t7 t24.t25.t41.t8))
% 0.68/0.92  (step t24.t25.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t25.t41.t6 t24.t25.t41.t9))
% 0.68/0.92  (step t24.t25.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t25.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t25.t41.t10 t24.t25.t41.t11))
% 0.68/0.92  (step t24.t25.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t25.t41.t12 t24.t25.t41.t13))
% 0.68/0.92  (step t24.t25.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t25.t41.t14 t24.t25.t41.t15))
% 0.68/0.92  (step t24.t25.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t25.t41.t16 t24.t25.t41.t17))
% 0.68/0.92  (step t24.t25.t41 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t24.t25.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t25.t40 t24.t25.t41))
% 0.68/0.92  (step t24.t25.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t25.t39 t24.t25.t42))
% 0.68/0.92  (step t24.t25.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t25.t36 t24.t25.t43 a5))
% 0.68/0.92  (step t24.t25.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t25.t16 t24.t25.t21 t24.t25.t30 a7 t24.t25.t35 t24.t25.t44 a4 a3 a2))
% 0.68/0.92  (step t24.t25.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t25.t45))
% 0.68/0.92  (step t24.t25.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t25.t45))
% 0.68/0.92  (step t24.t25.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t25.t46 t24.t25.t47))
% 0.68/0.92  (step t24.t25.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t25.t15 t24.t25.t48))
% 0.68/0.92  (step t24.t25.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t24.t25.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t25.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t25.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t24.t25.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t24.t25.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t25.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t24.t25.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t25.t52.t2.t2 t24.t25.t52.t2.t3))
% 0.68/0.92  (step t24.t25.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t25.t52.t2.t4 t24.t25.t52.t2.t5))
% 0.68/0.92  (step t24.t25.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t24.t25.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t25.t52.t2 t24.t25.t52.t3))
% 0.68/0.92  (step t24.t25.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t25.t52.t4))
% 0.68/0.92  (step t24.t25.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t25.t52.t5 t24.t25.t52.t6))
% 0.68/0.92  (step t24.t25.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t24.t25.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t24.t25.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t25.t52 t24.t25.t53))
% 0.68/0.92  (step t24.t25.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t25.t51 t24.t25.t54))
% 0.68/0.92  (step t24.t25.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t25.t50 t24.t25.t55))
% 0.68/0.92  (step t24.t25.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t25.t49 t24.t25.t56))
% 0.68/0.92  (step t24.t25.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t25.t14 t24.t25.t57 a10))
% 0.68/0.92  (step t24.t25.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t25.t4 t24.t25.t13 t24.t25.t58 t24.t25.t21 t24.t25.t30 a7 t24.t25.t35 t24.t25.t44 a4 a3 a2))
% 0.68/0.92  (step t24.t25.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t25.t59))
% 0.68/0.92  (step t24.t25.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t25.t59))
% 0.68/0.92  (step t24.t25.t62 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t25.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t25.t61 t24.t25.t62))
% 0.68/0.92  (step t24.t25.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t25.t60 t24.t25.t63))
% 0.68/0.92  (step t24.t25.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t24.t25.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t24.t25.t61 t24.t25.t65))
% 0.68/0.92  (step t24.t25.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t24.t25.t64 t24.t25.t66))
% 0.68/0.92  (step t24.t25.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t25.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t24.t25.t67 t24.t25.t68))
% 0.68/0.92  (step t24.t25 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t26 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t24.t24 t24.t25))
% 0.68/0.92  (step t24.t27 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.92  (anchor :step t24.t28 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t28.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t28.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t24.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t28.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t24.t28.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t28.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t28.t4 t24.t28.t5))
% 0.68/0.92  (step t24.t28.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t28.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t28.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t28.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t28.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t28.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t24.t28.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t24.t28.t8.t3 t24.t28.t8.t4))
% 0.68/0.92  (step t24.t28.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t24.t28.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t28.t7 t24.t28.t8))
% 0.68/0.92  (step t24.t28.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t24.t28.t6 t24.t28.t9))
% 0.68/0.92  (step t24.t28.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t28.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t24.t28.t10 t24.t28.t11))
% 0.68/0.92  (step t24.t28.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t28.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t28.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t28.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.92  (step t24.t28.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t28.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t24.t28.t14.t2 t24.t28.t14.t3))
% 0.68/0.92  (step t24.t28.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t24.t28.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t28.t13 t24.t28.t14))
% 0.68/0.92  (step t24.t28.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t24.t28.t12 t24.t28.t15))
% 0.68/0.92  (step t24.t28.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t28.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t24.t28.t16 t24.t28.t17))
% 0.68/0.92  (step t24.t28.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t28.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t24.t28.t18 t24.t28.t19))
% 0.68/0.92  (step t24.t28 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t24.t29 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t24.t27 t24.t28))
% 0.68/0.92  (step t24.t30 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t24.t26 t24.t29))
% 0.68/0.92  (step t24.t31 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t24.t23 t24.t30 a12))
% 0.68/0.92  (step t24.t32 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t33 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t34.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t24.t34.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t24.t34.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t34.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t24.t34.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t24.t34.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t34.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t24.t34.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t34.t9 t24.t34.t10))
% 0.68/0.92  (step t24.t34.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t34.t8 t24.t34.t11 a9))
% 0.68/0.92  (step t24.t34.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t34.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t24.t34.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t34.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t24.t34.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t24.t34.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t34.t15.t5 t24.t34.t15.t6))
% 0.68/0.92  (step t24.t34.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t34.t15.t4 t24.t34.t15.t7 a6))
% 0.68/0.92  (step t24.t34.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t34.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t24.t34.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t34.t15.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t24.t34.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t34.t15.t11.t5))
% 0.68/0.92  (step t24.t34.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t34.t15.t11.t5))
% 0.68/0.92  (step t24.t34.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t34.t15.t11.t7 t24.t34.t15.t11.t8))
% 0.68/0.92  (step t24.t34.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t34.t15.t11.t6 t24.t34.t15.t11.t9))
% 0.68/0.92  (step t24.t34.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t34.t15.t11.t10 t24.t34.t15.t11.t11))
% 0.68/0.92  (step t24.t34.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t34.t15.t11.t12 t24.t34.t15.t11.t13))
% 0.68/0.92  (step t24.t34.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t24.t34.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t34.t15.t10 t24.t34.t15.t11))
% 0.68/0.92  (step t24.t34.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.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)
% 0.68/0.92  (step t24.t34.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t34.t15.t14.t4 t24.t34.t15.t14.t5))
% 0.68/0.92  (step t24.t34.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t34.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t34.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t34.t15.t14.t8.t3 t24.t34.t15.t14.t8.t4))
% 0.68/0.92  (step t24.t34.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t24.t34.t15.t14.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 (t24.t34.t15.t14.t7 t24.t34.t15.t14.t8))
% 0.68/0.92  (step t24.t34.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t34.t15.t14.t6 t24.t34.t15.t14.t9))
% 0.68/0.92  (step t24.t34.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t34.t15.t14.t10 t24.t34.t15.t14.t11))
% 0.68/0.92  (step t24.t34.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t34.t15.t14.t12 t24.t34.t15.t14.t13))
% 0.68/0.92  (step t24.t34.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t34.t15.t14.t14 t24.t34.t15.t14.t15))
% 0.68/0.92  (step t24.t34.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t34.t15.t14.t16 t24.t34.t15.t14.t17))
% 0.68/0.92  (step t24.t34.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t24.t34.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t34.t15.t13 t24.t34.t15.t14))
% 0.68/0.92  (step t24.t34.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t34.t15.t12 t24.t34.t15.t15))
% 0.68/0.92  (step t24.t34.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t34.t15.t9 t24.t34.t15.t16 a5))
% 0.68/0.92  (step t24.t34.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t34.t15.t3 a7 t24.t34.t15.t8 t24.t34.t15.t17 a4 a3 a2))
% 0.68/0.92  (step t24.t34.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t34.t15.t18))
% 0.68/0.92  (step t24.t34.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t34.t15.t18))
% 0.68/0.92  (step t24.t34.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t34.t15.t20 t24.t34.t15.t21))
% 0.68/0.92  (step t24.t34.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t34.t15.t19 t24.t34.t15.t22))
% 0.68/0.92  (step t24.t34.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t34.t15.t23 t24.t34.t15.t24))
% 0.68/0.92  (step t24.t34.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t34.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t34.t14 t24.t34.t15))
% 0.68/0.92  (step t24.t34.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t34.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t24.t34.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t34.t18.t3 t24.t34.t18.t4))
% 0.68/0.92  (step t24.t34.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t34.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t34.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t34.t18.t7.t2))
% 0.68/0.92  (step t24.t34.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t24.t34.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t34.t18.t6 t24.t34.t18.t7))
% 0.68/0.92  (step t24.t34.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t34.t18.t5 t24.t34.t18.t8))
% 0.68/0.92  (step t24.t34.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t34.t18.t9 t24.t34.t18.t10))
% 0.68/0.92  (step t24.t34.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t34.t18.t11 t24.t34.t18.t12))
% 0.68/0.92  (step t24.t34.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t24.t34.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t34.t17 t24.t34.t18))
% 0.68/0.92  (step t24.t34.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t34.t16 t24.t34.t19))
% 0.68/0.92  (step t24.t34.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t34.t13 t24.t34.t20 a8))
% 0.68/0.92  (step t24.t34.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t34.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t24.t34.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t34.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t24.t34.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t24.t34.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t34.t23 t24.t34.t24))
% 0.68/0.92  (step t24.t34.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t34.t22 t24.t34.t25 a6))
% 0.68/0.92  (step t24.t34.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t34.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t24.t34.t29.t5 (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)))))) :rule resolution :premises (t24.t34.t29.t4 a4 a3 a2))
% 0.68/0.92  (step t24.t34.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t34.t29.t5))
% 0.68/0.92  (step t24.t34.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t34.t29.t5))
% 0.68/0.92  (step t24.t34.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t34.t29.t7 t24.t34.t29.t8))
% 0.68/0.92  (step t24.t34.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t34.t29.t6 t24.t34.t29.t9))
% 0.68/0.92  (step t24.t34.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t34.t29.t10 t24.t34.t29.t11))
% 0.68/0.92  (step t24.t34.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t34.t29.t12 t24.t34.t29.t13))
% 0.68/0.92  (step t24.t34.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t34.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t34.t28 t24.t34.t29))
% 0.68/0.92  (step t24.t34.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t24.t34.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t34.t32.t4 t24.t34.t32.t5))
% 0.68/0.92  (step t24.t34.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t24.t34.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t34.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t34.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t34.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t24.t34.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t34.t32.t8.t3 t24.t34.t32.t8.t4))
% 0.68/0.92  (step t24.t34.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t24.t34.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t34.t32.t7 t24.t34.t32.t8))
% 0.68/0.92  (step t24.t34.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t34.t32.t6 t24.t34.t32.t9))
% 0.68/0.92  (step t24.t34.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t34.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t34.t32.t10 t24.t34.t32.t11))
% 0.68/0.92  (step t24.t34.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t32.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 (t24.t34.t32.t12 t24.t34.t32.t13))
% 0.68/0.92  (step t24.t34.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t32.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 (t24.t34.t32.t14 t24.t34.t32.t15))
% 0.68/0.92  (step t24.t34.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t34.t32.t16 t24.t34.t32.t17))
% 0.68/0.92  (step t24.t34.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t24.t34.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t34.t31 t24.t34.t32))
% 0.68/0.92  (step t24.t34.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t34.t30 t24.t34.t33))
% 0.68/0.92  (step t24.t34.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t34.t27 t24.t34.t34 a5))
% 0.68/0.92  (step t24.t34.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t34.t7 t24.t34.t12 t24.t34.t21 a7 t24.t34.t26 t24.t34.t35 a4 a3 a2))
% 0.68/0.92  (step t24.t34.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t34.t36))
% 0.68/0.92  (step t24.t34.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t34.t36))
% 0.68/0.92  (step t24.t34.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t34.t37 t24.t34.t38))
% 0.68/0.92  (step t24.t34.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t34.t6 t24.t34.t39))
% 0.68/0.92  (step t24.t34.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t24.t34.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t34.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t34.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t24.t34.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t24.t34.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t34.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t24.t34.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t34.t43.t2.t2 t24.t34.t43.t2.t3))
% 0.68/0.92  (step t24.t34.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t34.t43.t2.t4 t24.t34.t43.t2.t5))
% 0.68/0.92  (step t24.t34.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t24.t34.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t34.t43.t2 t24.t34.t43.t3))
% 0.68/0.92  (step t24.t34.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t34.t43.t4))
% 0.68/0.92  (step t24.t34.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t34.t43.t5 t24.t34.t43.t6))
% 0.68/0.92  (step t24.t34.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t24.t34.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t24.t34.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t34.t43 t24.t34.t44))
% 0.68/0.92  (step t24.t34.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t34.t42 t24.t34.t45))
% 0.68/0.92  (step t24.t34.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t34.t41 t24.t34.t46))
% 0.68/0.92  (step t24.t34.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t34.t40 t24.t34.t47))
% 0.68/0.92  (step t24.t34.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t34.t5 t24.t34.t48 a10))
% 0.68/0.92  (step t24.t34.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t34.t4 t24.t34.t49 t24.t34.t12 t24.t34.t21 a7 t24.t34.t26 t24.t34.t35 a4 a3 a2))
% 0.68/0.92  (step t24.t34.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t24.t34.t50))
% 0.68/0.92  (step t24.t34.t52 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t34.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t24.t34.t51 t24.t34.t52))
% 0.68/0.92  (step t24.t34.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t24.t34.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t24.t34.t53 t24.t34.t54))
% 0.68/0.92  (step t24.t34.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t34.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t24.t34.t55 t24.t34.t56))
% 0.68/0.92  (step t24.t34 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t35 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t24.t33 t24.t34))
% 0.68/0.92  (step t24.t36 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t24.t37 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t37.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t37.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t24.t37.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t37.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t37.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t24.t37.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t24.t37.t4 t24.t37.t5))
% 0.68/0.92  (step t24.t37.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t37.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t24.t37.t6 t24.t37.t7))
% 0.68/0.92  (step t24.t37.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t37.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t24.t37.t8 t24.t37.t9))
% 0.68/0.92  (step t24.t37.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t24.t37.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t24.t37.t10 t24.t37.t11))
% 0.68/0.92  (step t24.t37 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t24.t38 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t24.t36 t24.t37))
% 0.68/0.92  (step t24.t39 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t24.t35 t24.t38))
% 0.68/0.92  (step t24.t40 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t24.t32 t24.t39 a11))
% 0.68/0.92  (step t24.t41 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t42 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t24.t43 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t24.t44 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t45 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t24.t46 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t24.t47 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t45 t24.t46))
% 0.68/0.92  (step t24.t48 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t24.t44 t24.t47 a9))
% 0.68/0.92  (step t24.t49 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t50 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t24.t51 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t51.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t51.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t51.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t24.t51.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t51.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t24.t51.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t24.t51.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t51.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t24.t51.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t51.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t24.t51.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t51.t5 t24.t51.t6))
% 0.68/0.92  (step t24.t51.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t51.t4 t24.t51.t7 a6))
% 0.68/0.92  (step t24.t51.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t51.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t51.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t51.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t51.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t51.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t51.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t24.t51.t11.t5 (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)))))) :rule resolution :premises (t24.t51.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t24.t51.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t51.t11.t5))
% 0.68/0.92  (step t24.t51.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t51.t11.t5))
% 0.68/0.92  (step t24.t51.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t51.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t51.t11.t7 t24.t51.t11.t8))
% 0.68/0.92  (step t24.t51.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t24.t51.t11.t6 t24.t51.t11.t9))
% 0.68/0.92  (step t24.t51.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t51.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t24.t51.t11.t10 t24.t51.t11.t11))
% 0.68/0.92  (step t24.t51.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t51.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t24.t51.t11.t12 t24.t51.t11.t13))
% 0.68/0.92  (step t24.t51.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t51.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t24.t51.t10 t24.t51.t11))
% 0.68/0.92  (step t24.t51.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t51.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t51.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t51.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t51.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t51.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t24.t51.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t51.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t24.t51.t14.t4 t24.t51.t14.t5))
% 0.68/0.92  (step t24.t51.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t24.t51.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t51.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t51.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t51.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t24.t51.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t24.t51.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t51.t14.t8.t3 t24.t51.t14.t8.t4))
% 0.68/0.92  (step t24.t51.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t24.t51.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t51.t14.t7 t24.t51.t14.t8))
% 0.68/0.92  (step t24.t51.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t24.t51.t14.t6 t24.t51.t14.t9))
% 0.68/0.92  (step t24.t51.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t51.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t24.t51.t14.t10 t24.t51.t14.t11))
% 0.68/0.92  (step t24.t51.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t51.t14.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 (t24.t51.t14.t12 t24.t51.t14.t13))
% 0.68/0.92  (step t24.t51.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t51.t14.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 (t24.t51.t14.t14 t24.t51.t14.t15))
% 0.68/0.92  (step t24.t51.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t24.t51.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t24.t51.t14.t16 t24.t51.t14.t17))
% 0.68/0.92  (step t24.t51.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t24.t51.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t51.t13 t24.t51.t14))
% 0.68/0.92  (step t24.t51.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t51.t12 t24.t51.t15))
% 0.68/0.92  (step t24.t51.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t51.t9 t24.t51.t16 a5))
% 0.68/0.92  (step t24.t51.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t51.t3 a7 t24.t51.t8 t24.t51.t17 a4 a3 a2))
% 0.68/0.92  (step t24.t51.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t51.t18))
% 0.68/0.92  (step t24.t51.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t24.t51.t18))
% 0.68/0.92  (step t24.t51.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t51.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t24.t51.t20 t24.t51.t21))
% 0.68/0.92  (step t24.t51.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t24.t51.t19 t24.t51.t22))
% 0.68/0.92  (step t24.t51.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t51.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t24.t51.t23 t24.t51.t24))
% 0.68/0.92  (step t24.t51 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t24.t52 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t24.t50 t24.t51))
% 0.68/0.92  (step t24.t53 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t24.t54 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t54.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t54.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t54.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t24.t54.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t54.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t54.t3 t24.t54.t4))
% 0.68/0.92  (step t24.t54.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t54.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t54.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t54.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t54.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t24.t54.t7.t2))
% 0.68/0.92  (step t24.t54.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t24.t54.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t54.t6 t24.t54.t7))
% 0.68/0.92  (step t24.t54.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t24.t54.t5 t24.t54.t8))
% 0.68/0.92  (step t24.t54.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t54.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t24.t54.t9 t24.t54.t10))
% 0.68/0.92  (step t24.t54.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t24.t54.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t24.t54.t11 t24.t54.t12))
% 0.68/0.92  (step t24.t54 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t24.t55 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t24.t53 t24.t54))
% 0.68/0.92  (step t24.t56 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t24.t52 t24.t55))
% 0.68/0.92  (step t24.t57 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t24.t49 t24.t56 a8))
% 0.68/0.92  (step t24.t58 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t59 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t24.t60 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t24.t60.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t60.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t24.t60.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t24.t60 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t24.t61 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t24.t59 t24.t60))
% 0.68/0.92  (step t24.t62 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t24.t58 t24.t61 a6))
% 0.68/0.92  (step t24.t63 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t24.t64 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t65 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t65.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t65.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t65.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t65.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t24.t65.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t65.t4 a4 a3 a2))
% 0.68/0.92  (step t24.t65.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t24.t65.t5))
% 0.68/0.92  (step t24.t65.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t24.t65.t5))
% 0.68/0.92  (step t24.t65.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t65.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t24.t65.t7 t24.t65.t8))
% 0.68/0.92  (step t24.t65.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t24.t65.t6 t24.t65.t9))
% 0.68/0.92  (step t24.t65.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t65.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t24.t65.t10 t24.t65.t11))
% 0.68/0.92  (step t24.t65.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t65.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t24.t65.t12 t24.t65.t13))
% 0.68/0.92  (step t24.t65 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t24.t66 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t24.t64 t24.t65))
% 0.68/0.92  (step t24.t67 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t24.t68 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t68.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t68.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t68.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t68.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)
% 0.68/0.92  (step t24.t68.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t68.t6 (cl (= (@ (lambda ((X (-> $$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 (t24.t68.t4 t24.t68.t5))
% 0.68/0.92  (step t24.t68.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t68.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t24.t68.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t68.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t24.t68.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t24.t68.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t24.t68.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t24.t68.t8.t3 t24.t68.t8.t4))
% 0.68/0.92  (step t24.t68.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t24.t68.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 (t24.t68.t7 t24.t68.t8))
% 0.68/0.92  (step t24.t68.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t24.t68.t6 t24.t68.t9))
% 0.68/0.92  (step t24.t68.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t24.t68.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t24.t68.t10 t24.t68.t11))
% 0.68/0.92  (step t24.t68.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t24.t68.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t24.t68.t12 t24.t68.t13))
% 0.68/0.92  (step t24.t68.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t68.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t24.t68.t14 t24.t68.t15))
% 0.68/0.92  (step t24.t68.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t24.t68.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t24.t68.t16 t24.t68.t17))
% 0.68/0.92  (step t24.t68 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t24.t69 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t24.t67 t24.t68))
% 0.68/0.92  (step t24.t70 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t24.t66 t24.t69))
% 0.68/0.92  (step t24.t71 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t24.t63 t24.t70 a5))
% 0.68/0.92  (step t24.t72 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t24.t43 t24.t48 t24.t57 a7 t24.t62 t24.t71 a4 a3 a2))
% 0.68/0.92  (step t24.t73 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t24.t72))
% 0.68/0.92  (step t24.t74 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t24.t72))
% 0.68/0.92  (step t24.t75 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t24.t73 t24.t74))
% 0.68/0.92  (step t24.t76 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t24.t42 t24.t75))
% 0.68/0.92  (step t24.t77 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t24.t78 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t24.t79 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t24.t79.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t24.t79.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t24.t79.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t24.t79.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t24.t79.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t79.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t24.t79.t2.t2 t24.t79.t2.t3))
% 0.68/0.92  (step t24.t79.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t79.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t24.t79.t2.t4 t24.t79.t2.t5))
% 0.68/0.92  (step t24.t79.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t24.t79.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t24.t79.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t24.t79.t2 t24.t79.t3))
% 0.68/0.92  (step t24.t79.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t24.t79.t4))
% 0.68/0.92  (step t24.t79.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t24.t79.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t24.t79.t5 t24.t79.t6))
% 0.68/0.92  (step t24.t79 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t24.t80 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t24.t81 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t79 t24.t80))
% 0.68/0.92  (step t24.t82 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t24.t78 t24.t81))
% 0.68/0.92  (step t24.t83 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t24.t77 t24.t82))
% 0.68/0.92  (step t24.t84 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t24.t76 t24.t83))
% 0.68/0.92  (step t24.t85 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t24.t41 t24.t84 a10))
% 0.68/0.92  (step t24.t86 (cl (and (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t24.t4 t24.t13 t24.t22 t24.t31 t24.t40 t24.t85 t24.t48 t24.t57 a7 t24.t62 t24.t71 a4 a3 a2))
% 0.68/0.92  (step t24.t87 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule and :premises (t24.t86))
% 0.68/0.92  (step t24.t88 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule and :premises (t24.t86))
% 0.68/0.92  (step t24.t89 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t24.t90 (cl (= (@ tptp.iimplies P) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t24.t88 t24.t89))
% 0.68/0.92  (step t24.t91 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t24.t92 (cl (= (@ (@ tptp.iimplies P) Q) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q))) :rule cong :premises (t24.t90 t24.t91))
% 0.68/0.92  (step t24.t93 (cl (= (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)))) :rule cong :premises (t24.t87 t24.t92))
% 0.68/0.92  (step t24.t94 (cl (= (@ tptp.iimplies Q) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t24.t88 t24.t91))
% 0.68/0.92  (step t24.t95 (cl (= (@ (@ tptp.iimplies Q) P) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P))) :rule cong :premises (t24.t94 t24.t89))
% 0.68/0.92  (step t24.t96 (cl (= (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)))) :rule cong :premises (t24.t93 t24.t95))
% 0.68/0.92  (step t24.t97 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t24.t98 (cl (= (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0))) :rule cong :premises (t24.t96 t24.t97))
% 0.68/0.92  (step t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t25 (cl (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0))))) :rule cong :premises (t23 t24))
% 0.68/0.92  (step t26 (cl (= tptp.iequiv tptp.iequiv)) :rule refl)
% 0.68/0.92  (anchor :step t27 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t27.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t27.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t27.t4 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule refl)
% 0.68/0.92  (step t27.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.92  (step t27.t6 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t27.t7 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t27.t5 t27.t6))
% 0.68/0.92  (step t27.t8 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.92  (step t27.t9 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t27.t7 t27.t8))
% 0.68/0.92  (step t27.t10 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t27.t4 t27.t9))
% 0.68/0.92  (step t27.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (@ Q __flatten_var_0))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t27.t12 :args ((Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t27.t12.t1 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t27.t12.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t27.t12.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t27.t12.t4 (cl (= (@ Q __flatten_var_0) (@ Q __flatten_var_0))) :rule refl)
% 0.68/0.92  (step t27.t12.t5 (cl (= (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (@ Q __flatten_var_0)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0)))) :rule cong :premises (t27.t12.t3 t27.t12.t4))
% 0.68/0.92  (step t27.t12 (cl (= (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t27.t13 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))))) :rule trans :premises (t27.t11 t27.t12))
% 0.68/0.92  (step t27.t14 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))))) :rule trans :premises (t27.t10 t27.t13))
% 0.68/0.92  (step t27.t15 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.92  (step t27.t16 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t27.t17 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t27.t15 t27.t16))
% 0.68/0.92  (step t27.t18 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.92  (step t27.t19 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t27.t17 t27.t18))
% 0.68/0.92  (step t27.t20 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t27.t14 t27.t19))
% 0.68/0.92  (step t27.t21 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t27.t22 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t27.t22.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t27.t22.t2 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule refl)
% 0.68/0.92  (step t27.t22.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t27.t22.t4 (cl (= (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule cong :premises (t27.t22.t2 t27.t22.t3))
% 0.68/0.92  (step t27.t22 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule bind)
% 0.68/0.92  (step t27.t23 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (@ Q __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t27.t21 t27.t22))
% 0.68/0.92  (step t27.t24 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t27.t20 t27.t23))
% 0.68/0.92  (step t27.t25 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t27.t26 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) __flatten_var_0))) :rule cong :premises (t27.t24 t27.t25))
% 0.68/0.92  (step t27.t27 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) __flatten_var_0) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.92  (step t27.t28 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t27.t26 t27.t27))
% 0.68/0.92  (step t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule bind)
% 0.68/0.92  (step t28 (cl (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) Q)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))))) :rule cong :premises (t26 t27))
% 0.68/0.92  (step t29 (cl (= (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))))) :rule trans :premises (t25 t28))
% 0.68/0.92  (step t30 (cl (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule resolution :premises (t22 t29 a15))
% 0.68/0.92  (step t31 (cl (not (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t32 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.68/0.92  (anchor :step t33 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t4 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t5 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t6 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t7.t7.t9 t33.t7.t7.t7.t10))
% 0.68/0.92  (step t33.t7.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t7.t7.t7.t8 t33.t7.t7.t7.t11 a9))
% 0.68/0.92  (step t33.t7.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t7.t7.t15.t5 t33.t7.t7.t7.t15.t6))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t7.t7.t15.t4 t33.t7.t7.t7.t15.t7 a6))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t7.t7.t15.t11.t5))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t7.t7.t15.t11.t5))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t7.t7.t15.t11.t7 t33.t7.t7.t7.t15.t11.t8))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t7.t7.t7.t15.t11.t6 t33.t7.t7.t7.t15.t11.t9))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t7.t15.t11.t10 t33.t7.t7.t7.t15.t11.t11))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t7.t15.t11.t12 t33.t7.t7.t7.t15.t11.t13))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t7.t7.t7.t15.t10 t33.t7.t7.t7.t15.t11))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.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)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t7.t7.t15.t14.t4 t33.t7.t7.t7.t15.t14.t5))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t7.t7.t15.t14.t8.t3 t33.t7.t7.t7.t15.t14.t8.t4))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.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 (t33.t7.t7.t7.t15.t14.t7 t33.t7.t7.t7.t15.t14.t8))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t7.t7.t15.t14.t6 t33.t7.t7.t7.t15.t14.t9))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t7.t15.t14.t10 t33.t7.t7.t7.t15.t14.t11))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t7.t7.t7.t15.t14.t12 t33.t7.t7.t7.t15.t14.t13))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t7.t15.t14.t14 t33.t7.t7.t7.t15.t14.t15))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t7.t7.t7.t15.t14.t16 t33.t7.t7.t7.t15.t14.t17))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t7.t7.t15.t13 t33.t7.t7.t7.t15.t14))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t7.t7.t15.t12 t33.t7.t7.t7.t15.t15))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t7.t7.t15.t9 t33.t7.t7.t7.t15.t16 a5))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t7.t7.t7.t15.t3 a7 t33.t7.t7.t7.t15.t8 t33.t7.t7.t7.t15.t17 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t7.t7.t15.t18))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t7.t7.t7.t15.t18))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t7.t7.t7.t15.t20 t33.t7.t7.t7.t15.t21))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t7.t7.t7.t15.t19 t33.t7.t7.t7.t15.t22))
% 0.68/0.92  (step t33.t7.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t7.t15.t23 t33.t7.t7.t7.t15.t24))
% 0.68/0.92  (step t33.t7.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t7.t7.t7.t14 t33.t7.t7.t7.t15))
% 0.68/0.92  (step t33.t7.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t7.t7.t18.t3 t33.t7.t7.t7.t18.t4))
% 0.68/0.92  (step t33.t7.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t7.t7.t7.t18.t7.t2))
% 0.68/0.92  (step t33.t7.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t7.t7.t18.t6 t33.t7.t7.t7.t18.t7))
% 0.68/0.92  (step t33.t7.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t7.t7.t18.t5 t33.t7.t7.t7.t18.t8))
% 0.68/0.92  (step t33.t7.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t7.t18.t9 t33.t7.t7.t7.t18.t10))
% 0.68/0.92  (step t33.t7.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t7.t7.t7.t18.t11 t33.t7.t7.t7.t18.t12))
% 0.68/0.92  (step t33.t7.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t7.t7.t7.t17 t33.t7.t7.t7.t18))
% 0.68/0.92  (step t33.t7.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t7.t7.t7.t16 t33.t7.t7.t7.t19))
% 0.68/0.92  (step t33.t7.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t7.t7.t7.t13 t33.t7.t7.t7.t20 a8))
% 0.68/0.92  (step t33.t7.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t7.t7.t23 t33.t7.t7.t7.t24))
% 0.68/0.92  (step t33.t7.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t7.t7.t22 t33.t7.t7.t7.t25 a6))
% 0.68/0.92  (step t33.t7.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t7.t29.t5 (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)))))) :rule resolution :premises (t33.t7.t7.t7.t29.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t7.t7.t29.t5))
% 0.68/0.92  (step t33.t7.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t7.t7.t29.t5))
% 0.68/0.92  (step t33.t7.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t7.t7.t29.t7 t33.t7.t7.t7.t29.t8))
% 0.68/0.92  (step t33.t7.t7.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t7.t7.t7.t29.t6 t33.t7.t7.t7.t29.t9))
% 0.68/0.92  (step t33.t7.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t7.t7.t7.t29.t10 t33.t7.t7.t7.t29.t11))
% 0.68/0.92  (step t33.t7.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t7.t29.t12 t33.t7.t7.t7.t29.t13))
% 0.68/0.92  (step t33.t7.t7.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t7.t7.t7.t28 t33.t7.t7.t7.t29))
% 0.68/0.92  (step t33.t7.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t7.t7.t7.t32.t4 t33.t7.t7.t7.t32.t5))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t7.t7.t32.t8.t3 t33.t7.t7.t7.t32.t8.t4))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t7.t7.t32.t7 t33.t7.t7.t7.t32.t8))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t7.t7.t32.t6 t33.t7.t7.t7.t32.t9))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t7.t7.t7.t32.t10 t33.t7.t7.t7.t32.t11))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t32.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 (t33.t7.t7.t7.t32.t12 t33.t7.t7.t7.t32.t13))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t32.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 (t33.t7.t7.t7.t32.t14 t33.t7.t7.t7.t32.t15))
% 0.68/0.92  (step t33.t7.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t7.t32.t16 t33.t7.t7.t7.t32.t17))
% 0.68/0.92  (step t33.t7.t7.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t7.t7.t31 t33.t7.t7.t7.t32))
% 0.68/0.92  (step t33.t7.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t7.t7.t30 t33.t7.t7.t7.t33))
% 0.68/0.92  (step t33.t7.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t7.t7.t27 t33.t7.t7.t7.t34 a5))
% 0.68/0.92  (step t33.t7.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t7.t7.t7 t33.t7.t7.t7.t12 t33.t7.t7.t7.t21 a7 t33.t7.t7.t7.t26 t33.t7.t7.t7.t35 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t7.t7.t7.t36))
% 0.68/0.92  (step t33.t7.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t7.t7.t7.t36))
% 0.68/0.92  (step t33.t7.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t7.t7.t37 t33.t7.t7.t7.t38))
% 0.68/0.92  (step t33.t7.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t7.t7.t7.t6 t33.t7.t7.t7.t39))
% 0.68/0.92  (step t33.t7.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t33.t7.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t7.t7.t7.t43.t2.t2 t33.t7.t7.t7.t43.t2.t3))
% 0.68/0.92  (step t33.t7.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t7.t7.t7.t43.t2.t4 t33.t7.t7.t7.t43.t2.t5))
% 0.68/0.92  (step t33.t7.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t7.t7.t7.t43.t2 t33.t7.t7.t7.t43.t3))
% 0.68/0.92  (step t33.t7.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t7.t7.t7.t43.t4))
% 0.68/0.92  (step t33.t7.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t7.t7.t7.t43.t5 t33.t7.t7.t7.t43.t6))
% 0.68/0.92  (step t33.t7.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t7.t7.t43 t33.t7.t7.t7.t44))
% 0.68/0.92  (step t33.t7.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t7.t7.t42 t33.t7.t7.t7.t45))
% 0.68/0.92  (step t33.t7.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t7.t7.t7.t41 t33.t7.t7.t7.t46))
% 0.68/0.92  (step t33.t7.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t7.t7.t7.t40 t33.t7.t7.t7.t47))
% 0.68/0.92  (step t33.t7.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t7.t7.t7.t5 t33.t7.t7.t7.t48 a10))
% 0.68/0.92  (step t33.t7.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t7.t7.t7.t4 t33.t7.t7.t7.t49 t33.t7.t7.t7.t12 t33.t7.t7.t7.t21 a7 t33.t7.t7.t7.t26 t33.t7.t7.t7.t35 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t7.t7.t50))
% 0.68/0.92  (step t33.t7.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t33.t7.t7.t7.t51 t33.t7.t7.t7.t52))
% 0.68/0.92  (step t33.t7.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t33.t7.t7.t7.t53 t33.t7.t7.t7.t54))
% 0.68/0.92  (step t33.t7.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t7.t55 t33.t7.t7.t7.t56))
% 0.68/0.92  (step t33.t7.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t33.t7.t7.t6 t33.t7.t7.t7))
% 0.68/0.92  (step t33.t7.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t33.t7.t7.t10.t4 t33.t7.t7.t10.t5))
% 0.68/0.92  (step t33.t7.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t33.t7.t7.t10.t6 t33.t7.t7.t10.t7))
% 0.68/0.92  (step t33.t7.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t10.t8 t33.t7.t7.t10.t9))
% 0.68/0.92  (step t33.t7.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t33.t7.t7.t10.t10 t33.t7.t7.t10.t11))
% 0.68/0.92  (step t33.t7.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t33.t7.t7.t9 t33.t7.t7.t10))
% 0.68/0.92  (step t33.t7.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t33.t7.t7.t8 t33.t7.t7.t11))
% 0.68/0.92  (step t33.t7.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t33.t7.t7.t5 t33.t7.t7.t12 a11))
% 0.68/0.92  (step t33.t7.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t7.t18 t33.t7.t7.t19))
% 0.68/0.92  (step t33.t7.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t7.t7.t17 t33.t7.t7.t20 a9))
% 0.68/0.92  (step t33.t7.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t7.t24.t5 t33.t7.t7.t24.t6))
% 0.68/0.92  (step t33.t7.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t7.t24.t4 t33.t7.t7.t24.t7 a6))
% 0.68/0.92  (step t33.t7.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t24.t11.t5 (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)))))) :rule resolution :premises (t33.t7.t7.t24.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t7.t24.t11.t5))
% 0.68/0.92  (step t33.t7.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t7.t24.t11.t5))
% 0.68/0.92  (step t33.t7.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t7.t24.t11.t7 t33.t7.t7.t24.t11.t8))
% 0.68/0.92  (step t33.t7.t7.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t7.t7.t24.t11.t6 t33.t7.t7.t24.t11.t9))
% 0.68/0.92  (step t33.t7.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t7.t7.t24.t11.t10 t33.t7.t7.t24.t11.t11))
% 0.68/0.92  (step t33.t7.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t24.t11.t12 t33.t7.t7.t24.t11.t13))
% 0.68/0.92  (step t33.t7.t7.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t7.t7.t24.t10 t33.t7.t7.t24.t11))
% 0.68/0.92  (step t33.t7.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t7.t7.t24.t14.t4 t33.t7.t7.t24.t14.t5))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t33.t7.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t7.t24.t14.t8.t3 t33.t7.t7.t24.t14.t8.t4))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t7.t24.t14.t7 t33.t7.t7.t24.t14.t8))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t7.t24.t14.t6 t33.t7.t7.t24.t14.t9))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t7.t7.t24.t14.t10 t33.t7.t7.t24.t14.t11))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t24.t14.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 (t33.t7.t7.t24.t14.t12 t33.t7.t7.t24.t14.t13))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t14.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 (t33.t7.t7.t24.t14.t14 t33.t7.t7.t24.t14.t15))
% 0.68/0.92  (step t33.t7.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t24.t14.t16 t33.t7.t7.t24.t14.t17))
% 0.68/0.92  (step t33.t7.t7.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t7.t24.t13 t33.t7.t7.t24.t14))
% 0.68/0.92  (step t33.t7.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t7.t24.t12 t33.t7.t7.t24.t15))
% 0.68/0.92  (step t33.t7.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t7.t24.t9 t33.t7.t7.t24.t16 a5))
% 0.68/0.92  (step t33.t7.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t7.t24.t3 a7 t33.t7.t7.t24.t8 t33.t7.t7.t24.t17 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t7.t24.t18))
% 0.68/0.92  (step t33.t7.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t7.t7.t24.t18))
% 0.68/0.92  (step t33.t7.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t7.t7.t24.t20 t33.t7.t7.t24.t21))
% 0.68/0.92  (step t33.t7.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t7.t7.t24.t19 t33.t7.t7.t24.t22))
% 0.68/0.92  (step t33.t7.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t24.t23 t33.t7.t7.t24.t24))
% 0.68/0.92  (step t33.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t7.t7.t23 t33.t7.t7.t24))
% 0.68/0.92  (step t33.t7.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t7.t27.t3 t33.t7.t7.t27.t4))
% 0.68/0.92  (step t33.t7.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t7.t7.t27.t7.t2))
% 0.68/0.92  (step t33.t7.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t7.t27.t6 t33.t7.t7.t27.t7))
% 0.68/0.92  (step t33.t7.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t7.t27.t5 t33.t7.t7.t27.t8))
% 0.68/0.92  (step t33.t7.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t27.t9 t33.t7.t7.t27.t10))
% 0.68/0.92  (step t33.t7.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t7.t7.t27.t11 t33.t7.t7.t27.t12))
% 0.68/0.92  (step t33.t7.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t7.t7.t26 t33.t7.t7.t27))
% 0.68/0.92  (step t33.t7.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t7.t7.t25 t33.t7.t7.t28))
% 0.68/0.92  (step t33.t7.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t7.t7.t22 t33.t7.t7.t29 a8))
% 0.68/0.92  (step t33.t7.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t7.t32 t33.t7.t7.t33))
% 0.68/0.92  (step t33.t7.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t7.t31 t33.t7.t7.t34 a6))
% 0.68/0.92  (step t33.t7.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t7.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t7.t38.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t7.t38.t5))
% 0.68/0.92  (step t33.t7.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t7.t38.t5))
% 0.68/0.92  (step t33.t7.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t7.t38.t7 t33.t7.t7.t38.t8))
% 0.68/0.92  (step t33.t7.t7.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t7.t7.t38.t6 t33.t7.t7.t38.t9))
% 0.68/0.92  (step t33.t7.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t38.t10 t33.t7.t7.t38.t11))
% 0.68/0.92  (step t33.t7.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t38.t12 t33.t7.t7.t38.t13))
% 0.68/0.92  (step t33.t7.t7.t38 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t7.t7.t37 t33.t7.t7.t38))
% 0.68/0.92  (step t33.t7.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.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)
% 0.68/0.92  (step t33.t7.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t7.t41.t4 t33.t7.t7.t41.t5))
% 0.68/0.92  (step t33.t7.t7.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t7.t41.t8.t3 t33.t7.t7.t41.t8.t4))
% 0.68/0.92  (step t33.t7.t7.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t33.t7.t7.t41.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 (t33.t7.t7.t41.t7 t33.t7.t7.t41.t8))
% 0.68/0.92  (step t33.t7.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t7.t41.t6 t33.t7.t7.t41.t9))
% 0.68/0.92  (step t33.t7.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t7.t7.t41.t10 t33.t7.t7.t41.t11))
% 0.68/0.92  (step t33.t7.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t7.t7.t41.t12 t33.t7.t7.t41.t13))
% 0.68/0.92  (step t33.t7.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t41.t14 t33.t7.t7.t41.t15))
% 0.68/0.92  (step t33.t7.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t7.t7.t41.t16 t33.t7.t7.t41.t17))
% 0.68/0.92  (step t33.t7.t7.t41 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t7.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t7.t40 t33.t7.t7.t41))
% 0.68/0.92  (step t33.t7.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t7.t39 t33.t7.t7.t42))
% 0.68/0.92  (step t33.t7.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t7.t36 t33.t7.t7.t43 a5))
% 0.68/0.92  (step t33.t7.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t7.t7.t16 t33.t7.t7.t21 t33.t7.t7.t30 a7 t33.t7.t7.t35 t33.t7.t7.t44 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t7.t7.t45))
% 0.68/0.92  (step t33.t7.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t7.t7.t45))
% 0.68/0.92  (step t33.t7.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t7.t46 t33.t7.t7.t47))
% 0.68/0.92  (step t33.t7.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t7.t7.t15 t33.t7.t7.t48))
% 0.68/0.92  (step t33.t7.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t33.t7.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t7.t7.t52.t2.t2 t33.t7.t7.t52.t2.t3))
% 0.68/0.92  (step t33.t7.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t7.t7.t52.t2.t4 t33.t7.t7.t52.t2.t5))
% 0.68/0.92  (step t33.t7.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t7.t7.t52.t2 t33.t7.t7.t52.t3))
% 0.68/0.92  (step t33.t7.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t7.t7.t52.t4))
% 0.68/0.92  (step t33.t7.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t7.t7.t52.t5 t33.t7.t7.t52.t6))
% 0.68/0.92  (step t33.t7.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t33.t7.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t7.t52 t33.t7.t7.t53))
% 0.68/0.92  (step t33.t7.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t7.t51 t33.t7.t7.t54))
% 0.68/0.92  (step t33.t7.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t7.t7.t50 t33.t7.t7.t55))
% 0.68/0.92  (step t33.t7.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t7.t7.t49 t33.t7.t7.t56))
% 0.68/0.92  (step t33.t7.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t7.t7.t14 t33.t7.t7.t57 a10))
% 0.68/0.92  (step t33.t7.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t7.t7.t4 t33.t7.t7.t13 t33.t7.t7.t58 t33.t7.t7.t21 t33.t7.t7.t30 a7 t33.t7.t7.t35 t33.t7.t7.t44 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t7.t59))
% 0.68/0.92  (step t33.t7.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t7.t7.t59))
% 0.68/0.92  (step t33.t7.t7.t62 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t7.t7.t61 t33.t7.t7.t62))
% 0.68/0.92  (step t33.t7.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t7.t7.t60 t33.t7.t7.t63))
% 0.68/0.92  (step t33.t7.t7.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t33.t7.t7.t61 t33.t7.t7.t65))
% 0.68/0.92  (step t33.t7.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t33.t7.t7.t64 t33.t7.t7.t66))
% 0.68/0.92  (step t33.t7.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t33.t7.t7.t67 t33.t7.t7.t68))
% 0.68/0.92  (step t33.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t33.t7.t6 t33.t7.t7))
% 0.68/0.92  (step t33.t7.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t10.t4 t33.t7.t10.t5))
% 0.68/0.92  (step t33.t7.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t33.t7.t10.t8.t3 t33.t7.t10.t8.t4))
% 0.68/0.92  (step t33.t7.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t7.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t33.t7.t10.t7 t33.t7.t10.t8))
% 0.68/0.92  (step t33.t7.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t33.t7.t10.t6 t33.t7.t10.t9))
% 0.68/0.92  (step t33.t7.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t33.t7.t10.t10 t33.t7.t10.t11))
% 0.68/0.92  (step t33.t7.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t33.t7.t10.t14.t2 t33.t7.t10.t14.t3))
% 0.68/0.92  (step t33.t7.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t33.t7.t10.t13 t33.t7.t10.t14))
% 0.68/0.92  (step t33.t7.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t33.t7.t10.t12 t33.t7.t10.t15))
% 0.68/0.92  (step t33.t7.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t33.t7.t10.t16 t33.t7.t10.t17))
% 0.68/0.92  (step t33.t7.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t33.t7.t10.t18 t33.t7.t10.t19))
% 0.68/0.92  (step t33.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t33.t7.t9 t33.t7.t10))
% 0.68/0.92  (step t33.t7.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t33.t7.t8 t33.t7.t11))
% 0.68/0.92  (step t33.t7.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t33.t7.t5 t33.t7.t12 a12))
% 0.68/0.92  (step t33.t7.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t16.t9 t33.t7.t16.t10))
% 0.68/0.92  (step t33.t7.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t7.t16.t8 t33.t7.t16.t11 a9))
% 0.68/0.92  (step t33.t7.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t16.t15.t5 t33.t7.t16.t15.t6))
% 0.68/0.92  (step t33.t7.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t16.t15.t4 t33.t7.t16.t15.t7 a6))
% 0.68/0.92  (step t33.t7.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t16.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t16.t15.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t16.t15.t11.t5))
% 0.68/0.92  (step t33.t7.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t16.t15.t11.t5))
% 0.68/0.92  (step t33.t7.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t16.t15.t11.t7 t33.t7.t16.t15.t11.t8))
% 0.68/0.92  (step t33.t7.t16.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t7.t16.t15.t11.t6 t33.t7.t16.t15.t11.t9))
% 0.68/0.92  (step t33.t7.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t7.t16.t15.t11.t10 t33.t7.t16.t15.t11.t11))
% 0.68/0.92  (step t33.t7.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t7.t16.t15.t11.t12 t33.t7.t16.t15.t11.t13))
% 0.68/0.92  (step t33.t7.t16.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t7.t16.t15.t10 t33.t7.t16.t15.t11))
% 0.68/0.92  (step t33.t7.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.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)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t16.t15.t14.t4 t33.t7.t16.t15.t14.t5))
% 0.68/0.92  (step t33.t7.t16.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t16.t15.t14.t8.t3 t33.t7.t16.t15.t14.t8.t4))
% 0.68/0.92  (step t33.t7.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t33.t7.t16.t15.t14.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 (t33.t7.t16.t15.t14.t7 t33.t7.t16.t15.t14.t8))
% 0.68/0.92  (step t33.t7.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t16.t15.t14.t6 t33.t7.t16.t15.t14.t9))
% 0.68/0.92  (step t33.t7.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t7.t16.t15.t14.t10 t33.t7.t16.t15.t14.t11))
% 0.68/0.92  (step t33.t7.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t7.t16.t15.t14.t12 t33.t7.t16.t15.t14.t13))
% 0.68/0.92  (step t33.t7.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t7.t16.t15.t14.t14 t33.t7.t16.t15.t14.t15))
% 0.68/0.92  (step t33.t7.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t7.t16.t15.t14.t16 t33.t7.t16.t15.t14.t17))
% 0.68/0.92  (step t33.t7.t16.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t16.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t16.t15.t13 t33.t7.t16.t15.t14))
% 0.68/0.92  (step t33.t7.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t16.t15.t12 t33.t7.t16.t15.t15))
% 0.68/0.92  (step t33.t7.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t16.t15.t9 t33.t7.t16.t15.t16 a5))
% 0.68/0.92  (step t33.t7.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t7.t16.t15.t3 a7 t33.t7.t16.t15.t8 t33.t7.t16.t15.t17 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t16.t15.t18))
% 0.68/0.92  (step t33.t7.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t7.t16.t15.t18))
% 0.68/0.92  (step t33.t7.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t7.t16.t15.t20 t33.t7.t16.t15.t21))
% 0.68/0.92  (step t33.t7.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t7.t16.t15.t19 t33.t7.t16.t15.t22))
% 0.68/0.92  (step t33.t7.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t7.t16.t15.t23 t33.t7.t16.t15.t24))
% 0.68/0.92  (step t33.t7.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t7.t16.t14 t33.t7.t16.t15))
% 0.68/0.92  (step t33.t7.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t16.t18.t3 t33.t7.t16.t18.t4))
% 0.68/0.92  (step t33.t7.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t7.t16.t18.t7.t2))
% 0.68/0.92  (step t33.t7.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t16.t18.t6 t33.t7.t16.t18.t7))
% 0.68/0.92  (step t33.t7.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t16.t18.t5 t33.t7.t16.t18.t8))
% 0.68/0.92  (step t33.t7.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t7.t16.t18.t9 t33.t7.t16.t18.t10))
% 0.68/0.92  (step t33.t7.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t7.t16.t18.t11 t33.t7.t16.t18.t12))
% 0.68/0.92  (step t33.t7.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t7.t16.t17 t33.t7.t16.t18))
% 0.68/0.92  (step t33.t7.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t7.t16.t16 t33.t7.t16.t19))
% 0.68/0.92  (step t33.t7.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t7.t16.t13 t33.t7.t16.t20 a8))
% 0.68/0.92  (step t33.t7.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t16.t23 t33.t7.t16.t24))
% 0.68/0.92  (step t33.t7.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t16.t22 t33.t7.t16.t25 a6))
% 0.68/0.92  (step t33.t7.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t29.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t16.t29.t5 (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)))))) :rule resolution :premises (t33.t7.t16.t29.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t16.t29.t5))
% 0.68/0.92  (step t33.t7.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t16.t29.t5))
% 0.68/0.92  (step t33.t7.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t16.t29.t7 t33.t7.t16.t29.t8))
% 0.68/0.92  (step t33.t7.t16.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t7.t16.t29.t6 t33.t7.t16.t29.t9))
% 0.68/0.92  (step t33.t7.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t7.t16.t29.t10 t33.t7.t16.t29.t11))
% 0.68/0.92  (step t33.t7.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t16.t29.t12 t33.t7.t16.t29.t13))
% 0.68/0.92  (step t33.t7.t16.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t7.t16.t28 t33.t7.t16.t29))
% 0.68/0.92  (step t33.t7.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t7.t16.t32.t4 t33.t7.t16.t32.t5))
% 0.68/0.92  (step t33.t7.t16.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t33.t7.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t16.t32.t8.t3 t33.t7.t16.t32.t8.t4))
% 0.68/0.92  (step t33.t7.t16.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t16.t32.t7 t33.t7.t16.t32.t8))
% 0.68/0.92  (step t33.t7.t16.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t16.t32.t6 t33.t7.t16.t32.t9))
% 0.68/0.92  (step t33.t7.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t7.t16.t32.t10 t33.t7.t16.t32.t11))
% 0.68/0.92  (step t33.t7.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t32.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 (t33.t7.t16.t32.t12 t33.t7.t16.t32.t13))
% 0.68/0.92  (step t33.t7.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t32.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 (t33.t7.t16.t32.t14 t33.t7.t16.t32.t15))
% 0.68/0.92  (step t33.t7.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t16.t32.t16 t33.t7.t16.t32.t17))
% 0.68/0.92  (step t33.t7.t16.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t16.t31 t33.t7.t16.t32))
% 0.68/0.92  (step t33.t7.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t16.t30 t33.t7.t16.t33))
% 0.68/0.92  (step t33.t7.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t16.t27 t33.t7.t16.t34 a5))
% 0.68/0.92  (step t33.t7.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t16.t7 t33.t7.t16.t12 t33.t7.t16.t21 a7 t33.t7.t16.t26 t33.t7.t16.t35 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t7.t16.t36))
% 0.68/0.92  (step t33.t7.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t7.t16.t36))
% 0.68/0.92  (step t33.t7.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t16.t37 t33.t7.t16.t38))
% 0.68/0.92  (step t33.t7.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t7.t16.t6 t33.t7.t16.t39))
% 0.68/0.92  (step t33.t7.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t33.t7.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t7.t16.t43.t2.t2 t33.t7.t16.t43.t2.t3))
% 0.68/0.92  (step t33.t7.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t7.t16.t43.t2.t4 t33.t7.t16.t43.t2.t5))
% 0.68/0.92  (step t33.t7.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t7.t16.t43.t2 t33.t7.t16.t43.t3))
% 0.68/0.92  (step t33.t7.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t7.t16.t43.t4))
% 0.68/0.92  (step t33.t7.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t7.t16.t43.t5 t33.t7.t16.t43.t6))
% 0.68/0.92  (step t33.t7.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t33.t7.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t16.t43 t33.t7.t16.t44))
% 0.68/0.92  (step t33.t7.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t16.t42 t33.t7.t16.t45))
% 0.68/0.92  (step t33.t7.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t7.t16.t41 t33.t7.t16.t46))
% 0.68/0.92  (step t33.t7.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t7.t16.t40 t33.t7.t16.t47))
% 0.68/0.92  (step t33.t7.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t7.t16.t5 t33.t7.t16.t48 a10))
% 0.68/0.92  (step t33.t7.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t7.t16.t4 t33.t7.t16.t49 t33.t7.t16.t12 t33.t7.t16.t21 a7 t33.t7.t16.t26 t33.t7.t16.t35 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t16.t50))
% 0.68/0.92  (step t33.t7.t16.t52 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t33.t7.t16.t51 t33.t7.t16.t52))
% 0.68/0.92  (step t33.t7.t16.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t33.t7.t16.t53 t33.t7.t16.t54))
% 0.68/0.92  (step t33.t7.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t33.t7.t16.t55 t33.t7.t16.t56))
% 0.68/0.92  (step t33.t7.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t33.t7.t15 t33.t7.t16))
% 0.68/0.92  (step t33.t7.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t19.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t33.t7.t19.t4 t33.t7.t19.t5))
% 0.68/0.92  (step t33.t7.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t33.t7.t19.t6 t33.t7.t19.t7))
% 0.68/0.92  (step t33.t7.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t33.t7.t19.t8 t33.t7.t19.t9))
% 0.68/0.92  (step t33.t7.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t33.t7.t19.t10 t33.t7.t19.t11))
% 0.68/0.92  (step t33.t7.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t7.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t33.t7.t18 t33.t7.t19))
% 0.68/0.92  (step t33.t7.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t33.t7.t17 t33.t7.t20))
% 0.68/0.92  (step t33.t7.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t33.t7.t14 t33.t7.t21 a11))
% 0.68/0.92  (step t33.t7.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t33.t7.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t27 t33.t7.t28))
% 0.68/0.92  (step t33.t7.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t7.t26 t33.t7.t29 a9))
% 0.68/0.92  (step t33.t7.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t33.t5 t33.t7.t33.t6))
% 0.68/0.92  (step t33.t7.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t33.t4 t33.t7.t33.t7 a6))
% 0.68/0.92  (step t33.t7.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t33.t11.t5 (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)))))) :rule resolution :premises (t33.t7.t33.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t33.t11.t5))
% 0.68/0.92  (step t33.t7.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t33.t11.t5))
% 0.68/0.92  (step t33.t7.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t33.t11.t7 t33.t7.t33.t11.t8))
% 0.68/0.92  (step t33.t7.t33.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t7.t33.t11.t6 t33.t7.t33.t11.t9))
% 0.68/0.92  (step t33.t7.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t7.t33.t11.t10 t33.t7.t33.t11.t11))
% 0.68/0.92  (step t33.t7.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t33.t11.t12 t33.t7.t33.t11.t13))
% 0.68/0.92  (step t33.t7.t33.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t7.t33.t10 t33.t7.t33.t11))
% 0.68/0.92  (step t33.t7.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t33.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t7.t33.t14.t4 t33.t7.t33.t14.t5))
% 0.68/0.92  (step t33.t7.t33.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t33.t7.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t33.t14.t8.t3 t33.t7.t33.t14.t8.t4))
% 0.68/0.92  (step t33.t7.t33.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t7.t33.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t33.t14.t7 t33.t7.t33.t14.t8))
% 0.68/0.92  (step t33.t7.t33.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t33.t14.t6 t33.t7.t33.t14.t9))
% 0.68/0.92  (step t33.t7.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t7.t33.t14.t10 t33.t7.t33.t14.t11))
% 0.68/0.92  (step t33.t7.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t33.t14.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 (t33.t7.t33.t14.t12 t33.t7.t33.t14.t13))
% 0.68/0.92  (step t33.t7.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t14.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 (t33.t7.t33.t14.t14 t33.t7.t33.t14.t15))
% 0.68/0.92  (step t33.t7.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t7.t33.t14.t16 t33.t7.t33.t14.t17))
% 0.68/0.92  (step t33.t7.t33.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t7.t33.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t33.t13 t33.t7.t33.t14))
% 0.68/0.92  (step t33.t7.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t33.t12 t33.t7.t33.t15))
% 0.68/0.92  (step t33.t7.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t33.t9 t33.t7.t33.t16 a5))
% 0.68/0.92  (step t33.t7.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t33.t3 a7 t33.t7.t33.t8 t33.t7.t33.t17 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t33.t18))
% 0.68/0.92  (step t33.t7.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t7.t33.t18))
% 0.68/0.92  (step t33.t7.t33.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t7.t33.t20 t33.t7.t33.t21))
% 0.68/0.92  (step t33.t7.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t7.t33.t19 t33.t7.t33.t22))
% 0.68/0.92  (step t33.t7.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t7.t33.t23 t33.t7.t33.t24))
% 0.68/0.92  (step t33.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t7.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t7.t32 t33.t7.t33))
% 0.68/0.92  (step t33.t7.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t36.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t33.t7.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t36.t3 t33.t7.t36.t4))
% 0.68/0.92  (step t33.t7.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t7.t36.t7.t2))
% 0.68/0.92  (step t33.t7.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t36.t6 t33.t7.t36.t7))
% 0.68/0.92  (step t33.t7.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t7.t36.t5 t33.t7.t36.t8))
% 0.68/0.92  (step t33.t7.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t7.t36.t9 t33.t7.t36.t10))
% 0.68/0.92  (step t33.t7.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t7.t36.t11 t33.t7.t36.t12))
% 0.68/0.92  (step t33.t7.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t7.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t7.t35 t33.t7.t36))
% 0.68/0.92  (step t33.t7.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t7.t34 t33.t7.t37))
% 0.68/0.92  (step t33.t7.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t7.t31 t33.t7.t38 a8))
% 0.68/0.92  (step t33.t7.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t7.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t42.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t7.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t7.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t7.t41 t33.t7.t42))
% 0.68/0.92  (step t33.t7.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t7.t40 t33.t7.t43 a6))
% 0.68/0.92  (step t33.t7.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t7.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t47.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t47.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t47.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t7.t47.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t47.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t7.t47.t5))
% 0.68/0.92  (step t33.t7.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t7.t47.t5))
% 0.68/0.92  (step t33.t7.t47.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t7.t47.t7 t33.t7.t47.t8))
% 0.68/0.92  (step t33.t7.t47.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t7.t47.t6 t33.t7.t47.t9))
% 0.68/0.92  (step t33.t7.t47.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t47.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t7.t47.t10 t33.t7.t47.t11))
% 0.68/0.92  (step t33.t7.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t47.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t7.t47.t12 t33.t7.t47.t13))
% 0.68/0.92  (step t33.t7.t47 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t7.t46 t33.t7.t47))
% 0.68/0.92  (step t33.t7.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t50.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t50.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t50.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)
% 0.68/0.92  (step t33.t7.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t50.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t7.t50.t4 t33.t7.t50.t5))
% 0.68/0.92  (step t33.t7.t50.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t7.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t7.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t7.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t7.t50.t8.t3 t33.t7.t50.t8.t4))
% 0.68/0.92  (step t33.t7.t50.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t33.t7.t50.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 (t33.t7.t50.t7 t33.t7.t50.t8))
% 0.68/0.92  (step t33.t7.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t7.t50.t6 t33.t7.t50.t9))
% 0.68/0.92  (step t33.t7.t50.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t7.t50.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t7.t50.t10 t33.t7.t50.t11))
% 0.68/0.92  (step t33.t7.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t50.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t7.t50.t12 t33.t7.t50.t13))
% 0.68/0.92  (step t33.t7.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t50.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t7.t50.t14 t33.t7.t50.t15))
% 0.68/0.92  (step t33.t7.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t7.t50.t16 t33.t7.t50.t17))
% 0.68/0.92  (step t33.t7.t50 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t7.t51 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t7.t49 t33.t7.t50))
% 0.68/0.92  (step t33.t7.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t7.t48 t33.t7.t51))
% 0.68/0.92  (step t33.t7.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t7.t45 t33.t7.t52 a5))
% 0.68/0.92  (step t33.t7.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t7.t25 t33.t7.t30 t33.t7.t39 a7 t33.t7.t44 t33.t7.t53 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t7.t54))
% 0.68/0.92  (step t33.t7.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t7.t54))
% 0.68/0.92  (step t33.t7.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t7.t55 t33.t7.t56))
% 0.68/0.92  (step t33.t7.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t7.t24 t33.t7.t57))
% 0.68/0.92  (step t33.t7.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t7.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t7.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t7.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t33.t7.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t33.t7.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t7.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t33.t7.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t7.t61.t2.t2 t33.t7.t61.t2.t3))
% 0.68/0.92  (step t33.t7.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t7.t61.t2.t4 t33.t7.t61.t2.t5))
% 0.68/0.92  (step t33.t7.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t33.t7.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t7.t61.t2 t33.t7.t61.t3))
% 0.68/0.92  (step t33.t7.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t7.t61.t4))
% 0.68/0.92  (step t33.t7.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t7.t61.t5 t33.t7.t61.t6))
% 0.68/0.92  (step t33.t7.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t33.t7.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t33.t7.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t61 t33.t7.t62))
% 0.68/0.92  (step t33.t7.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t7.t60 t33.t7.t63))
% 0.68/0.92  (step t33.t7.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t7.t59 t33.t7.t64))
% 0.68/0.92  (step t33.t7.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t7.t58 t33.t7.t65))
% 0.68/0.92  (step t33.t7.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t7.t23 t33.t7.t66 a10))
% 0.68/0.92  (step t33.t7.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t7.t4 t33.t7.t13 t33.t7.t22 t33.t7.t67 t33.t7.t30 t33.t7.t39 a7 t33.t7.t44 t33.t7.t53 a4 a3 a2))
% 0.68/0.92  (step t33.t7.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t33.t7.t68))
% 0.68/0.92  (step t33.t7.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t7.t68))
% 0.68/0.92  (step t33.t7.t71 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t7.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t7.t70 t33.t7.t71))
% 0.68/0.92  (step t33.t7.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t7.t69 t33.t7.t72))
% 0.68/0.92  (step t33.t7.t74 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t7.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t33.t7.t70 t33.t7.t74))
% 0.68/0.92  (step t33.t7.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t33.t7.t73 t33.t7.t75))
% 0.68/0.92  (step t33.t7.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t7.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t33.t7.t76 t33.t7.t77))
% 0.68/0.92  (step t33.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t8 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t33.t6 t33.t7))
% 0.68/0.92  (step t33.t9 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t10.t4 (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)
% 0.68/0.92  (step t33.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t10.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t10.t4 t33.t10.t5))
% 0.68/0.92  (step t33.t10.t7 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t10.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t10.t8.t1 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t10.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t10.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t33.t10.t8.t3))
% 0.68/0.92  (step t33.t10.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.68/0.92  (step t33.t10.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t33.t10.t8.t4 t33.t10.t8.t5))
% 0.68/0.92  (step t33.t10.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t10.t9 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t33.t10.t7 t33.t10.t8))
% 0.68/0.92  (step t33.t10.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t33.t10.t6 t33.t10.t9))
% 0.68/0.92  (step t33.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t10.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t33.t10.t10 t33.t10.t11))
% 0.68/0.92  (step t33.t10.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t10.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t10.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t10.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.68/0.92  (step t33.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t10.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t33.t10.t14.t2 t33.t10.t14.t3))
% 0.68/0.92  (step t33.t10.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t33.t10.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t33.t10.t13 t33.t10.t14))
% 0.68/0.92  (step t33.t10.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t33.t10.t12 t33.t10.t15))
% 0.68/0.92  (step t33.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t10.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t33.t10.t16 t33.t10.t17))
% 0.68/0.92  (step t33.t10.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t10.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t33.t10.t18 t33.t10.t19))
% 0.68/0.92  (step t33.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t33.t11 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t33.t9 t33.t10))
% 0.68/0.92  (step t33.t12 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t33.t8 t33.t11))
% 0.68/0.92  (step t33.t13 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t33.t5 t33.t12 a13))
% 0.68/0.92  (step t33.t14 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t15 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t16.t7.t9 t33.t16.t7.t10))
% 0.68/0.92  (step t33.t16.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t16.t7.t8 t33.t16.t7.t11 a9))
% 0.68/0.92  (step t33.t16.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t16.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t16.t7.t15.t5 t33.t16.t7.t15.t6))
% 0.68/0.92  (step t33.t16.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t16.t7.t15.t4 t33.t16.t7.t15.t7 a6))
% 0.68/0.92  (step t33.t16.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t33.t16.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t16.t7.t15.t11.t5))
% 0.68/0.92  (step t33.t16.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t16.t7.t15.t11.t5))
% 0.68/0.92  (step t33.t16.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t16.t7.t15.t11.t7 t33.t16.t7.t15.t11.t8))
% 0.68/0.92  (step t33.t16.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t16.t7.t15.t11.t6 t33.t16.t7.t15.t11.t9))
% 0.68/0.92  (step t33.t16.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t16.t7.t15.t11.t10 t33.t16.t7.t15.t11.t11))
% 0.68/0.92  (step t33.t16.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t16.t7.t15.t11.t12 t33.t16.t7.t15.t11.t13))
% 0.68/0.92  (step t33.t16.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t16.t7.t15.t10 t33.t16.t7.t15.t11))
% 0.68/0.92  (step t33.t16.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t16.t7.t15.t14.t4 t33.t16.t7.t15.t14.t5))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t33.t16.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t16.t7.t15.t14.t8.t3 t33.t16.t7.t15.t14.t8.t4))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t16.t7.t15.t14.t7 t33.t16.t7.t15.t14.t8))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t16.t7.t15.t14.t6 t33.t16.t7.t15.t14.t9))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t16.t7.t15.t14.t10 t33.t16.t7.t15.t14.t11))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t15.t14.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 (t33.t16.t7.t15.t14.t12 t33.t16.t7.t15.t14.t13))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t14.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 (t33.t16.t7.t15.t14.t14 t33.t16.t7.t15.t14.t15))
% 0.68/0.92  (step t33.t16.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t16.t7.t15.t14.t16 t33.t16.t7.t15.t14.t17))
% 0.68/0.92  (step t33.t16.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t16.t7.t15.t13 t33.t16.t7.t15.t14))
% 0.68/0.92  (step t33.t16.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t16.t7.t15.t12 t33.t16.t7.t15.t15))
% 0.68/0.92  (step t33.t16.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t16.t7.t15.t9 t33.t16.t7.t15.t16 a5))
% 0.68/0.92  (step t33.t16.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t16.t7.t15.t3 a7 t33.t16.t7.t15.t8 t33.t16.t7.t15.t17 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t16.t7.t15.t18))
% 0.68/0.92  (step t33.t16.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t16.t7.t15.t18))
% 0.68/0.92  (step t33.t16.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t16.t7.t15.t20 t33.t16.t7.t15.t21))
% 0.68/0.92  (step t33.t16.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t16.t7.t15.t19 t33.t16.t7.t15.t22))
% 0.68/0.92  (step t33.t16.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t16.t7.t15.t23 t33.t16.t7.t15.t24))
% 0.68/0.92  (step t33.t16.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t16.t7.t14 t33.t16.t7.t15))
% 0.68/0.92  (step t33.t16.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t16.t7.t18.t3 t33.t16.t7.t18.t4))
% 0.68/0.92  (step t33.t16.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t16.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t16.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t16.t7.t18.t7.t2))
% 0.68/0.92  (step t33.t16.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t16.t7.t18.t6 t33.t16.t7.t18.t7))
% 0.68/0.92  (step t33.t16.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t16.t7.t18.t5 t33.t16.t7.t18.t8))
% 0.68/0.92  (step t33.t16.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t16.t7.t18.t9 t33.t16.t7.t18.t10))
% 0.68/0.92  (step t33.t16.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t16.t7.t18.t11 t33.t16.t7.t18.t12))
% 0.68/0.92  (step t33.t16.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t16.t7.t17 t33.t16.t7.t18))
% 0.68/0.92  (step t33.t16.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t16.t7.t16 t33.t16.t7.t19))
% 0.68/0.92  (step t33.t16.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t16.t7.t13 t33.t16.t7.t20 a8))
% 0.68/0.92  (step t33.t16.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t16.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t16.t7.t23 t33.t16.t7.t24))
% 0.68/0.92  (step t33.t16.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t16.t7.t22 t33.t16.t7.t25 a6))
% 0.68/0.92  (step t33.t16.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t16.t7.t29.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t16.t7.t29.t5))
% 0.68/0.92  (step t33.t16.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t16.t7.t29.t5))
% 0.68/0.92  (step t33.t16.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t16.t7.t29.t7 t33.t16.t7.t29.t8))
% 0.68/0.92  (step t33.t16.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t16.t7.t29.t6 t33.t16.t7.t29.t9))
% 0.68/0.92  (step t33.t16.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t16.t7.t29.t10 t33.t16.t7.t29.t11))
% 0.68/0.92  (step t33.t16.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t16.t7.t29.t12 t33.t16.t7.t29.t13))
% 0.68/0.92  (step t33.t16.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t16.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t16.t7.t28 t33.t16.t7.t29))
% 0.68/0.92  (step t33.t16.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.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)
% 0.68/0.92  (step t33.t16.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t16.t7.t32.t4 t33.t16.t7.t32.t5))
% 0.68/0.92  (step t33.t16.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t16.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t16.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t16.t7.t32.t8.t3 t33.t16.t7.t32.t8.t4))
% 0.68/0.92  (step t33.t16.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t33.t16.t7.t32.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 (t33.t16.t7.t32.t7 t33.t16.t7.t32.t8))
% 0.68/0.92  (step t33.t16.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t16.t7.t32.t6 t33.t16.t7.t32.t9))
% 0.68/0.92  (step t33.t16.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t16.t7.t32.t10 t33.t16.t7.t32.t11))
% 0.68/0.92  (step t33.t16.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t16.t7.t32.t12 t33.t16.t7.t32.t13))
% 0.68/0.92  (step t33.t16.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t16.t7.t32.t14 t33.t16.t7.t32.t15))
% 0.68/0.92  (step t33.t16.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t16.t7.t32.t16 t33.t16.t7.t32.t17))
% 0.68/0.92  (step t33.t16.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t16.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t16.t7.t31 t33.t16.t7.t32))
% 0.68/0.92  (step t33.t16.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t16.t7.t30 t33.t16.t7.t33))
% 0.68/0.92  (step t33.t16.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t16.t7.t27 t33.t16.t7.t34 a5))
% 0.68/0.92  (step t33.t16.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t16.t7.t7 t33.t16.t7.t12 t33.t16.t7.t21 a7 t33.t16.t7.t26 t33.t16.t7.t35 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t16.t7.t36))
% 0.68/0.92  (step t33.t16.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t16.t7.t36))
% 0.68/0.92  (step t33.t16.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t16.t7.t37 t33.t16.t7.t38))
% 0.68/0.92  (step t33.t16.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t16.t7.t6 t33.t16.t7.t39))
% 0.68/0.92  (step t33.t16.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t16.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t33.t16.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t16.t7.t43.t2.t2 t33.t16.t7.t43.t2.t3))
% 0.68/0.92  (step t33.t16.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t16.t7.t43.t2.t4 t33.t16.t7.t43.t2.t5))
% 0.68/0.92  (step t33.t16.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t16.t7.t43.t2 t33.t16.t7.t43.t3))
% 0.68/0.92  (step t33.t16.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t16.t7.t43.t4))
% 0.68/0.92  (step t33.t16.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t16.t7.t43.t5 t33.t16.t7.t43.t6))
% 0.68/0.92  (step t33.t16.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t33.t16.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t16.t7.t43 t33.t16.t7.t44))
% 0.68/0.92  (step t33.t16.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t16.t7.t42 t33.t16.t7.t45))
% 0.68/0.92  (step t33.t16.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t16.t7.t41 t33.t16.t7.t46))
% 0.68/0.92  (step t33.t16.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t16.t7.t40 t33.t16.t7.t47))
% 0.68/0.92  (step t33.t16.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t16.t7.t5 t33.t16.t7.t48 a10))
% 0.68/0.92  (step t33.t16.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t16.t7.t4 t33.t16.t7.t49 t33.t16.t7.t12 t33.t16.t7.t21 a7 t33.t16.t7.t26 t33.t16.t7.t35 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t33.t16.t7.t50))
% 0.68/0.92  (step t33.t16.t7.t52 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t33.t16.t7.t51 t33.t16.t7.t52))
% 0.68/0.92  (step t33.t16.t7.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t33.t16.t7.t53 t33.t16.t7.t54))
% 0.68/0.92  (step t33.t16.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t33.t16.t7.t55 t33.t16.t7.t56))
% 0.68/0.92  (step t33.t16.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t16.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t33.t16.t6 t33.t16.t7))
% 0.68/0.92  (step t33.t16.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t10.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t10.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t16.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t10.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t16.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t33.t16.t10.t4 t33.t16.t10.t5))
% 0.68/0.92  (step t33.t16.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t33.t16.t10.t6 t33.t16.t10.t7))
% 0.68/0.92  (step t33.t16.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t33.t16.t10.t8 t33.t16.t10.t9))
% 0.68/0.92  (step t33.t16.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t33.t16.t10.t10 t33.t16.t10.t11))
% 0.68/0.92  (step t33.t16.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t16.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t33.t16.t9 t33.t16.t10))
% 0.68/0.92  (step t33.t16.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t33.t16.t8 t33.t16.t11))
% 0.68/0.92  (step t33.t16.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t33.t16.t5 t33.t16.t12 a11))
% 0.68/0.92  (step t33.t16.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t16.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.92  (step t33.t16.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t16.t18 t33.t16.t19))
% 0.68/0.92  (step t33.t16.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t16.t17 t33.t16.t20 a9))
% 0.68/0.92  (step t33.t16.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t16.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t16.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t16.t24.t5 t33.t16.t24.t6))
% 0.68/0.92  (step t33.t16.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t16.t24.t4 t33.t16.t24.t7 a6))
% 0.68/0.92  (step t33.t16.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t16.t24.t11.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t16.t24.t11.t5))
% 0.68/0.92  (step t33.t16.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t16.t24.t11.t5))
% 0.68/0.92  (step t33.t16.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t16.t24.t11.t7 t33.t16.t24.t11.t8))
% 0.68/0.92  (step t33.t16.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t16.t24.t11.t6 t33.t16.t24.t11.t9))
% 0.68/0.92  (step t33.t16.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t16.t24.t11.t10 t33.t16.t24.t11.t11))
% 0.68/0.92  (step t33.t16.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t16.t24.t11.t12 t33.t16.t24.t11.t13))
% 0.68/0.92  (step t33.t16.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t16.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t16.t24.t10 t33.t16.t24.t11))
% 0.68/0.92  (step t33.t16.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.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)
% 0.68/0.92  (step t33.t16.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t16.t24.t14.t4 t33.t16.t24.t14.t5))
% 0.68/0.92  (step t33.t16.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t16.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t16.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t16.t24.t14.t8.t3 t33.t16.t24.t14.t8.t4))
% 0.68/0.92  (step t33.t16.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.92  (step t33.t16.t24.t14.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 (t33.t16.t24.t14.t7 t33.t16.t24.t14.t8))
% 0.68/0.92  (step t33.t16.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t16.t24.t14.t6 t33.t16.t24.t14.t9))
% 0.68/0.92  (step t33.t16.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t16.t24.t14.t10 t33.t16.t24.t14.t11))
% 0.68/0.92  (step t33.t16.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t16.t24.t14.t12 t33.t16.t24.t14.t13))
% 0.68/0.92  (step t33.t16.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t16.t24.t14.t14 t33.t16.t24.t14.t15))
% 0.68/0.92  (step t33.t16.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t16.t24.t14.t16 t33.t16.t24.t14.t17))
% 0.68/0.92  (step t33.t16.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.92  (step t33.t16.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t16.t24.t13 t33.t16.t24.t14))
% 0.68/0.92  (step t33.t16.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t16.t24.t12 t33.t16.t24.t15))
% 0.68/0.92  (step t33.t16.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t16.t24.t9 t33.t16.t24.t16 a5))
% 0.68/0.92  (step t33.t16.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t16.t24.t3 a7 t33.t16.t24.t8 t33.t16.t24.t17 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t16.t24.t18))
% 0.68/0.92  (step t33.t16.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t16.t24.t18))
% 0.68/0.92  (step t33.t16.t24.t21 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t16.t24.t20 t33.t16.t24.t21))
% 0.68/0.92  (step t33.t16.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t16.t24.t19 t33.t16.t24.t22))
% 0.68/0.92  (step t33.t16.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t16.t24.t23 t33.t16.t24.t24))
% 0.68/0.92  (step t33.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t16.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t16.t23 t33.t16.t24))
% 0.68/0.92  (step t33.t16.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t27.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.92  (step t33.t16.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t16.t27.t3 t33.t16.t27.t4))
% 0.68/0.92  (step t33.t16.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t16.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t16.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t16.t27.t7.t2))
% 0.68/0.92  (step t33.t16.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t16.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t16.t27.t6 t33.t16.t27.t7))
% 0.68/0.92  (step t33.t16.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t16.t27.t5 t33.t16.t27.t8))
% 0.68/0.92  (step t33.t16.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t16.t27.t9 t33.t16.t27.t10))
% 0.68/0.92  (step t33.t16.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t16.t27.t11 t33.t16.t27.t12))
% 0.68/0.92  (step t33.t16.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.92  (step t33.t16.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t16.t26 t33.t16.t27))
% 0.68/0.92  (step t33.t16.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t16.t25 t33.t16.t28))
% 0.68/0.92  (step t33.t16.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t16.t22 t33.t16.t29 a8))
% 0.68/0.92  (step t33.t16.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.92  (step t33.t16.t33.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t33.t2 (cl (= X X)) :rule refl)
% 0.68/0.92  (step t33.t16.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.92  (step t33.t16.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t16.t32 t33.t16.t33))
% 0.68/0.92  (step t33.t16.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t16.t31 t33.t16.t34 a6))
% 0.68/0.92  (step t33.t16.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t16.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t38.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t38.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t38.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))))) (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)))))) :rule and_neg)
% 0.68/0.92  (step t33.t16.t38.t5 (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)))))) :rule resolution :premises (t33.t16.t38.t4 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t16.t38.t5))
% 0.68/0.92  (step t33.t16.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t16.t38.t5))
% 0.68/0.92  (step t33.t16.t38.t8 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t16.t38.t7 t33.t16.t38.t8))
% 0.68/0.92  (step t33.t16.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t16.t38.t6 t33.t16.t38.t9))
% 0.68/0.92  (step t33.t16.t38.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t16.t38.t10 t33.t16.t38.t11))
% 0.68/0.92  (step t33.t16.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t16.t38.t12 t33.t16.t38.t13))
% 0.68/0.92  (step t33.t16.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t16.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t16.t37 t33.t16.t38))
% 0.68/0.92  (step t33.t16.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t41.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t41.t2 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.92  (step t33.t16.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t16.t41.t4 t33.t16.t41.t5))
% 0.68/0.92  (step t33.t16.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.92  (anchor :step t33.t16.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t16.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t16.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t16.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t16.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t16.t41.t8.t3 t33.t16.t41.t8.t4))
% 0.68/0.92  (step t33.t16.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t16.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t16.t41.t7 t33.t16.t41.t8))
% 0.68/0.92  (step t33.t16.t41.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t16.t41.t6 t33.t16.t41.t9))
% 0.68/0.92  (step t33.t16.t41.t11 (cl (= V V)) :rule refl)
% 0.68/0.92  (step t33.t16.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t16.t41.t10 t33.t16.t41.t11))
% 0.68/0.92  (step t33.t16.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t41.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 (t33.t16.t41.t12 t33.t16.t41.t13))
% 0.68/0.92  (step t33.t16.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t41.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 (t33.t16.t41.t14 t33.t16.t41.t15))
% 0.68/0.92  (step t33.t16.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t16.t41.t16 t33.t16.t41.t17))
% 0.68/0.92  (step t33.t16.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.92  (step t33.t16.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t16.t40 t33.t16.t41))
% 0.68/0.92  (step t33.t16.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t16.t39 t33.t16.t42))
% 0.68/0.92  (step t33.t16.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t16.t36 t33.t16.t43 a5))
% 0.68/0.92  (step t33.t16.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t16.t16 t33.t16.t21 t33.t16.t30 a7 t33.t16.t35 t33.t16.t44 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t16.t45))
% 0.68/0.92  (step t33.t16.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t16.t45))
% 0.68/0.92  (step t33.t16.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t16.t46 t33.t16.t47))
% 0.68/0.92  (step t33.t16.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t16.t15 t33.t16.t48))
% 0.68/0.92  (step t33.t16.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t16.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t16.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t16.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (anchor :step t33.t16.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.92  (step t33.t16.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t16.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.92  (step t33.t16.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t16.t52.t2.t2 t33.t16.t52.t2.t3))
% 0.68/0.92  (step t33.t16.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t16.t52.t2.t4 t33.t16.t52.t2.t5))
% 0.68/0.92  (step t33.t16.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.92  (step t33.t16.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t16.t52.t2 t33.t16.t52.t3))
% 0.68/0.92  (step t33.t16.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t16.t52.t4))
% 0.68/0.92  (step t33.t16.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t16.t52.t5 t33.t16.t52.t6))
% 0.68/0.92  (step t33.t16.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.92  (step t33.t16.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.92  (step t33.t16.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t16.t52 t33.t16.t53))
% 0.68/0.92  (step t33.t16.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t16.t51 t33.t16.t54))
% 0.68/0.92  (step t33.t16.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t16.t50 t33.t16.t55))
% 0.68/0.92  (step t33.t16.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t16.t49 t33.t16.t56))
% 0.68/0.92  (step t33.t16.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t16.t14 t33.t16.t57 a10))
% 0.68/0.92  (step t33.t16.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t16.t4 t33.t16.t13 t33.t16.t58 t33.t16.t21 t33.t16.t30 a7 t33.t16.t35 t33.t16.t44 a4 a3 a2))
% 0.68/0.92  (step t33.t16.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t16.t59))
% 0.68/0.92  (step t33.t16.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t16.t59))
% 0.68/0.92  (step t33.t16.t62 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t16.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t16.t61 t33.t16.t62))
% 0.68/0.92  (step t33.t16.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t16.t60 t33.t16.t63))
% 0.68/0.92  (step t33.t16.t65 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t16.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t33.t16.t61 t33.t16.t65))
% 0.68/0.92  (step t33.t16.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t33.t16.t64 t33.t16.t66))
% 0.68/0.92  (step t33.t16.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t16.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t33.t16.t67 t33.t16.t68))
% 0.68/0.92  (step t33.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.68/0.92  (step t33.t17 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t33.t15 t33.t16))
% 0.68/0.92  (step t33.t18 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.92  (anchor :step t33.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t19.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t19.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t19.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)
% 0.68/0.92  (step t33.t19.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t19.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t19.t4 t33.t19.t5))
% 0.68/0.92  (step t33.t19.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t19.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t19.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.92  (step t33.t19.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t19.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t19.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.92  (step t33.t19.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t33.t19.t8.t3 t33.t19.t8.t4))
% 0.68/0.92  (step t33.t19.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.68/0.92  (step t33.t19.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t33.t19.t7 t33.t19.t8))
% 0.68/0.92  (step t33.t19.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t33.t19.t6 t33.t19.t9))
% 0.68/0.92  (step t33.t19.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t19.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t33.t19.t10 t33.t19.t11))
% 0.68/0.92  (step t33.t19.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.68/0.92  (anchor :step t33.t19.t14 :args ((U $$unsorted) (:= U U)))
% 0.68/0.92  (step t33.t19.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.92  (step t33.t19.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.68/0.92  (step t33.t19.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.68/0.92  (step t33.t19.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t33.t19.t14.t2 t33.t19.t14.t3))
% 0.68/0.92  (step t33.t19.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t33.t19.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t33.t19.t13 t33.t19.t14))
% 0.68/0.92  (step t33.t19.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t33.t19.t12 t33.t19.t15))
% 0.68/0.92  (step t33.t19.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t19.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t33.t19.t16 t33.t19.t17))
% 0.68/0.92  (step t33.t19.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.68/0.92  (step t33.t19.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t33.t19.t18 t33.t19.t19))
% 0.68/0.92  (step t33.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.68/0.92  (step t33.t20 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t33.t18 t33.t19))
% 0.68/0.92  (step t33.t21 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t33.t17 t33.t20))
% 0.68/0.92  (step t33.t22 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t33.t14 t33.t21 a12))
% 0.68/0.92  (step t33.t23 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t24 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.92  (anchor :step t33.t25 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.92  (step t33.t25.t1 (cl (= P P)) :rule refl)
% 0.68/0.92  (step t33.t25.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.92  (step t33.t25.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.92  (step t33.t25.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.92  (step t33.t25.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.92  (step t33.t25.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.92  (step t33.t25.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.93  (step t33.t25.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t25.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.93  (step t33.t25.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t25.t9 t33.t25.t10))
% 0.68/0.93  (step t33.t25.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t25.t8 t33.t25.t11 a9))
% 0.68/0.93  (step t33.t25.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t25.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t25.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.93  (step t33.t25.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t25.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.93  (step t33.t25.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.93  (step t33.t25.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t25.t15.t5 t33.t25.t15.t6))
% 0.68/0.93  (step t33.t25.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t25.t15.t4 t33.t25.t15.t7 a6))
% 0.68/0.93  (step t33.t25.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t25.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t25.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.93  (step t33.t25.t15.t11.t5 (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)))))) :rule resolution :premises (t33.t25.t15.t11.t4 a4 a3 a2))
% 0.68/0.93  (step t33.t25.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t25.t15.t11.t5))
% 0.68/0.93  (step t33.t25.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t25.t15.t11.t5))
% 0.68/0.93  (step t33.t25.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t25.t15.t11.t7 t33.t25.t15.t11.t8))
% 0.68/0.93  (step t33.t25.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t25.t15.t11.t6 t33.t25.t15.t11.t9))
% 0.68/0.93  (step t33.t25.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t25.t15.t11.t10 t33.t25.t15.t11.t11))
% 0.68/0.93  (step t33.t25.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t25.t15.t11.t12 t33.t25.t15.t11.t13))
% 0.68/0.93  (step t33.t25.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t33.t25.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t25.t15.t10 t33.t25.t15.t11))
% 0.68/0.93  (step t33.t25.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t25.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t25.t15.t14.t4 t33.t25.t15.t14.t5))
% 0.68/0.93  (step t33.t25.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.93  (anchor :step t33.t25.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.93  (step t33.t25.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t25.t15.t14.t8.t3 t33.t25.t15.t14.t8.t4))
% 0.68/0.93  (step t33.t25.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.93  (step t33.t25.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t25.t15.t14.t7 t33.t25.t15.t14.t8))
% 0.68/0.93  (step t33.t25.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t25.t15.t14.t6 t33.t25.t15.t14.t9))
% 0.68/0.93  (step t33.t25.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t25.t15.t14.t10 t33.t25.t15.t14.t11))
% 0.68/0.93  (step t33.t25.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t15.t14.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 (t33.t25.t15.t14.t12 t33.t25.t15.t14.t13))
% 0.68/0.93  (step t33.t25.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t14.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 (t33.t25.t15.t14.t14 t33.t25.t15.t14.t15))
% 0.68/0.93  (step t33.t25.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t25.t15.t14.t16 t33.t25.t15.t14.t17))
% 0.68/0.93  (step t33.t25.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.93  (step t33.t25.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t25.t15.t13 t33.t25.t15.t14))
% 0.68/0.93  (step t33.t25.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t25.t15.t12 t33.t25.t15.t15))
% 0.68/0.93  (step t33.t25.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t25.t15.t9 t33.t25.t15.t16 a5))
% 0.68/0.93  (step t33.t25.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t25.t15.t3 a7 t33.t25.t15.t8 t33.t25.t15.t17 a4 a3 a2))
% 0.68/0.93  (step t33.t25.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t25.t15.t18))
% 0.68/0.93  (step t33.t25.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t25.t15.t18))
% 0.68/0.93  (step t33.t25.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t25.t15.t20 t33.t25.t15.t21))
% 0.68/0.93  (step t33.t25.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t25.t15.t19 t33.t25.t15.t22))
% 0.68/0.93  (step t33.t25.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t25.t15.t23 t33.t25.t15.t24))
% 0.68/0.93  (step t33.t25.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t33.t25.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t25.t14 t33.t25.t15))
% 0.68/0.93  (step t33.t25.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t25.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t25.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.93  (step t33.t25.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t25.t18.t3 t33.t25.t18.t4))
% 0.68/0.93  (step t33.t25.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.93  (anchor :step t33.t25.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.93  (step t33.t25.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t25.t18.t7.t2))
% 0.68/0.93  (step t33.t25.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.93  (step t33.t25.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t25.t18.t6 t33.t25.t18.t7))
% 0.68/0.93  (step t33.t25.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t25.t18.t5 t33.t25.t18.t8))
% 0.68/0.93  (step t33.t25.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t25.t18.t9 t33.t25.t18.t10))
% 0.68/0.93  (step t33.t25.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t25.t18.t11 t33.t25.t18.t12))
% 0.68/0.93  (step t33.t25.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.93  (step t33.t25.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t25.t17 t33.t25.t18))
% 0.68/0.93  (step t33.t25.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t25.t16 t33.t25.t19))
% 0.68/0.93  (step t33.t25.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t25.t13 t33.t25.t20 a8))
% 0.68/0.93  (step t33.t25.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t25.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.93  (step t33.t25.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t25.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.93  (step t33.t25.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.93  (step t33.t25.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t25.t23 t33.t25.t24))
% 0.68/0.93  (step t33.t25.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t25.t22 t33.t25.t25 a6))
% 0.68/0.93  (step t33.t25.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t25.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t25.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.93  (step t33.t25.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t25.t29.t4 a4 a3 a2))
% 0.68/0.93  (step t33.t25.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t25.t29.t5))
% 0.68/0.93  (step t33.t25.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t25.t29.t5))
% 0.68/0.93  (step t33.t25.t29.t8 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t25.t29.t7 t33.t25.t29.t8))
% 0.68/0.93  (step t33.t25.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t25.t29.t6 t33.t25.t29.t9))
% 0.68/0.93  (step t33.t25.t29.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t25.t29.t10 t33.t25.t29.t11))
% 0.68/0.93  (step t33.t25.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t25.t29.t12 t33.t25.t29.t13))
% 0.68/0.93  (step t33.t25.t29 (cl (= (lambda ((U (-> $$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)
% 0.68/0.93  (step t33.t25.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t25.t28 t33.t25.t29))
% 0.68/0.93  (step t33.t25.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t25.t32.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t32.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t32.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)
% 0.68/0.93  (step t33.t25.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t32.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t25.t32.t4 t33.t25.t32.t5))
% 0.68/0.93  (step t33.t25.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.93  (anchor :step t33.t25.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.93  (step t33.t25.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.93  (step t33.t25.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t25.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.93  (step t33.t25.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t25.t32.t8.t3 t33.t25.t32.t8.t4))
% 0.68/0.93  (step t33.t25.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.93  (step t33.t25.t32.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 (t33.t25.t32.t7 t33.t25.t32.t8))
% 0.68/0.93  (step t33.t25.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t25.t32.t6 t33.t25.t32.t9))
% 0.68/0.93  (step t33.t25.t32.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t25.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t25.t32.t10 t33.t25.t32.t11))
% 0.68/0.93  (step t33.t25.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t25.t32.t12 t33.t25.t32.t13))
% 0.68/0.93  (step t33.t25.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t25.t32.t14 t33.t25.t32.t15))
% 0.68/0.93  (step t33.t25.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t25.t32.t16 t33.t25.t32.t17))
% 0.68/0.93  (step t33.t25.t32 (cl (= (lambda ((U (-> $$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)
% 0.68/0.93  (step t33.t25.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t25.t31 t33.t25.t32))
% 0.68/0.93  (step t33.t25.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t25.t30 t33.t25.t33))
% 0.68/0.93  (step t33.t25.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t25.t27 t33.t25.t34 a5))
% 0.68/0.93  (step t33.t25.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t25.t7 t33.t25.t12 t33.t25.t21 a7 t33.t25.t26 t33.t25.t35 a4 a3 a2))
% 0.68/0.93  (step t33.t25.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t25.t36))
% 0.68/0.93  (step t33.t25.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t25.t36))
% 0.68/0.93  (step t33.t25.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t25.t37 t33.t25.t38))
% 0.68/0.93  (step t33.t25.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t25.t6 t33.t25.t39))
% 0.68/0.93  (step t33.t25.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.93  (step t33.t25.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.93  (anchor :step t33.t25.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t25.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (anchor :step t33.t25.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.93  (step t33.t25.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.93  (step t33.t25.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.93  (step t33.t25.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t25.t43.t2.t2 t33.t25.t43.t2.t3))
% 0.68/0.93  (step t33.t25.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t25.t43.t2.t4 t33.t25.t43.t2.t5))
% 0.68/0.93  (step t33.t25.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.93  (step t33.t25.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t25.t43.t2 t33.t25.t43.t3))
% 0.68/0.93  (step t33.t25.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t25.t43.t4))
% 0.68/0.93  (step t33.t25.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t25.t43.t5 t33.t25.t43.t6))
% 0.68/0.93  (step t33.t25.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.93  (step t33.t25.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.93  (step t33.t25.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t25.t43 t33.t25.t44))
% 0.68/0.93  (step t33.t25.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t25.t42 t33.t25.t45))
% 0.68/0.93  (step t33.t25.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t25.t41 t33.t25.t46))
% 0.68/0.93  (step t33.t25.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t25.t40 t33.t25.t47))
% 0.68/0.93  (step t33.t25.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t25.t5 t33.t25.t48 a10))
% 0.68/0.93  (step t33.t25.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t25.t4 t33.t25.t49 t33.t25.t12 t33.t25.t21 a7 t33.t25.t26 t33.t25.t35 a4 a3 a2))
% 0.68/0.93  (step t33.t25.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t33.t25.t50))
% 0.68/0.93  (step t33.t25.t52 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t25.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t33.t25.t51 t33.t25.t52))
% 0.68/0.93  (step t33.t25.t54 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t33.t25.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t33.t25.t53 t33.t25.t54))
% 0.68/0.93  (step t33.t25.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t25.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t33.t25.t55 t33.t25.t56))
% 0.68/0.93  (step t33.t25 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t33.t26 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t33.t24 t33.t25))
% 0.68/0.93  (step t33.t27 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.93  (anchor :step t33.t28 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t28.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t28.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t33.t28.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t28.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t28.t5 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t33.t28.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t33.t28.t4 t33.t28.t5))
% 0.68/0.93  (step t33.t28.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t28.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t33.t28.t6 t33.t28.t7))
% 0.68/0.93  (step t33.t28.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t28.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t33.t28.t8 t33.t28.t9))
% 0.68/0.93  (step t33.t28.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.68/0.93  (step t33.t28.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t33.t28.t10 t33.t28.t11))
% 0.68/0.93  (step t33.t28 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.68/0.93  (step t33.t29 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t33.t27 t33.t28))
% 0.68/0.93  (step t33.t30 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t33.t26 t33.t29))
% 0.68/0.93  (step t33.t31 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t33.t23 t33.t30 a11))
% 0.68/0.93  (step t33.t32 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t33 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.93  (step t33.t34 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.93  (step t33.t35 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t36 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.93  (step t33.t37 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.93  (step t33.t38 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t36 t33.t37))
% 0.68/0.93  (step t33.t39 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t33.t35 t33.t38 a9))
% 0.68/0.93  (step t33.t40 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t41 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.93  (anchor :step t33.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t42.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t42.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.93  (step t33.t42.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t42.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.93  (anchor :step t33.t42.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.93  (step t33.t42.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t42.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.93  (step t33.t42.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t33.t42.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.93  (step t33.t42.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t42.t5 t33.t42.t6))
% 0.68/0.93  (step t33.t42.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t42.t4 t33.t42.t7 a6))
% 0.68/0.93  (step t33.t42.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t42.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t42.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t42.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t42.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t42.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t42.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.93  (step t33.t42.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t42.t11.t4 a4 a3 a2))
% 0.68/0.93  (step t33.t42.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t42.t11.t5))
% 0.68/0.93  (step t33.t42.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t42.t11.t5))
% 0.68/0.93  (step t33.t42.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t42.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t42.t11.t7 t33.t42.t11.t8))
% 0.68/0.93  (step t33.t42.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t33.t42.t11.t6 t33.t42.t11.t9))
% 0.68/0.93  (step t33.t42.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t42.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t33.t42.t11.t10 t33.t42.t11.t11))
% 0.68/0.93  (step t33.t42.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t42.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t33.t42.t11.t12 t33.t42.t11.t13))
% 0.68/0.93  (step t33.t42.t11 (cl (= (lambda ((U (-> $$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)
% 0.68/0.93  (step t33.t42.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t33.t42.t10 t33.t42.t11))
% 0.68/0.93  (step t33.t42.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t42.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t42.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t42.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t42.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t42.t14.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)
% 0.68/0.93  (step t33.t42.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t42.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t33.t42.t14.t4 t33.t42.t14.t5))
% 0.68/0.93  (step t33.t42.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.68/0.93  (anchor :step t33.t42.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.93  (step t33.t42.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.93  (step t33.t42.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t42.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.93  (step t33.t42.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.93  (step t33.t42.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t42.t14.t8.t3 t33.t42.t14.t8.t4))
% 0.68/0.93  (step t33.t42.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.68/0.93  (step t33.t42.t14.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 (t33.t42.t14.t7 t33.t42.t14.t8))
% 0.68/0.93  (step t33.t42.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t42.t14.t6 t33.t42.t14.t9))
% 0.68/0.93  (step t33.t42.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t42.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t33.t42.t14.t10 t33.t42.t14.t11))
% 0.68/0.93  (step t33.t42.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t42.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t33.t42.t14.t12 t33.t42.t14.t13))
% 0.68/0.93  (step t33.t42.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t42.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t33.t42.t14.t14 t33.t42.t14.t15))
% 0.68/0.93  (step t33.t42.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.93  (step t33.t42.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t33.t42.t14.t16 t33.t42.t14.t17))
% 0.68/0.93  (step t33.t42.t14 (cl (= (lambda ((U (-> $$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)
% 0.68/0.93  (step t33.t42.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t42.t13 t33.t42.t14))
% 0.68/0.93  (step t33.t42.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t42.t12 t33.t42.t15))
% 0.68/0.93  (step t33.t42.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t42.t9 t33.t42.t16 a5))
% 0.68/0.93  (step t33.t42.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t33.t42.t3 a7 t33.t42.t8 t33.t42.t17 a4 a3 a2))
% 0.68/0.93  (step t33.t42.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t42.t18))
% 0.68/0.93  (step t33.t42.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t33.t42.t18))
% 0.68/0.93  (step t33.t42.t21 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t42.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t33.t42.t20 t33.t42.t21))
% 0.68/0.93  (step t33.t42.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t33.t42.t19 t33.t42.t22))
% 0.68/0.93  (step t33.t42.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t42.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t33.t42.t23 t33.t42.t24))
% 0.68/0.93  (step t33.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t33.t43 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t33.t41 t33.t42))
% 0.68/0.93  (step t33.t44 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.93  (anchor :step t33.t45 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t45.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t45.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t45.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.93  (step t33.t45.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.93  (step t33.t45.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t45.t3 t33.t45.t4))
% 0.68/0.93  (step t33.t45.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.93  (anchor :step t33.t45.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.93  (step t33.t45.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t45.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t33.t45.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t33.t45.t7.t2))
% 0.68/0.93  (step t33.t45.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.93  (step t33.t45.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t45.t6 t33.t45.t7))
% 0.68/0.93  (step t33.t45.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t33.t45.t5 t33.t45.t8))
% 0.68/0.93  (step t33.t45.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t45.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t33.t45.t9 t33.t45.t10))
% 0.68/0.93  (step t33.t45.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.93  (step t33.t45.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t33.t45.t11 t33.t45.t12))
% 0.68/0.93  (step t33.t45 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.93  (step t33.t46 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t33.t44 t33.t45))
% 0.68/0.93  (step t33.t47 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t33.t43 t33.t46))
% 0.68/0.93  (step t33.t48 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t33.t40 t33.t47 a8))
% 0.68/0.93  (step t33.t49 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t50 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.93  (anchor :step t33.t51 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.93  (step t33.t51.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t51.t2 (cl (= X X)) :rule refl)
% 0.68/0.93  (step t33.t51.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t33.t51 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.93  (step t33.t52 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t33.t50 t33.t51))
% 0.68/0.93  (step t33.t53 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t33.t49 t33.t52 a6))
% 0.68/0.93  (step t33.t54 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.93  (step t33.t55 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t56 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t56.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t56.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t56.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t56.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))))) (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)))))) :rule and_neg)
% 0.68/0.93  (step t33.t56.t5 (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)))))) :rule resolution :premises (t33.t56.t4 a4 a3 a2))
% 0.68/0.93  (step t33.t56.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t33.t56.t5))
% 0.68/0.93  (step t33.t56.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t33.t56.t5))
% 0.68/0.93  (step t33.t56.t8 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t56.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t33.t56.t7 t33.t56.t8))
% 0.68/0.93  (step t33.t56.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t33.t56.t6 t33.t56.t9))
% 0.68/0.93  (step t33.t56.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t56.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t33.t56.t10 t33.t56.t11))
% 0.68/0.93  (step t33.t56.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t56.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t33.t56.t12 t33.t56.t13))
% 0.68/0.93  (step t33.t56 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t33.t57 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t33.t55 t33.t56))
% 0.68/0.93  (step t33.t58 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t33.t59 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t59.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t59.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t59.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t59.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.93  (step t33.t59.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t59.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t33.t59.t4 t33.t59.t5))
% 0.68/0.93  (step t33.t59.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.93  (anchor :step t33.t59.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.93  (step t33.t59.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.93  (step t33.t59.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t33.t59.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.93  (step t33.t59.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.93  (step t33.t59.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t33.t59.t8.t3 t33.t59.t8.t4))
% 0.68/0.93  (step t33.t59.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.93  (step t33.t59.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t33.t59.t7 t33.t59.t8))
% 0.68/0.93  (step t33.t59.t10 (cl (= (@ (lambda ((X (-> $$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 (t33.t59.t6 t33.t59.t9))
% 0.68/0.93  (step t33.t59.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t33.t59.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t33.t59.t10 t33.t59.t11))
% 0.68/0.93  (step t33.t59.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.93  (step t33.t59.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 (t33.t59.t12 t33.t59.t13))
% 0.68/0.93  (step t33.t59.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t59.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 (t33.t59.t14 t33.t59.t15))
% 0.68/0.93  (step t33.t59.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.93  (step t33.t59.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t33.t59.t16 t33.t59.t17))
% 0.68/0.93  (step t33.t59 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.93  (step t33.t60 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t33.t58 t33.t59))
% 0.68/0.93  (step t33.t61 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t33.t57 t33.t60))
% 0.68/0.93  (step t33.t62 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t33.t54 t33.t61 a5))
% 0.68/0.93  (step t33.t63 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t34 t33.t39 t33.t48 a7 t33.t53 t33.t62 a4 a3 a2))
% 0.68/0.93  (step t33.t64 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t33.t63))
% 0.68/0.93  (step t33.t65 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t33.t63))
% 0.68/0.93  (step t33.t66 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t33.t64 t33.t65))
% 0.68/0.93  (step t33.t67 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t33.t33 t33.t66))
% 0.68/0.93  (step t33.t68 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.93  (step t33.t69 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.68/0.93  (anchor :step t33.t70 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t33.t70.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (anchor :step t33.t70.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.68/0.93  (step t33.t70.t2.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.93  (step t33.t70.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.68/0.93  (step t33.t70.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.68/0.93  (step t33.t70.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t33.t70.t2.t2 t33.t70.t2.t3))
% 0.68/0.93  (step t33.t70.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.68/0.93  (step t33.t70.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t33.t70.t2.t4 t33.t70.t2.t5))
% 0.68/0.93  (step t33.t70.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.68/0.93  (step t33.t70.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.68/0.93  (step t33.t70.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t33.t70.t2 t33.t70.t3))
% 0.68/0.93  (step t33.t70.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t33.t70.t4))
% 0.68/0.93  (step t33.t70.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.68/0.93  (step t33.t70.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t33.t70.t5 t33.t70.t6))
% 0.68/0.93  (step t33.t70 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.68/0.93  (step t33.t71 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.68/0.93  (step t33.t72 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t70 t33.t71))
% 0.68/0.93  (step t33.t73 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t33.t69 t33.t72))
% 0.68/0.93  (step t33.t74 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t33.t68 t33.t73))
% 0.68/0.93  (step t33.t75 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t33.t67 t33.t74))
% 0.68/0.93  (step t33.t76 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t33.t32 t33.t75 a10))
% 0.68/0.93  (step t33.t77 (cl (and (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t33.t4 t33.t13 t33.t22 t33.t31 t33.t76 t33.t39 t33.t48 a7 t33.t53 t33.t62 a4 a3 a2))
% 0.68/0.93  (step t33.t78 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule and :premises (t33.t77))
% 0.68/0.93  (step t33.t79 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t33.t80 (cl (= (@ tptp.iimplies Q) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q))) :rule cong :premises (t33.t78 t33.t79))
% 0.68/0.93  (step t33.t81 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t33.t82 (cl (= (@ (@ tptp.iimplies Q) P) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P))) :rule cong :premises (t33.t80 t33.t81))
% 0.68/0.93  (step t33.t83 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t33.t84 (cl (= (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) :rule cong :premises (t33.t82 t33.t83))
% 0.68/0.93  (step t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t34 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))))) :rule cong :premises (t32 t33))
% 0.68/0.93  (step t35 (cl (= tptp.iimplied tptp.iimplied)) :rule refl)
% 0.68/0.93  (anchor :step t36 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t36.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t36.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t36.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule all_simplify)
% 0.68/0.93  (step t36.t5 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t36.t6 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P))) :rule cong :premises (t36.t4 t36.t5))
% 0.68/0.93  (step t36.t7 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule all_simplify)
% 0.68/0.93  (step t36.t8 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule trans :premises (t36.t6 t36.t7))
% 0.68/0.93  (step t36.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t36.t10 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t36.t8 t36.t9))
% 0.68/0.93  (step t36.t11 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.93  (step t36.t12 (cl (= (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t36.t10 t36.t11))
% 0.68/0.93  (step t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.93  (step t37 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t35 t36))
% 0.68/0.93  (step t38 (cl (= (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t34 t37))
% 0.68/0.93  (step t39 (cl (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t31 t38 a14))
% 0.68/0.93  (step t40 (cl (not (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.93  (step t41 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.68/0.93  (anchor :step t42 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t42.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t4 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.93  (step t42.t5 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t6 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t42.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.93  (step t42.t7.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t7.t7.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t2 (cl (= Q Q)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.93  (step t42.t7.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.68/0.93  (step t42.t7.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t7.t7.t9 t42.t7.t7.t10))
% 0.68/0.93  (step t42.t7.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t42.t7.t7.t8 t42.t7.t7.t11 a9))
% 0.68/0.93  (step t42.t7.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t7.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.68/0.93  (step t42.t7.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.93  (step t42.t7.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t7.t7.t15.t5 t42.t7.t7.t15.t6))
% 0.68/0.93  (step t42.t7.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t7.t7.t15.t4 t42.t7.t7.t15.t7 a6))
% 0.68/0.93  (step t42.t7.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t7.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.68/0.93  (step t42.t7.t7.t15.t11.t5 (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)))))) :rule resolution :premises (t42.t7.t7.t15.t11.t4 a4 a3 a2))
% 0.68/0.93  (step t42.t7.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t7.t7.t15.t11.t5))
% 0.68/0.93  (step t42.t7.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t7.t7.t15.t11.t5))
% 0.68/0.93  (step t42.t7.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t7.t7.t15.t11.t7 t42.t7.t7.t15.t11.t8))
% 0.68/0.93  (step t42.t7.t7.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t42.t7.t7.t15.t11.t6 t42.t7.t7.t15.t11.t9))
% 0.68/0.93  (step t42.t7.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t42.t7.t7.t15.t11.t10 t42.t7.t7.t15.t11.t11))
% 0.68/0.93  (step t42.t7.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t42.t7.t7.t15.t11.t12 t42.t7.t7.t15.t11.t13))
% 0.68/0.93  (step t42.t7.t7.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t42.t7.t7.t15.t10 t42.t7.t7.t15.t11))
% 0.68/0.93  (step t42.t7.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t42.t7.t7.t15.t14.t4 t42.t7.t7.t15.t14.t5))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.68/0.93  (anchor :step t42.t7.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t7.t7.t15.t14.t8.t3 t42.t7.t7.t15.t14.t8.t4))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t7.t7.t15.t14.t7 t42.t7.t7.t15.t14.t8))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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.t7.t7.t15.t14.t6 t42.t7.t7.t15.t14.t9))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t42.t7.t7.t15.t14.t10 t42.t7.t7.t15.t14.t11))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t15.t14.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.t7.t7.t15.t14.t12 t42.t7.t7.t15.t14.t13))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t14.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.t7.t7.t15.t14.t14 t42.t7.t7.t15.t14.t15))
% 0.68/0.93  (step t42.t7.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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.t7.t7.t15.t14.t16 t42.t7.t7.t15.t14.t17))
% 0.68/0.93  (step t42.t7.t7.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t7.t7.t15.t13 t42.t7.t7.t15.t14))
% 0.68/0.93  (step t42.t7.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t7.t7.t15.t12 t42.t7.t7.t15.t15))
% 0.68/0.93  (step t42.t7.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t7.t7.t15.t9 t42.t7.t7.t15.t16 a5))
% 0.68/0.93  (step t42.t7.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t7.t7.t15.t3 a7 t42.t7.t7.t15.t8 t42.t7.t7.t15.t17 a4 a3 a2))
% 0.68/0.93  (step t42.t7.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t7.t7.t15.t18))
% 0.68/0.93  (step t42.t7.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t42.t7.t7.t15.t18))
% 0.68/0.93  (step t42.t7.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t42.t7.t7.t15.t20 t42.t7.t7.t15.t21))
% 0.68/0.93  (step t42.t7.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t42.t7.t7.t15.t19 t42.t7.t7.t15.t22))
% 0.68/0.93  (step t42.t7.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t42.t7.t7.t15.t23 t42.t7.t7.t15.t24))
% 0.68/0.93  (step t42.t7.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t42.t7.t7.t14 t42.t7.t7.t15))
% 0.68/0.93  (step t42.t7.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t7.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t7.t7.t18.t3 t42.t7.t7.t18.t4))
% 0.68/0.93  (step t42.t7.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.68/0.93  (anchor :step t42.t7.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.68/0.93  (step t42.t7.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t42.t7.t7.t18.t7.t2))
% 0.68/0.93  (step t42.t7.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t7.t7.t18.t6 t42.t7.t7.t18.t7))
% 0.68/0.93  (step t42.t7.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t7.t7.t18.t5 t42.t7.t7.t18.t8))
% 0.68/0.93  (step t42.t7.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t42.t7.t7.t18.t9 t42.t7.t7.t18.t10))
% 0.68/0.93  (step t42.t7.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t42.t7.t7.t18.t11 t42.t7.t7.t18.t12))
% 0.68/0.93  (step t42.t7.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t42.t7.t7.t17 t42.t7.t7.t18))
% 0.68/0.93  (step t42.t7.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t42.t7.t7.t16 t42.t7.t7.t19))
% 0.68/0.93  (step t42.t7.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t42.t7.t7.t13 t42.t7.t7.t20 a8))
% 0.68/0.93  (step t42.t7.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.68/0.93  (step t42.t7.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.68/0.93  (step t42.t7.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.68/0.93  (step t42.t7.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t7.t7.t23 t42.t7.t7.t24))
% 0.68/0.93  (step t42.t7.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t7.t7.t22 t42.t7.t7.t25 a6))
% 0.68/0.93  (step t42.t7.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.68/0.93  (step t42.t7.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.68/0.93  (anchor :step t42.t7.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.68/0.93  (step t42.t7.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.68/0.93  (step t42.t7.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t7.t7.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t7.t7.t29.t4 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t7.t7.t29.t5))
% 0.72/0.93  (step t42.t7.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t7.t7.t29.t5))
% 0.72/0.93  (step t42.t7.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t7.t7.t29.t7 t42.t7.t7.t29.t8))
% 0.72/0.93  (step t42.t7.t7.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t42.t7.t7.t29.t6 t42.t7.t7.t29.t9))
% 0.72/0.93  (step t42.t7.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t42.t7.t7.t29.t10 t42.t7.t7.t29.t11))
% 0.72/0.93  (step t42.t7.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t42.t7.t7.t29.t12 t42.t7.t7.t29.t13))
% 0.72/0.93  (step t42.t7.t7.t29 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t7.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t42.t7.t7.t28 t42.t7.t7.t29))
% 0.72/0.93  (step t42.t7.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.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)
% 0.72/0.93  (step t42.t7.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t32.t6 (cl (= (@ (lambda ((X (-> $$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.t7.t7.t32.t4 t42.t7.t7.t32.t5))
% 0.72/0.93  (step t42.t7.t7.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t7.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t7.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t7.t7.t32.t8.t3 t42.t7.t7.t32.t8.t4))
% 0.72/0.93  (step t42.t7.t7.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.93  (step t42.t7.t7.t32.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.t7.t32.t7 t42.t7.t7.t32.t8))
% 0.72/0.93  (step t42.t7.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t7.t7.t32.t6 t42.t7.t7.t32.t9))
% 0.72/0.93  (step t42.t7.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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.t7.t7.t32.t10 t42.t7.t7.t32.t11))
% 0.72/0.93  (step t42.t7.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t42.t7.t7.t32.t12 t42.t7.t7.t32.t13))
% 0.72/0.93  (step t42.t7.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t42.t7.t7.t32.t14 t42.t7.t7.t32.t15))
% 0.72/0.93  (step t42.t7.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t42.t7.t7.t32.t16 t42.t7.t7.t32.t17))
% 0.72/0.93  (step t42.t7.t7.t32 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t7.t7.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t7.t7.t31 t42.t7.t7.t32))
% 0.72/0.93  (step t42.t7.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t7.t7.t30 t42.t7.t7.t33))
% 0.72/0.93  (step t42.t7.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t7.t7.t27 t42.t7.t7.t34 a5))
% 0.72/0.93  (step t42.t7.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t42.t7.t7.t7 t42.t7.t7.t12 t42.t7.t7.t21 a7 t42.t7.t7.t26 t42.t7.t7.t35 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t42.t7.t7.t36))
% 0.72/0.93  (step t42.t7.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t42.t7.t7.t36))
% 0.72/0.93  (step t42.t7.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t7.t7.t37 t42.t7.t7.t38))
% 0.72/0.93  (step t42.t7.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t42.t7.t7.t6 t42.t7.t7.t39))
% 0.72/0.93  (step t42.t7.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t7.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.93  (step t42.t7.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t42.t7.t7.t43.t2.t2 t42.t7.t7.t43.t2.t3))
% 0.72/0.93  (step t42.t7.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t42.t7.t7.t43.t2.t4 t42.t7.t7.t43.t2.t5))
% 0.72/0.93  (step t42.t7.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.93  (step t42.t7.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t42.t7.t7.t43.t2 t42.t7.t7.t43.t3))
% 0.72/0.93  (step t42.t7.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t42.t7.t7.t43.t4))
% 0.72/0.93  (step t42.t7.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t42.t7.t7.t43.t5 t42.t7.t7.t43.t6))
% 0.72/0.93  (step t42.t7.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.93  (step t42.t7.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t7.t7.t43 t42.t7.t7.t44))
% 0.72/0.93  (step t42.t7.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t7.t7.t42 t42.t7.t7.t45))
% 0.72/0.93  (step t42.t7.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t42.t7.t7.t41 t42.t7.t7.t46))
% 0.72/0.93  (step t42.t7.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t42.t7.t7.t40 t42.t7.t7.t47))
% 0.72/0.93  (step t42.t7.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t42.t7.t7.t5 t42.t7.t7.t48 a10))
% 0.72/0.93  (step t42.t7.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t7.t7.t4 t42.t7.t7.t49 t42.t7.t7.t12 t42.t7.t7.t21 a7 t42.t7.t7.t26 t42.t7.t7.t35 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t42.t7.t7.t50))
% 0.72/0.93  (step t42.t7.t7.t52 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t42.t7.t7.t51 t42.t7.t7.t52))
% 0.72/0.93  (step t42.t7.t7.t54 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t42.t7.t7.t53 t42.t7.t7.t54))
% 0.72/0.93  (step t42.t7.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t42.t7.t7.t55 t42.t7.t7.t56))
% 0.72/0.93  (step t42.t7.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t7.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t42.t7.t6 t42.t7.t7))
% 0.72/0.93  (step t42.t7.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t10.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t10.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t7.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t10.t5 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t7.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t42.t7.t10.t4 t42.t7.t10.t5))
% 0.72/0.93  (step t42.t7.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t42.t7.t10.t6 t42.t7.t10.t7))
% 0.72/0.93  (step t42.t7.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t42.t7.t10.t8 t42.t7.t10.t9))
% 0.72/0.93  (step t42.t7.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t42.t7.t10.t10 t42.t7.t10.t11))
% 0.72/0.93  (step t42.t7.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t42.t7.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t42.t7.t9 t42.t7.t10))
% 0.72/0.93  (step t42.t7.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t42.t7.t8 t42.t7.t11))
% 0.72/0.93  (step t42.t7.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t42.t7.t5 t42.t7.t12 a11))
% 0.72/0.93  (step t42.t7.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t7.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t42.t7.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t42.t7.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t7.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.72/0.93  (step t42.t7.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t7.t18 t42.t7.t19))
% 0.72/0.93  (step t42.t7.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t42.t7.t17 t42.t7.t20 a9))
% 0.72/0.93  (step t42.t7.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t7.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t7.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t7.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t42.t7.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t42.t7.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t7.t24.t5 t42.t7.t24.t6))
% 0.72/0.93  (step t42.t7.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t7.t24.t4 t42.t7.t24.t7 a6))
% 0.72/0.93  (step t42.t7.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t7.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t7.t24.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t7.t24.t11.t4 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t7.t24.t11.t5))
% 0.72/0.93  (step t42.t7.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t7.t24.t11.t5))
% 0.72/0.93  (step t42.t7.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t7.t24.t11.t7 t42.t7.t24.t11.t8))
% 0.72/0.93  (step t42.t7.t24.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t42.t7.t24.t11.t6 t42.t7.t24.t11.t9))
% 0.72/0.93  (step t42.t7.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t42.t7.t24.t11.t10 t42.t7.t24.t11.t11))
% 0.72/0.93  (step t42.t7.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t42.t7.t24.t11.t12 t42.t7.t24.t11.t13))
% 0.72/0.93  (step t42.t7.t24.t11 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t7.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t42.t7.t24.t10 t42.t7.t24.t11))
% 0.72/0.93  (step t42.t7.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.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)
% 0.72/0.93  (step t42.t7.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t24.t14.t6 (cl (= (@ (lambda ((X (-> $$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.t7.t24.t14.t4 t42.t7.t24.t14.t5))
% 0.72/0.93  (step t42.t7.t24.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t7.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t7.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t7.t24.t14.t8.t3 t42.t7.t24.t14.t8.t4))
% 0.72/0.93  (step t42.t7.t24.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.93  (step t42.t7.t24.t14.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.t24.t14.t7 t42.t7.t24.t14.t8))
% 0.72/0.93  (step t42.t7.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t7.t24.t14.t6 t42.t7.t24.t14.t9))
% 0.72/0.93  (step t42.t7.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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.t7.t24.t14.t10 t42.t7.t24.t14.t11))
% 0.72/0.93  (step t42.t7.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t24.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t42.t7.t24.t14.t12 t42.t7.t24.t14.t13))
% 0.72/0.93  (step t42.t7.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t42.t7.t24.t14.t14 t42.t7.t24.t14.t15))
% 0.72/0.93  (step t42.t7.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t42.t7.t24.t14.t16 t42.t7.t24.t14.t17))
% 0.72/0.93  (step t42.t7.t24.t14 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t7.t24.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t7.t24.t13 t42.t7.t24.t14))
% 0.72/0.93  (step t42.t7.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t7.t24.t12 t42.t7.t24.t15))
% 0.72/0.93  (step t42.t7.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t7.t24.t9 t42.t7.t24.t16 a5))
% 0.72/0.93  (step t42.t7.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t42.t7.t24.t3 a7 t42.t7.t24.t8 t42.t7.t24.t17 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t7.t24.t18))
% 0.72/0.93  (step t42.t7.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t42.t7.t24.t18))
% 0.72/0.93  (step t42.t7.t24.t21 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t42.t7.t24.t20 t42.t7.t24.t21))
% 0.72/0.93  (step t42.t7.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t42.t7.t24.t19 t42.t7.t24.t22))
% 0.72/0.93  (step t42.t7.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t42.t7.t24.t23 t42.t7.t24.t24))
% 0.72/0.93  (step t42.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t7.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t42.t7.t23 t42.t7.t24))
% 0.72/0.93  (step t42.t7.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t27.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.72/0.93  (step t42.t7.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t7.t27.t3 t42.t7.t27.t4))
% 0.72/0.93  (step t42.t7.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t7.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t7.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t42.t7.t27.t7.t2))
% 0.72/0.93  (step t42.t7.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t42.t7.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t7.t27.t6 t42.t7.t27.t7))
% 0.72/0.93  (step t42.t7.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t7.t27.t5 t42.t7.t27.t8))
% 0.72/0.93  (step t42.t7.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t42.t7.t27.t9 t42.t7.t27.t10))
% 0.72/0.93  (step t42.t7.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t42.t7.t27.t11 t42.t7.t27.t12))
% 0.72/0.93  (step t42.t7.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t42.t7.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t42.t7.t26 t42.t7.t27))
% 0.72/0.93  (step t42.t7.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t42.t7.t25 t42.t7.t28))
% 0.72/0.93  (step t42.t7.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t42.t7.t22 t42.t7.t29 a8))
% 0.72/0.93  (step t42.t7.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t7.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t42.t7.t33.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t33.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t42.t7.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t42.t7.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t7.t32 t42.t7.t33))
% 0.72/0.93  (step t42.t7.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t7.t31 t42.t7.t34 a6))
% 0.72/0.93  (step t42.t7.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t7.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t38.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t38.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t38.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))))) (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)))))) :rule and_neg)
% 0.72/0.93  (step t42.t7.t38.t5 (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)))))) :rule resolution :premises (t42.t7.t38.t4 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t7.t38.t5))
% 0.72/0.93  (step t42.t7.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t7.t38.t5))
% 0.72/0.93  (step t42.t7.t38.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t7.t38.t7 t42.t7.t38.t8))
% 0.72/0.93  (step t42.t7.t38.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t42.t7.t38.t6 t42.t7.t38.t9))
% 0.72/0.93  (step t42.t7.t38.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t38.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t42.t7.t38.t10 t42.t7.t38.t11))
% 0.72/0.93  (step t42.t7.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t38.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t42.t7.t38.t12 t42.t7.t38.t13))
% 0.72/0.93  (step t42.t7.t38 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t7.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t42.t7.t37 t42.t7.t38))
% 0.72/0.93  (step t42.t7.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t41.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t41.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t41.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t42.t7.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t41.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t42.t7.t41.t4 t42.t7.t41.t5))
% 0.72/0.93  (step t42.t7.t41.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.72/0.93  (anchor :step t42.t7.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t7.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t7.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t7.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t7.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t7.t41.t8.t3 t42.t7.t41.t8.t4))
% 0.72/0.93  (step t42.t7.t41.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t42.t7.t41.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t7.t41.t7 t42.t7.t41.t8))
% 0.72/0.93  (step t42.t7.t41.t10 (cl (= (@ (lambda ((X (-> $$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.t7.t41.t6 t42.t7.t41.t9))
% 0.72/0.93  (step t42.t7.t41.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t7.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t42.t7.t41.t10 t42.t7.t41.t11))
% 0.72/0.93  (step t42.t7.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t41.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.t7.t41.t12 t42.t7.t41.t13))
% 0.72/0.93  (step t42.t7.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t41.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.t7.t41.t14 t42.t7.t41.t15))
% 0.72/0.93  (step t42.t7.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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.t7.t41.t16 t42.t7.t41.t17))
% 0.72/0.93  (step t42.t7.t41 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t42.t7.t42 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t7.t40 t42.t7.t41))
% 0.72/0.93  (step t42.t7.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t7.t39 t42.t7.t42))
% 0.72/0.93  (step t42.t7.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t7.t36 t42.t7.t43 a5))
% 0.72/0.93  (step t42.t7.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t7.t16 t42.t7.t21 t42.t7.t30 a7 t42.t7.t35 t42.t7.t44 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t42.t7.t45))
% 0.72/0.93  (step t42.t7.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t42.t7.t45))
% 0.72/0.93  (step t42.t7.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t7.t46 t42.t7.t47))
% 0.72/0.93  (step t42.t7.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t42.t7.t15 t42.t7.t48))
% 0.72/0.93  (step t42.t7.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t42.t7.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t7.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t7.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (anchor :step t42.t7.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.93  (step t42.t7.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t7.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.93  (step t42.t7.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t42.t7.t52.t2.t2 t42.t7.t52.t2.t3))
% 0.72/0.93  (step t42.t7.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t42.t7.t52.t2.t4 t42.t7.t52.t2.t5))
% 0.72/0.93  (step t42.t7.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.93  (step t42.t7.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t42.t7.t52.t2 t42.t7.t52.t3))
% 0.72/0.93  (step t42.t7.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t42.t7.t52.t4))
% 0.72/0.93  (step t42.t7.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t42.t7.t52.t5 t42.t7.t52.t6))
% 0.72/0.93  (step t42.t7.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.93  (step t42.t7.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.93  (step t42.t7.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t7.t52 t42.t7.t53))
% 0.72/0.93  (step t42.t7.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t7.t51 t42.t7.t54))
% 0.72/0.93  (step t42.t7.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t42.t7.t50 t42.t7.t55))
% 0.72/0.93  (step t42.t7.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t42.t7.t49 t42.t7.t56))
% 0.72/0.93  (step t42.t7.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t42.t7.t14 t42.t7.t57 a10))
% 0.72/0.93  (step t42.t7.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t7.t4 t42.t7.t13 t42.t7.t58 t42.t7.t21 t42.t7.t30 a7 t42.t7.t35 t42.t7.t44 a4 a3 a2))
% 0.72/0.93  (step t42.t7.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t7.t59))
% 0.72/0.93  (step t42.t7.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t42.t7.t59))
% 0.72/0.93  (step t42.t7.t62 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t7.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t42.t7.t61 t42.t7.t62))
% 0.72/0.93  (step t42.t7.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t42.t7.t60 t42.t7.t63))
% 0.72/0.93  (step t42.t7.t65 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t7.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t42.t7.t61 t42.t7.t65))
% 0.72/0.93  (step t42.t7.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t42.t7.t64 t42.t7.t66))
% 0.72/0.93  (step t42.t7.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t7.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t42.t7.t67 t42.t7.t68))
% 0.72/0.93  (step t42.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t8 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t42.t6 t42.t7))
% 0.72/0.93  (step t42.t9 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.72/0.93  (anchor :step t42.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t10.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t10.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.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)
% 0.72/0.93  (step t42.t10.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t10.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t10.t4 t42.t10.t5))
% 0.72/0.93  (step t42.t10.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t10.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t10.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t10.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t10.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t10.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t10.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t42.t10.t8.t3 t42.t10.t8.t4))
% 0.72/0.93  (step t42.t10.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t42.t10.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t42.t10.t7 t42.t10.t8))
% 0.72/0.93  (step t42.t10.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t42.t10.t6 t42.t10.t9))
% 0.72/0.93  (step t42.t10.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t10.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t42.t10.t10 t42.t10.t11))
% 0.72/0.93  (step t42.t10.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t10.t14 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t10.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t10.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.72/0.93  (step t42.t10.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t10.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t42.t10.t14.t2 t42.t10.t14.t3))
% 0.72/0.93  (step t42.t10.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.72/0.93  (step t42.t10.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t42.t10.t13 t42.t10.t14))
% 0.72/0.93  (step t42.t10.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t42.t10.t12 t42.t10.t15))
% 0.72/0.93  (step t42.t10.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t10.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t42.t10.t16 t42.t10.t17))
% 0.72/0.93  (step t42.t10.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t10.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t42.t10.t18 t42.t10.t19))
% 0.72/0.93  (step t42.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.72/0.93  (step t42.t11 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t42.t9 t42.t10))
% 0.72/0.93  (step t42.t12 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t42.t8 t42.t11))
% 0.72/0.93  (step t42.t13 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t42.t5 t42.t12 a12))
% 0.72/0.93  (step t42.t14 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t15 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t16.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t16.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t16.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t16.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t42.t16.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t16.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t16.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.72/0.93  (step t42.t16.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t16.t9 t42.t16.t10))
% 0.72/0.93  (step t42.t16.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t42.t16.t8 t42.t16.t11 a9))
% 0.72/0.93  (step t42.t16.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t16.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t15.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t42.t16.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t16.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t42.t16.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t42.t16.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t16.t15.t5 t42.t16.t15.t6))
% 0.72/0.93  (step t42.t16.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t16.t15.t4 t42.t16.t15.t7 a6))
% 0.72/0.93  (step t42.t16.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t16.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t11.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))))) (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)))))) :rule and_neg)
% 0.72/0.93  (step t42.t16.t15.t11.t5 (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)))))) :rule resolution :premises (t42.t16.t15.t11.t4 a4 a3 a2))
% 0.72/0.93  (step t42.t16.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t16.t15.t11.t5))
% 0.72/0.93  (step t42.t16.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t16.t15.t11.t5))
% 0.72/0.93  (step t42.t16.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t16.t15.t11.t7 t42.t16.t15.t11.t8))
% 0.72/0.93  (step t42.t16.t15.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t42.t16.t15.t11.t6 t42.t16.t15.t11.t9))
% 0.72/0.93  (step t42.t16.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t42.t16.t15.t11.t10 t42.t16.t15.t11.t11))
% 0.72/0.93  (step t42.t16.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t42.t16.t15.t11.t12 t42.t16.t15.t11.t13))
% 0.72/0.93  (step t42.t16.t15.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t16.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t42.t16.t15.t10 t42.t16.t15.t11))
% 0.72/0.93  (step t42.t16.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t15.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t42.t16.t15.t14.t4 t42.t16.t15.t14.t5))
% 0.72/0.93  (step t42.t16.t15.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.72/0.93  (anchor :step t42.t16.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t16.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t16.t15.t14.t8.t3 t42.t16.t15.t14.t8.t4))
% 0.72/0.93  (step t42.t16.t15.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t42.t16.t15.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t16.t15.t14.t7 t42.t16.t15.t14.t8))
% 0.72/0.93  (step t42.t16.t15.t14.t10 (cl (= (@ (lambda ((X (-> $$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.t16.t15.t14.t6 t42.t16.t15.t14.t9))
% 0.72/0.93  (step t42.t16.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t42.t16.t15.t14.t10 t42.t16.t15.t14.t11))
% 0.72/0.93  (step t42.t16.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t15.t14.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.t16.t15.t14.t12 t42.t16.t15.t14.t13))
% 0.72/0.93  (step t42.t16.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t14.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.t16.t15.t14.t14 t42.t16.t15.t14.t15))
% 0.72/0.93  (step t42.t16.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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.t15.t14.t16 t42.t16.t15.t14.t17))
% 0.72/0.93  (step t42.t16.t15.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t42.t16.t15.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t16.t15.t13 t42.t16.t15.t14))
% 0.72/0.93  (step t42.t16.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t16.t15.t12 t42.t16.t15.t15))
% 0.72/0.93  (step t42.t16.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t16.t15.t9 t42.t16.t15.t16 a5))
% 0.72/0.93  (step t42.t16.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t16.t15.t3 a7 t42.t16.t15.t8 t42.t16.t15.t17 a4 a3 a2))
% 0.72/0.93  (step t42.t16.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t16.t15.t18))
% 0.72/0.93  (step t42.t16.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t42.t16.t15.t18))
% 0.72/0.93  (step t42.t16.t15.t21 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t42.t16.t15.t20 t42.t16.t15.t21))
% 0.72/0.93  (step t42.t16.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t42.t16.t15.t19 t42.t16.t15.t22))
% 0.72/0.93  (step t42.t16.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t42.t16.t15.t23 t42.t16.t15.t24))
% 0.72/0.93  (step t42.t16.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t16.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t42.t16.t14 t42.t16.t15))
% 0.72/0.93  (step t42.t16.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t18.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t16.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.72/0.93  (step t42.t16.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t16.t18.t3 t42.t16.t18.t4))
% 0.72/0.93  (step t42.t16.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t16.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t16.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t42.t16.t18.t7.t2))
% 0.72/0.93  (step t42.t16.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t42.t16.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t16.t18.t6 t42.t16.t18.t7))
% 0.72/0.93  (step t42.t16.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t16.t18.t5 t42.t16.t18.t8))
% 0.72/0.93  (step t42.t16.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t42.t16.t18.t9 t42.t16.t18.t10))
% 0.72/0.93  (step t42.t16.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t42.t16.t18.t11 t42.t16.t18.t12))
% 0.72/0.93  (step t42.t16.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t42.t16.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t42.t16.t17 t42.t16.t18))
% 0.72/0.93  (step t42.t16.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t42.t16.t16 t42.t16.t19))
% 0.72/0.93  (step t42.t16.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t42.t16.t13 t42.t16.t20 a8))
% 0.72/0.93  (step t42.t16.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t16.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t42.t16.t24.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t16.t24.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t42.t16.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t42.t16.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t16.t23 t42.t16.t24))
% 0.72/0.93  (step t42.t16.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t16.t22 t42.t16.t25 a6))
% 0.72/0.93  (step t42.t16.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t16.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t29.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t29.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t29.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t16.t29.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t16.t29.t4 a4 a3 a2))
% 0.72/0.93  (step t42.t16.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t16.t29.t5))
% 0.72/0.93  (step t42.t16.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t16.t29.t5))
% 0.72/0.93  (step t42.t16.t29.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t16.t29.t7 t42.t16.t29.t8))
% 0.72/0.93  (step t42.t16.t29.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t42.t16.t29.t6 t42.t16.t29.t9))
% 0.72/0.93  (step t42.t16.t29.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t29.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t42.t16.t29.t10 t42.t16.t29.t11))
% 0.72/0.93  (step t42.t16.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t29.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t42.t16.t29.t12 t42.t16.t29.t13))
% 0.72/0.93  (step t42.t16.t29 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t16.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t42.t16.t28 t42.t16.t29))
% 0.72/0.93  (step t42.t16.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t32.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t32.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t32.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)
% 0.72/0.93  (step t42.t16.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t32.t6 (cl (= (@ (lambda ((X (-> $$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.t16.t32.t4 t42.t16.t32.t5))
% 0.72/0.93  (step t42.t16.t32.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t16.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t16.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t16.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t16.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t16.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t16.t32.t8.t3 t42.t16.t32.t8.t4))
% 0.72/0.93  (step t42.t16.t32.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.93  (step t42.t16.t32.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.t16.t32.t7 t42.t16.t32.t8))
% 0.72/0.93  (step t42.t16.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t16.t32.t6 t42.t16.t32.t9))
% 0.72/0.93  (step t42.t16.t32.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t16.t32.t12 (cl (= (@ (@ (lambda ((X (-> $$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.t16.t32.t10 t42.t16.t32.t11))
% 0.72/0.93  (step t42.t16.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t32.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t42.t16.t32.t12 t42.t16.t32.t13))
% 0.72/0.93  (step t42.t16.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t32.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t42.t16.t32.t14 t42.t16.t32.t15))
% 0.72/0.93  (step t42.t16.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t42.t16.t32.t16 t42.t16.t32.t17))
% 0.72/0.93  (step t42.t16.t32 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t16.t33 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t16.t31 t42.t16.t32))
% 0.72/0.93  (step t42.t16.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t16.t30 t42.t16.t33))
% 0.72/0.93  (step t42.t16.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t16.t27 t42.t16.t34 a5))
% 0.72/0.93  (step t42.t16.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t42.t16.t7 t42.t16.t12 t42.t16.t21 a7 t42.t16.t26 t42.t16.t35 a4 a3 a2))
% 0.72/0.93  (step t42.t16.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t42.t16.t36))
% 0.72/0.93  (step t42.t16.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t42.t16.t36))
% 0.72/0.93  (step t42.t16.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t16.t37 t42.t16.t38))
% 0.72/0.93  (step t42.t16.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t42.t16.t6 t42.t16.t39))
% 0.72/0.93  (step t42.t16.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t42.t16.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t16.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t16.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (anchor :step t42.t16.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.93  (step t42.t16.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t16.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.93  (step t42.t16.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t42.t16.t43.t2.t2 t42.t16.t43.t2.t3))
% 0.72/0.93  (step t42.t16.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t42.t16.t43.t2.t4 t42.t16.t43.t2.t5))
% 0.72/0.93  (step t42.t16.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.93  (step t42.t16.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t42.t16.t43.t2 t42.t16.t43.t3))
% 0.72/0.93  (step t42.t16.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t42.t16.t43.t4))
% 0.72/0.93  (step t42.t16.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t42.t16.t43.t5 t42.t16.t43.t6))
% 0.72/0.93  (step t42.t16.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.93  (step t42.t16.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.93  (step t42.t16.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t16.t43 t42.t16.t44))
% 0.72/0.93  (step t42.t16.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t16.t42 t42.t16.t45))
% 0.72/0.93  (step t42.t16.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t42.t16.t41 t42.t16.t46))
% 0.72/0.93  (step t42.t16.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t42.t16.t40 t42.t16.t47))
% 0.72/0.93  (step t42.t16.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t42.t16.t5 t42.t16.t48 a10))
% 0.72/0.93  (step t42.t16.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t16.t4 t42.t16.t49 t42.t16.t12 t42.t16.t21 a7 t42.t16.t26 t42.t16.t35 a4 a3 a2))
% 0.72/0.93  (step t42.t16.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t42.t16.t50))
% 0.72/0.93  (step t42.t16.t52 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t16.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t42.t16.t51 t42.t16.t52))
% 0.72/0.93  (step t42.t16.t54 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t16.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t42.t16.t53 t42.t16.t54))
% 0.72/0.93  (step t42.t16.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t16.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t42.t16.t55 t42.t16.t56))
% 0.72/0.93  (step t42.t16 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t17 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t42.t15 t42.t16))
% 0.72/0.93  (step t42.t18 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.72/0.93  (anchor :step t42.t19 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t19.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t19.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t19.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t19.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t19.t5 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t19.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t42.t19.t4 t42.t19.t5))
% 0.72/0.93  (step t42.t19.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t19.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t42.t19.t6 t42.t19.t7))
% 0.72/0.93  (step t42.t19.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t19.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t42.t19.t8 t42.t19.t9))
% 0.72/0.93  (step t42.t19.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t19.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t42.t19.t10 t42.t19.t11))
% 0.72/0.93  (step t42.t19 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t42.t20 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t42.t18 t42.t19))
% 0.72/0.93  (step t42.t21 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t42.t17 t42.t20))
% 0.72/0.93  (step t42.t22 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t42.t14 t42.t21 a11))
% 0.72/0.93  (step t42.t23 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t24 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t42.t25 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t42.t26 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t27 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.72/0.93  (step t42.t28 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.72/0.93  (step t42.t29 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t27 t42.t28))
% 0.72/0.93  (step t42.t30 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t42.t26 t42.t29 a9))
% 0.72/0.93  (step t42.t31 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t32 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t42.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t33.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t33.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t33.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t33.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t33.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t42.t33.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t42.t33.t6.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t33.t6.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t42.t33.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t33.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t42.t33.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t33.t5 t42.t33.t6))
% 0.72/0.93  (step t42.t33.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t33.t4 t42.t33.t7 a6))
% 0.72/0.93  (step t42.t33.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t33.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t33.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t33.t11.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t33.t11.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t33.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t33.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t42.t33.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t33.t11.t4 a4 a3 a2))
% 0.72/0.93  (step t42.t33.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t33.t11.t5))
% 0.72/0.93  (step t42.t33.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t33.t11.t5))
% 0.72/0.93  (step t42.t33.t11.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t33.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t33.t11.t7 t42.t33.t11.t8))
% 0.72/0.93  (step t42.t33.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t42.t33.t11.t6 t42.t33.t11.t9))
% 0.72/0.93  (step t42.t33.t11.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t33.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t42.t33.t11.t10 t42.t33.t11.t11))
% 0.72/0.93  (step t42.t33.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t33.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t42.t33.t11.t12 t42.t33.t11.t13))
% 0.72/0.93  (step t42.t33.t11 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t33.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t42.t33.t10 t42.t33.t11))
% 0.72/0.93  (step t42.t33.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t33.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t33.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t33.t14.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t33.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t33.t14.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)
% 0.72/0.93  (step t42.t33.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t33.t14.t6 (cl (= (@ (lambda ((X (-> $$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.t33.t14.t4 t42.t33.t14.t5))
% 0.72/0.93  (step t42.t33.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t33.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t33.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t33.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t33.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t42.t33.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t33.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t33.t14.t8.t3 t42.t33.t14.t8.t4))
% 0.72/0.93  (step t42.t33.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.93  (step t42.t33.t14.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.t33.t14.t7 t42.t33.t14.t8))
% 0.72/0.93  (step t42.t33.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t33.t14.t6 t42.t33.t14.t9))
% 0.72/0.93  (step t42.t33.t14.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t33.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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.t33.t14.t10 t42.t33.t14.t11))
% 0.72/0.93  (step t42.t33.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t33.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t42.t33.t14.t12 t42.t33.t14.t13))
% 0.72/0.93  (step t42.t33.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t33.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t42.t33.t14.t14 t42.t33.t14.t15))
% 0.72/0.93  (step t42.t33.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t33.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t42.t33.t14.t16 t42.t33.t14.t17))
% 0.72/0.93  (step t42.t33.t14 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t42.t33.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t33.t13 t42.t33.t14))
% 0.72/0.93  (step t42.t33.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t33.t12 t42.t33.t15))
% 0.72/0.93  (step t42.t33.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t33.t9 t42.t33.t16 a5))
% 0.72/0.93  (step t42.t33.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t42.t33.t3 a7 t42.t33.t8 t42.t33.t17 a4 a3 a2))
% 0.72/0.93  (step t42.t33.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t33.t18))
% 0.72/0.93  (step t42.t33.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t42.t33.t18))
% 0.72/0.93  (step t42.t33.t21 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t33.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t42.t33.t20 t42.t33.t21))
% 0.72/0.93  (step t42.t33.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t42.t33.t19 t42.t33.t22))
% 0.72/0.93  (step t42.t33.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t33.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t42.t33.t23 t42.t33.t24))
% 0.72/0.93  (step t42.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t34 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t42.t32 t42.t33))
% 0.72/0.93  (step t42.t35 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t42.t36 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t36.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t36.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t36.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.72/0.93  (step t42.t36.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t36.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t36.t3 t42.t36.t4))
% 0.72/0.93  (step t42.t36.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t36.t7 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t36.t7.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t36.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t36.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t42.t36.t7.t2))
% 0.72/0.93  (step t42.t36.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t42.t36.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t36.t6 t42.t36.t7))
% 0.72/0.93  (step t42.t36.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t42.t36.t5 t42.t36.t8))
% 0.72/0.93  (step t42.t36.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t36.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t42.t36.t9 t42.t36.t10))
% 0.72/0.93  (step t42.t36.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t42.t36.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t42.t36.t11 t42.t36.t12))
% 0.72/0.93  (step t42.t36 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t42.t37 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t42.t35 t42.t36))
% 0.72/0.93  (step t42.t38 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t42.t34 t42.t37))
% 0.72/0.93  (step t42.t39 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t42.t31 t42.t38 a8))
% 0.72/0.93  (step t42.t40 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t41 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t42.t42 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t42.t42.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t42.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t42.t42.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t42.t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t42.t43 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t42.t41 t42.t42))
% 0.72/0.93  (step t42.t44 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t42.t40 t42.t43 a6))
% 0.72/0.93  (step t42.t45 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t42.t46 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t47 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t47.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t47.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t47.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t47.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))))) (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)))))) :rule and_neg)
% 0.72/0.93  (step t42.t47.t5 (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)))))) :rule resolution :premises (t42.t47.t4 a4 a3 a2))
% 0.72/0.93  (step t42.t47.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t42.t47.t5))
% 0.72/0.93  (step t42.t47.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t42.t47.t5))
% 0.72/0.93  (step t42.t47.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t47.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t42.t47.t7 t42.t47.t8))
% 0.72/0.93  (step t42.t47.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t42.t47.t6 t42.t47.t9))
% 0.72/0.93  (step t42.t47.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t47.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t42.t47.t10 t42.t47.t11))
% 0.72/0.93  (step t42.t47.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t47.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t42.t47.t12 t42.t47.t13))
% 0.72/0.93  (step t42.t47 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t42.t48 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t42.t46 t42.t47))
% 0.72/0.93  (step t42.t49 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t42.t50 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t50.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t50.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t50.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t50.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t42.t50.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t50.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t42.t50.t4 t42.t50.t5))
% 0.72/0.93  (step t42.t50.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.72/0.93  (anchor :step t42.t50.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t42.t50.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t50.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t42.t50.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t42.t50.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t42.t50.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t42.t50.t8.t3 t42.t50.t8.t4))
% 0.72/0.93  (step t42.t50.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t42.t50.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t42.t50.t7 t42.t50.t8))
% 0.72/0.93  (step t42.t50.t10 (cl (= (@ (lambda ((X (-> $$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.t50.t6 t42.t50.t9))
% 0.72/0.93  (step t42.t50.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t42.t50.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t42.t50.t10 t42.t50.t11))
% 0.72/0.93  (step t42.t50.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t42.t50.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.t50.t12 t42.t50.t13))
% 0.72/0.93  (step t42.t50.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t50.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.t50.t14 t42.t50.t15))
% 0.72/0.93  (step t42.t50.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t42.t50.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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.t50.t16 t42.t50.t17))
% 0.72/0.93  (step t42.t50 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t42.t51 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t42.t49 t42.t50))
% 0.72/0.93  (step t42.t52 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t42.t48 t42.t51))
% 0.72/0.93  (step t42.t53 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t42.t45 t42.t52 a5))
% 0.72/0.93  (step t42.t54 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t42.t25 t42.t30 t42.t39 a7 t42.t44 t42.t53 a4 a3 a2))
% 0.72/0.93  (step t42.t55 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t42.t54))
% 0.72/0.93  (step t42.t56 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t42.t54))
% 0.72/0.93  (step t42.t57 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t42.t55 t42.t56))
% 0.72/0.93  (step t42.t58 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t42.t24 t42.t57))
% 0.72/0.93  (step t42.t59 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t42.t60 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t42.t61 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t42.t61.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (anchor :step t42.t61.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.93  (step t42.t61.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t42.t61.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.93  (step t42.t61.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t61.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t42.t61.t2.t2 t42.t61.t2.t3))
% 0.72/0.93  (step t42.t61.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t61.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t42.t61.t2.t4 t42.t61.t2.t5))
% 0.72/0.93  (step t42.t61.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.93  (step t42.t61.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t42.t61.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t42.t61.t2 t42.t61.t3))
% 0.72/0.93  (step t42.t61.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t42.t61.t4))
% 0.72/0.93  (step t42.t61.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.93  (step t42.t61.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t42.t61.t5 t42.t61.t6))
% 0.72/0.93  (step t42.t61 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.93  (step t42.t62 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.93  (step t42.t63 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t61 t42.t62))
% 0.72/0.93  (step t42.t64 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t42.t60 t42.t63))
% 0.72/0.93  (step t42.t65 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t42.t59 t42.t64))
% 0.72/0.93  (step t42.t66 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t42.t58 t42.t65))
% 0.72/0.93  (step t42.t67 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t42.t23 t42.t66 a10))
% 0.72/0.93  (step t42.t68 (cl (and (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t42.t4 t42.t13 t42.t22 t42.t67 t42.t30 t42.t39 a7 t42.t44 t42.t53 a4 a3 a2))
% 0.72/0.93  (step t42.t69 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule and :premises (t42.t68))
% 0.72/0.93  (step t42.t70 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t42.t68))
% 0.72/0.93  (step t42.t71 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t42.t72 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t42.t70 t42.t71))
% 0.72/0.93  (step t42.t73 (cl (= (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t42.t69 t42.t72))
% 0.72/0.93  (step t42.t74 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t42.t75 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t42.t70 t42.t74))
% 0.72/0.93  (step t42.t76 (cl (= (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t42.t73 t42.t75))
% 0.72/0.93  (step t42.t77 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t42.t78 (cl (= (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t42.t76 t42.t77))
% 0.72/0.93  (step t42 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t43 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t41 t42))
% 0.72/0.93  (step t44 (cl (= tptp.iimplies tptp.iimplies)) :rule refl)
% 0.72/0.93  (anchor :step t45 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t45.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t45.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t45.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t45.t4 (cl (= (lambda ((U (-> $$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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule refl)
% 0.72/0.93  (step t45.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t45.t6 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t45.t4 t45.t5))
% 0.72/0.93  (step t45.t7 (cl (= (@ (lambda ((U (-> $$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.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t45.t8 :args ((V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t45.t8.t1 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t45.t8.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t45.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t45.t8.t4 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule cong :premises (t45.t8.t3))
% 0.72/0.93  (step t45.t8.t5 (cl (= (@ V __flatten_var_0) (@ V __flatten_var_0))) :rule refl)
% 0.72/0.93  (step t45.t8.t6 (cl (= (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0)))) :rule cong :premises (t45.t8.t4 t45.t8.t5))
% 0.72/0.93  (step t45.t8 (cl (= (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) __flatten_var_0)) (@ V __flatten_var_0))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t45.t9 (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 $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t45.t7 t45.t8))
% 0.72/0.93  (step t45.t10 (cl (= (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))))) :rule trans :premises (t45.t6 t45.t9))
% 0.72/0.93  (step t45.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.72/0.93  (step t45.t12 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t45.t10 t45.t11))
% 0.72/0.93  (step t45.t13 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t45.t14 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t45.t14.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t45.t14.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule refl)
% 0.72/0.93  (step t45.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule all_simplify)
% 0.72/0.93  (step t45.t14.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t45.t14.t2 t45.t14.t3))
% 0.72/0.93  (step t45.t14 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.72/0.93  (step t45.t15 (cl (= (@ (lambda ((V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (@ V __flatten_var_0))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t45.t13 t45.t14))
% 0.72/0.93  (step t45.t16 (cl (= (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule trans :premises (t45.t12 t45.t15))
% 0.72/0.93  (step t45.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t45.t18 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t45.t16 t45.t17))
% 0.72/0.93  (step t45.t19 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.72/0.93  (step t45.t20 (cl (= (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t45.t18 t45.t19))
% 0.72/0.93  (step t45 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.72/0.93  (step t46 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t44 t45))
% 0.72/0.93  (step t47 (cl (= (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t43 t46))
% 0.72/0.93  (step t48 (cl (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t40 t47 a13))
% 0.72/0.93  (step t49 (cl (not (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) (not (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t50 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.72/0.93  (anchor :step t51 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t51.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t4 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t51.t5 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t6 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t7.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t51.t7.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t51.t7.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t7.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t51.t7.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t51.t7.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t7.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.72/0.93  (step t51.t7.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t51.t7.t9 t51.t7.t10))
% 0.72/0.93  (step t51.t7.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t51.t7.t8 t51.t7.t11 a9))
% 0.72/0.93  (step t51.t7.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t7.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t15.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t51.t7.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t7.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t51.t7.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t51.t7.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t51.t7.t15.t5 t51.t7.t15.t6))
% 0.72/0.93  (step t51.t7.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t51.t7.t15.t4 t51.t7.t15.t7 a6))
% 0.72/0.93  (step t51.t7.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t7.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t51.t7.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t51.t7.t15.t11.t4 a4 a3 a2))
% 0.72/0.93  (step t51.t7.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t51.t7.t15.t11.t5))
% 0.72/0.93  (step t51.t7.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t51.t7.t15.t11.t5))
% 0.72/0.93  (step t51.t7.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t51.t7.t15.t11.t7 t51.t7.t15.t11.t8))
% 0.72/0.93  (step t51.t7.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t51.t7.t15.t11.t6 t51.t7.t15.t11.t9))
% 0.72/0.93  (step t51.t7.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t51.t7.t15.t11.t10 t51.t7.t15.t11.t11))
% 0.72/0.93  (step t51.t7.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t51.t7.t15.t11.t12 t51.t7.t15.t11.t13))
% 0.72/0.93  (step t51.t7.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t51.t7.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t51.t7.t15.t10 t51.t7.t15.t11))
% 0.72/0.93  (step t51.t7.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.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)
% 0.72/0.93  (step t51.t7.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t51.t7.t15.t14.t4 t51.t7.t15.t14.t5))
% 0.72/0.93  (step t51.t7.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t51.t7.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t51.t7.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t51.t7.t15.t14.t8.t3 t51.t7.t15.t14.t8.t4))
% 0.72/0.93  (step t51.t7.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.93  (step t51.t7.t15.t14.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 (t51.t7.t15.t14.t7 t51.t7.t15.t14.t8))
% 0.72/0.93  (step t51.t7.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t51.t7.t15.t14.t6 t51.t7.t15.t14.t9))
% 0.72/0.93  (step t51.t7.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t51.t7.t15.t14.t10 t51.t7.t15.t14.t11))
% 0.72/0.93  (step t51.t7.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t51.t7.t15.t14.t12 t51.t7.t15.t14.t13))
% 0.72/0.93  (step t51.t7.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t51.t7.t15.t14.t14 t51.t7.t15.t14.t15))
% 0.72/0.93  (step t51.t7.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t51.t7.t15.t14.t16 t51.t7.t15.t14.t17))
% 0.72/0.93  (step t51.t7.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t51.t7.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t51.t7.t15.t13 t51.t7.t15.t14))
% 0.72/0.93  (step t51.t7.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t51.t7.t15.t12 t51.t7.t15.t15))
% 0.72/0.93  (step t51.t7.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t51.t7.t15.t9 t51.t7.t15.t16 a5))
% 0.72/0.93  (step t51.t7.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t51.t7.t15.t3 a7 t51.t7.t15.t8 t51.t7.t15.t17 a4 a3 a2))
% 0.72/0.93  (step t51.t7.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t51.t7.t15.t18))
% 0.72/0.93  (step t51.t7.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t51.t7.t15.t18))
% 0.72/0.93  (step t51.t7.t15.t21 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t51.t7.t15.t20 t51.t7.t15.t21))
% 0.72/0.93  (step t51.t7.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t51.t7.t15.t19 t51.t7.t15.t22))
% 0.72/0.93  (step t51.t7.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t51.t7.t15.t23 t51.t7.t15.t24))
% 0.72/0.93  (step t51.t7.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t51.t7.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t51.t7.t14 t51.t7.t15))
% 0.72/0.93  (step t51.t7.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t18.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t7.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.72/0.93  (step t51.t7.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t51.t7.t18.t3 t51.t7.t18.t4))
% 0.72/0.93  (step t51.t7.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t51.t7.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t51.t7.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t51.t7.t18.t7.t2))
% 0.72/0.93  (step t51.t7.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t51.t7.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t51.t7.t18.t6 t51.t7.t18.t7))
% 0.72/0.93  (step t51.t7.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t51.t7.t18.t5 t51.t7.t18.t8))
% 0.72/0.93  (step t51.t7.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t51.t7.t18.t9 t51.t7.t18.t10))
% 0.72/0.93  (step t51.t7.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t51.t7.t18.t11 t51.t7.t18.t12))
% 0.72/0.93  (step t51.t7.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t51.t7.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t51.t7.t17 t51.t7.t18))
% 0.72/0.93  (step t51.t7.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t51.t7.t16 t51.t7.t19))
% 0.72/0.93  (step t51.t7.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t51.t7.t13 t51.t7.t20 a8))
% 0.72/0.93  (step t51.t7.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t7.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t51.t7.t24.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t7.t24.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t51.t7.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t51.t7.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t51.t7.t23 t51.t7.t24))
% 0.72/0.93  (step t51.t7.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t51.t7.t22 t51.t7.t25 a6))
% 0.72/0.93  (step t51.t7.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t7.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t29.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t29.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t29.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))))) (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)))))) :rule and_neg)
% 0.72/0.93  (step t51.t7.t29.t5 (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)))))) :rule resolution :premises (t51.t7.t29.t4 a4 a3 a2))
% 0.72/0.93  (step t51.t7.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t51.t7.t29.t5))
% 0.72/0.93  (step t51.t7.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t51.t7.t29.t5))
% 0.72/0.93  (step t51.t7.t29.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t51.t7.t29.t7 t51.t7.t29.t8))
% 0.72/0.93  (step t51.t7.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t51.t7.t29.t6 t51.t7.t29.t9))
% 0.72/0.93  (step t51.t7.t29.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t51.t7.t29.t10 t51.t7.t29.t11))
% 0.72/0.93  (step t51.t7.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t51.t7.t29.t12 t51.t7.t29.t13))
% 0.72/0.93  (step t51.t7.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t51.t7.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t51.t7.t28 t51.t7.t29))
% 0.72/0.93  (step t51.t7.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t32.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t32.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t51.t7.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t51.t7.t32.t4 t51.t7.t32.t5))
% 0.72/0.93  (step t51.t7.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.72/0.93  (anchor :step t51.t7.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t51.t7.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t51.t7.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t7.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t51.t7.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t51.t7.t32.t8.t3 t51.t7.t32.t8.t4))
% 0.72/0.93  (step t51.t7.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t51.t7.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t51.t7.t32.t7 t51.t7.t32.t8))
% 0.72/0.93  (step t51.t7.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t51.t7.t32.t6 t51.t7.t32.t9))
% 0.72/0.93  (step t51.t7.t32.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t7.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t51.t7.t32.t10 t51.t7.t32.t11))
% 0.72/0.93  (step t51.t7.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t32.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 (t51.t7.t32.t12 t51.t7.t32.t13))
% 0.72/0.93  (step t51.t7.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t32.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 (t51.t7.t32.t14 t51.t7.t32.t15))
% 0.72/0.93  (step t51.t7.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t51.t7.t32.t16 t51.t7.t32.t17))
% 0.72/0.93  (step t51.t7.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t51.t7.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t51.t7.t31 t51.t7.t32))
% 0.72/0.93  (step t51.t7.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t51.t7.t30 t51.t7.t33))
% 0.72/0.93  (step t51.t7.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t51.t7.t27 t51.t7.t34 a5))
% 0.72/0.93  (step t51.t7.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t51.t7.t7 t51.t7.t12 t51.t7.t21 a7 t51.t7.t26 t51.t7.t35 a4 a3 a2))
% 0.72/0.93  (step t51.t7.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t51.t7.t36))
% 0.72/0.93  (step t51.t7.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t51.t7.t36))
% 0.72/0.93  (step t51.t7.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t51.t7.t37 t51.t7.t38))
% 0.72/0.93  (step t51.t7.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t51.t7.t6 t51.t7.t39))
% 0.72/0.93  (step t51.t7.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t51.t7.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t51.t7.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t7.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (anchor :step t51.t7.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.93  (step t51.t7.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t51.t7.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.93  (step t51.t7.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t51.t7.t43.t2.t2 t51.t7.t43.t2.t3))
% 0.72/0.93  (step t51.t7.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t51.t7.t43.t2.t4 t51.t7.t43.t2.t5))
% 0.72/0.93  (step t51.t7.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.93  (step t51.t7.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t51.t7.t43.t2 t51.t7.t43.t3))
% 0.72/0.93  (step t51.t7.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t51.t7.t43.t4))
% 0.72/0.93  (step t51.t7.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t51.t7.t43.t5 t51.t7.t43.t6))
% 0.72/0.93  (step t51.t7.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.93  (step t51.t7.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.93  (step t51.t7.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t51.t7.t43 t51.t7.t44))
% 0.72/0.93  (step t51.t7.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t51.t7.t42 t51.t7.t45))
% 0.72/0.93  (step t51.t7.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t51.t7.t41 t51.t7.t46))
% 0.72/0.93  (step t51.t7.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t51.t7.t40 t51.t7.t47))
% 0.72/0.93  (step t51.t7.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t51.t7.t5 t51.t7.t48 a10))
% 0.72/0.93  (step t51.t7.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t51.t7.t4 t51.t7.t49 t51.t7.t12 t51.t7.t21 a7 t51.t7.t26 t51.t7.t35 a4 a3 a2))
% 0.72/0.93  (step t51.t7.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t51.t7.t50))
% 0.72/0.93  (step t51.t7.t52 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t7.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t51.t7.t51 t51.t7.t52))
% 0.72/0.93  (step t51.t7.t54 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t51.t7.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t51.t7.t53 t51.t7.t54))
% 0.72/0.93  (step t51.t7.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t7.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t51.t7.t55 t51.t7.t56))
% 0.72/0.93  (step t51.t7 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t51.t8 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t51.t6 t51.t7))
% 0.72/0.93  (step t51.t9 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.72/0.93  (anchor :step t51.t10 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t10.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t10.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t51.t10.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t10.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t10.t5 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t51.t10.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t51.t10.t4 t51.t10.t5))
% 0.72/0.93  (step t51.t10.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t10.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t51.t10.t6 t51.t10.t7))
% 0.72/0.93  (step t51.t10.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t10.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t51.t10.t8 t51.t10.t9))
% 0.72/0.93  (step t51.t10.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t51.t10.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t51.t10.t10 t51.t10.t11))
% 0.72/0.93  (step t51.t10 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t51.t11 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t51.t9 t51.t10))
% 0.72/0.93  (step t51.t12 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t51.t8 t51.t11))
% 0.72/0.93  (step t51.t13 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t51.t5 t51.t12 a11))
% 0.72/0.93  (step t51.t14 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t15 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t51.t16 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t51.t17 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t18 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.72/0.93  (step t51.t19 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.72/0.93  (step t51.t20 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t51.t18 t51.t19))
% 0.72/0.93  (step t51.t21 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t51.t17 t51.t20 a9))
% 0.72/0.93  (step t51.t22 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t23 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t51.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t24.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t24.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t24.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t51.t24.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t24.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t51.t24.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t51.t24.t6.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t24.t6.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t51.t24.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t51.t24.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t51.t24.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t51.t24.t5 t51.t24.t6))
% 0.72/0.93  (step t51.t24.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t51.t24.t4 t51.t24.t7 a6))
% 0.72/0.93  (step t51.t24.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t24.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t24.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t24.t11.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t24.t11.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t24.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t24.t11.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))))) (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)))))) :rule and_neg)
% 0.72/0.93  (step t51.t24.t11.t5 (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)))))) :rule resolution :premises (t51.t24.t11.t4 a4 a3 a2))
% 0.72/0.93  (step t51.t24.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t51.t24.t11.t5))
% 0.72/0.93  (step t51.t24.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t51.t24.t11.t5))
% 0.72/0.93  (step t51.t24.t11.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t24.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t51.t24.t11.t7 t51.t24.t11.t8))
% 0.72/0.93  (step t51.t24.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t51.t24.t11.t6 t51.t24.t11.t9))
% 0.72/0.93  (step t51.t24.t11.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t24.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t51.t24.t11.t10 t51.t24.t11.t11))
% 0.72/0.93  (step t51.t24.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t24.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t51.t24.t11.t12 t51.t24.t11.t13))
% 0.72/0.93  (step t51.t24.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t51.t24.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t51.t24.t10 t51.t24.t11))
% 0.72/0.93  (step t51.t24.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t24.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t24.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t24.t14.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t24.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t24.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t51.t24.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t24.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t51.t24.t14.t4 t51.t24.t14.t5))
% 0.72/0.93  (step t51.t24.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.72/0.93  (anchor :step t51.t24.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t51.t24.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t51.t24.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t24.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t51.t24.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t51.t24.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t51.t24.t14.t8.t3 t51.t24.t14.t8.t4))
% 0.72/0.93  (step t51.t24.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t51.t24.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t51.t24.t14.t7 t51.t24.t14.t8))
% 0.72/0.93  (step t51.t24.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t51.t24.t14.t6 t51.t24.t14.t9))
% 0.72/0.93  (step t51.t24.t14.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t24.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t51.t24.t14.t10 t51.t24.t14.t11))
% 0.72/0.93  (step t51.t24.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t24.t14.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 (t51.t24.t14.t12 t51.t24.t14.t13))
% 0.72/0.93  (step t51.t24.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t24.t14.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 (t51.t24.t14.t14 t51.t24.t14.t15))
% 0.72/0.93  (step t51.t24.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t51.t24.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t51.t24.t14.t16 t51.t24.t14.t17))
% 0.72/0.93  (step t51.t24.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t51.t24.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t51.t24.t13 t51.t24.t14))
% 0.72/0.93  (step t51.t24.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t51.t24.t12 t51.t24.t15))
% 0.72/0.93  (step t51.t24.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t51.t24.t9 t51.t24.t16 a5))
% 0.72/0.93  (step t51.t24.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t51.t24.t3 a7 t51.t24.t8 t51.t24.t17 a4 a3 a2))
% 0.72/0.93  (step t51.t24.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t51.t24.t18))
% 0.72/0.93  (step t51.t24.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t51.t24.t18))
% 0.72/0.93  (step t51.t24.t21 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t24.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t51.t24.t20 t51.t24.t21))
% 0.72/0.93  (step t51.t24.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t51.t24.t19 t51.t24.t22))
% 0.72/0.93  (step t51.t24.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t24.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t51.t24.t23 t51.t24.t24))
% 0.72/0.93  (step t51.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t51.t25 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t51.t23 t51.t24))
% 0.72/0.93  (step t51.t26 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t51.t27 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t27.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t27.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t27.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.72/0.93  (step t51.t27.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t51.t27.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t51.t27.t3 t51.t27.t4))
% 0.72/0.93  (step t51.t27.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t51.t27.t7 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t51.t27.t7.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t27.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t51.t27.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t51.t27.t7.t2))
% 0.72/0.93  (step t51.t27.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t51.t27.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t51.t27.t6 t51.t27.t7))
% 0.72/0.93  (step t51.t27.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t51.t27.t5 t51.t27.t8))
% 0.72/0.93  (step t51.t27.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t27.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t51.t27.t9 t51.t27.t10))
% 0.72/0.93  (step t51.t27.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t51.t27.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t51.t27.t11 t51.t27.t12))
% 0.72/0.93  (step t51.t27 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t51.t28 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t51.t26 t51.t27))
% 0.72/0.93  (step t51.t29 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t51.t25 t51.t28))
% 0.72/0.93  (step t51.t30 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t51.t22 t51.t29 a8))
% 0.72/0.93  (step t51.t31 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t32 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t51.t33 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t51.t33.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t33.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t51.t33.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t51.t33 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t51.t34 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t51.t32 t51.t33))
% 0.72/0.93  (step t51.t35 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t51.t31 t51.t34 a6))
% 0.72/0.93  (step t51.t36 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t51.t37 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t38 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t38.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t38.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t38.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t38.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t51.t38.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t51.t38.t4 a4 a3 a2))
% 0.72/0.93  (step t51.t38.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t51.t38.t5))
% 0.72/0.93  (step t51.t38.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t51.t38.t5))
% 0.72/0.93  (step t51.t38.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t38.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t51.t38.t7 t51.t38.t8))
% 0.72/0.93  (step t51.t38.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t51.t38.t6 t51.t38.t9))
% 0.72/0.93  (step t51.t38.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t38.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t51.t38.t10 t51.t38.t11))
% 0.72/0.93  (step t51.t38.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t38.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t51.t38.t12 t51.t38.t13))
% 0.72/0.93  (step t51.t38 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t51.t39 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t51.t37 t51.t38))
% 0.72/0.93  (step t51.t40 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t51.t41 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t41.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t41.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t41.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t41.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)
% 0.72/0.93  (step t51.t41.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t41.t6 (cl (= (@ (lambda ((X (-> $$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 (t51.t41.t4 t51.t41.t5))
% 0.72/0.93  (step t51.t41.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t51.t41.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t51.t41.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t51.t41.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t51.t41.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t51.t41.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t51.t41.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t51.t41.t8.t3 t51.t41.t8.t4))
% 0.72/0.93  (step t51.t41.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.93  (step t51.t41.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 (t51.t41.t7 t51.t41.t8))
% 0.72/0.93  (step t51.t41.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t51.t41.t6 t51.t41.t9))
% 0.72/0.93  (step t51.t41.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t51.t41.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t51.t41.t10 t51.t41.t11))
% 0.72/0.93  (step t51.t41.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t51.t41.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t51.t41.t12 t51.t41.t13))
% 0.72/0.93  (step t51.t41.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t41.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t51.t41.t14 t51.t41.t15))
% 0.72/0.93  (step t51.t41.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t51.t41.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t51.t41.t16 t51.t41.t17))
% 0.72/0.93  (step t51.t41 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t51.t42 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t51.t40 t51.t41))
% 0.72/0.93  (step t51.t43 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t51.t39 t51.t42))
% 0.72/0.93  (step t51.t44 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t51.t36 t51.t43 a5))
% 0.72/0.93  (step t51.t45 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t51.t16 t51.t21 t51.t30 a7 t51.t35 t51.t44 a4 a3 a2))
% 0.72/0.93  (step t51.t46 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t51.t45))
% 0.72/0.93  (step t51.t47 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t51.t45))
% 0.72/0.93  (step t51.t48 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t51.t46 t51.t47))
% 0.72/0.93  (step t51.t49 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t51.t15 t51.t48))
% 0.72/0.93  (step t51.t50 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t51.t51 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t51.t52 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t51.t52.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (anchor :step t51.t52.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.93  (step t51.t52.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t51.t52.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.93  (step t51.t52.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.93  (step t51.t52.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t51.t52.t2.t2 t51.t52.t2.t3))
% 0.72/0.93  (step t51.t52.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t51.t52.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t51.t52.t2.t4 t51.t52.t2.t5))
% 0.72/0.93  (step t51.t52.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.93  (step t51.t52.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t51.t52.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t51.t52.t2 t51.t52.t3))
% 0.72/0.93  (step t51.t52.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t51.t52.t4))
% 0.72/0.93  (step t51.t52.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.93  (step t51.t52.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t51.t52.t5 t51.t52.t6))
% 0.72/0.93  (step t51.t52 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.93  (step t51.t53 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.93  (step t51.t54 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t51.t52 t51.t53))
% 0.72/0.93  (step t51.t55 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t51.t51 t51.t54))
% 0.72/0.93  (step t51.t56 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t51.t50 t51.t55))
% 0.72/0.93  (step t51.t57 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t51.t49 t51.t56))
% 0.72/0.93  (step t51.t58 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t51.t14 t51.t57 a10))
% 0.72/0.93  (step t51.t59 (cl (and (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t51.t4 t51.t13 t51.t58 t51.t21 t51.t30 a7 t51.t35 t51.t44 a4 a3 a2))
% 0.72/0.93  (step t51.t60 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t51.t59))
% 0.72/0.93  (step t51.t61 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t51.t59))
% 0.72/0.93  (step t51.t62 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t51.t63 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t51.t61 t51.t62))
% 0.72/0.93  (step t51.t64 (cl (= (@ tptp.mor (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t51.t60 t51.t63))
% 0.72/0.93  (step t51.t65 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t51.t66 (cl (= (@ tptp.mbox_s4 Q) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q))) :rule cong :premises (t51.t61 t51.t65))
% 0.72/0.93  (step t51.t67 (cl (= (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)))) :rule cong :premises (t51.t64 t51.t66))
% 0.72/0.93  (step t51.t68 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t51.t69 (cl (= (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) :rule cong :premises (t51.t67 t51.t68))
% 0.72/0.93  (step t51 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t52 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))))) :rule cong :premises (t50 t51))
% 0.72/0.93  (step t53 (cl (= tptp.ior tptp.ior)) :rule refl)
% 0.72/0.93  (anchor :step t54 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t54.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t54.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t54.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t54.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t54.t5 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t54.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t54.t4 t54.t5))
% 0.72/0.93  (step t54.t7 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t54.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t54.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t54.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t54.t8.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t54.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t54.t8.t5 (cl (= (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U)))) :rule cong :premises (t54.t8.t3 t54.t8.t4))
% 0.72/0.93  (step t54.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t54.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t54.t7 t54.t8))
% 0.72/0.93  (step t54.t10 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))))) :rule trans :premises (t54.t6 t54.t9))
% 0.72/0.93  (step t54.t11 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.72/0.93  (step t54.t12 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))))) :rule cong :premises (t54.t10 t54.t11))
% 0.72/0.93  (step t54.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t54.t14 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t54.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t54.t14.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule refl)
% 0.72/0.93  (step t54.t14.t3 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) :rule all_simplify)
% 0.72/0.93  (step t54.t14.t4 (cl (= (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y)))))) :rule cong :premises (t54.t14.t2 t54.t14.t3))
% 0.72/0.93  (step t54.t14 (cl (= (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y)))) U))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule bind)
% 0.72/0.93  (step t54.t15 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (@ Y U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ Q Y))))) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t54.t13 t54.t14))
% 0.72/0.93  (step t54.t16 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))))) :rule trans :premises (t54.t12 t54.t15))
% 0.72/0.93  (step t54.t17 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t54.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0))) :rule cong :premises (t54.t16 t54.t17))
% 0.72/0.93  (step t54.t19 (cl (= (@ (lambda ((U $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ Q Y))))) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule all_simplify)
% 0.72/0.93  (step t54.t20 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule trans :premises (t54.t18 t54.t19))
% 0.72/0.93  (step t54 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule bind)
% 0.72/0.93  (step t55 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule cong :premises (t53 t54))
% 0.72/0.93  (step t56 (cl (= (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))))) :rule trans :premises (t52 t55))
% 0.72/0.93  (step t57 (cl (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))))) :rule resolution :premises (t49 t56 a12))
% 0.72/0.93  (step t58 (cl (not (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) (not (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t59 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.72/0.93  (anchor :step t60 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t60.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t60.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t4 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t60.t5 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.72/0.93  (step t60.t6 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t60.t7 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t60.t8 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.72/0.93  (step t60.t9 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.72/0.93  (step t60.t10 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.72/0.93  (step t60.t11 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t60.t9 t60.t10))
% 0.72/0.93  (step t60.t12 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t60.t8 t60.t11 a9))
% 0.72/0.93  (step t60.t13 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t60.t14 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t60.t15 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t15.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t60.t15.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t15.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t60.t15.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t60.t15.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t60.t15.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t60.t15.t6.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t60.t15.t6.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t60.t15.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t60.t15.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t60.t15.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t60.t15.t5 t60.t15.t6))
% 0.72/0.93  (step t60.t15.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t60.t15.t4 t60.t15.t7 a6))
% 0.72/0.93  (step t60.t15.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t60.t15.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t60.t15.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t15.t11.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t15.t11.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t15.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t15.t11.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t60.t15.t11.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t60.t15.t11.t4 a4 a3 a2))
% 0.72/0.93  (step t60.t15.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t60.t15.t11.t5))
% 0.72/0.93  (step t60.t15.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t60.t15.t11.t5))
% 0.72/0.93  (step t60.t15.t11.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t15.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t60.t15.t11.t7 t60.t15.t11.t8))
% 0.72/0.93  (step t60.t15.t11.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t60.t15.t11.t6 t60.t15.t11.t9))
% 0.72/0.93  (step t60.t15.t11.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t15.t11.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t60.t15.t11.t10 t60.t15.t11.t11))
% 0.72/0.93  (step t60.t15.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t15.t11.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t60.t15.t11.t12 t60.t15.t11.t13))
% 0.72/0.93  (step t60.t15.t11 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t60.t15.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t60.t15.t10 t60.t15.t11))
% 0.72/0.93  (step t60.t15.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t60.t15.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t15.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t15.t14.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t15.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t15.t14.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)
% 0.72/0.93  (step t60.t15.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t60.t15.t14.t6 (cl (= (@ (lambda ((X (-> $$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 (t60.t15.t14.t4 t60.t15.t14.t5))
% 0.72/0.93  (step t60.t15.t14.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t60.t15.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t60.t15.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t60.t15.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t15.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t60.t15.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t60.t15.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t60.t15.t14.t8.t3 t60.t15.t14.t8.t4))
% 0.72/0.93  (step t60.t15.t14.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.93  (step t60.t15.t14.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 (t60.t15.t14.t7 t60.t15.t14.t8))
% 0.72/0.93  (step t60.t15.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t60.t15.t14.t6 t60.t15.t14.t9))
% 0.72/0.93  (step t60.t15.t14.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t15.t14.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t60.t15.t14.t10 t60.t15.t14.t11))
% 0.72/0.93  (step t60.t15.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t60.t15.t14.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t60.t15.t14.t12 t60.t15.t14.t13))
% 0.72/0.93  (step t60.t15.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t15.t14.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t60.t15.t14.t14 t60.t15.t14.t15))
% 0.72/0.93  (step t60.t15.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t60.t15.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t60.t15.t14.t16 t60.t15.t14.t17))
% 0.72/0.93  (step t60.t15.t14 (cl (= (lambda ((U (-> $$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)
% 0.72/0.93  (step t60.t15.t15 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t60.t15.t13 t60.t15.t14))
% 0.72/0.93  (step t60.t15.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t60.t15.t12 t60.t15.t15))
% 0.72/0.93  (step t60.t15.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t60.t15.t9 t60.t15.t16 a5))
% 0.72/0.93  (step t60.t15.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t60.t15.t3 a7 t60.t15.t8 t60.t15.t17 a4 a3 a2))
% 0.72/0.93  (step t60.t15.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t60.t15.t18))
% 0.72/0.93  (step t60.t15.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t60.t15.t18))
% 0.72/0.93  (step t60.t15.t21 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t60.t15.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t60.t15.t20 t60.t15.t21))
% 0.72/0.93  (step t60.t15.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t60.t15.t19 t60.t15.t22))
% 0.72/0.93  (step t60.t15.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t15.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t60.t15.t23 t60.t15.t24))
% 0.72/0.93  (step t60.t15 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t60.t16 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t60.t14 t60.t15))
% 0.72/0.93  (step t60.t17 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t60.t18 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t18.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t60.t18.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t18.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.72/0.93  (step t60.t18.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t60.t18.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t60.t18.t3 t60.t18.t4))
% 0.72/0.93  (step t60.t18.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t60.t18.t7 :args ((U $$unsorted) (:= U U)))
% 0.72/0.93  (step t60.t18.t7.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t18.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t60.t18.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t60.t18.t7.t2))
% 0.72/0.93  (step t60.t18.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t60.t18.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t60.t18.t6 t60.t18.t7))
% 0.72/0.93  (step t60.t18.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t60.t18.t5 t60.t18.t8))
% 0.72/0.93  (step t60.t18.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t18.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t60.t18.t9 t60.t18.t10))
% 0.72/0.93  (step t60.t18.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.93  (step t60.t18.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t60.t18.t11 t60.t18.t12))
% 0.72/0.93  (step t60.t18 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.93  (step t60.t19 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t60.t17 t60.t18))
% 0.72/0.93  (step t60.t20 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t60.t16 t60.t19))
% 0.72/0.93  (step t60.t21 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t60.t13 t60.t20 a8))
% 0.72/0.93  (step t60.t22 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t60.t23 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t60.t24 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t60.t24.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t60.t24.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t60.t24.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t60.t24 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t60.t25 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t60.t23 t60.t24))
% 0.72/0.93  (step t60.t26 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t60.t22 t60.t25 a6))
% 0.72/0.93  (step t60.t27 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t60.t28 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t60.t29 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t29.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t29.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t29.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t29.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))))) (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)))))) :rule and_neg)
% 0.72/0.93  (step t60.t29.t5 (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)))))) :rule resolution :premises (t60.t29.t4 a4 a3 a2))
% 0.72/0.93  (step t60.t29.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t60.t29.t5))
% 0.72/0.93  (step t60.t29.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t60.t29.t5))
% 0.72/0.93  (step t60.t29.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t29.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t60.t29.t7 t60.t29.t8))
% 0.72/0.93  (step t60.t29.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t60.t29.t6 t60.t29.t9))
% 0.72/0.93  (step t60.t29.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t29.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t60.t29.t10 t60.t29.t11))
% 0.72/0.93  (step t60.t29.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t29.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t60.t29.t12 t60.t29.t13))
% 0.72/0.93  (step t60.t29 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t60.t30 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t60.t28 t60.t29))
% 0.72/0.93  (step t60.t31 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t60.t32 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t32.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t32.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t32.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t32.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t60.t32.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t60.t32.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t60.t32.t4 t60.t32.t5))
% 0.72/0.93  (step t60.t32.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.72/0.93  (anchor :step t60.t32.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t60.t32.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t60.t32.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t60.t32.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t60.t32.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t60.t32.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t60.t32.t8.t3 t60.t32.t8.t4))
% 0.72/0.93  (step t60.t32.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t60.t32.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t60.t32.t7 t60.t32.t8))
% 0.72/0.93  (step t60.t32.t10 (cl (= (@ (lambda ((X (-> $$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 (t60.t32.t6 t60.t32.t9))
% 0.72/0.93  (step t60.t32.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t60.t32.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t60.t32.t10 t60.t32.t11))
% 0.72/0.93  (step t60.t32.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t60.t32.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 (t60.t32.t12 t60.t32.t13))
% 0.72/0.93  (step t60.t32.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t32.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 (t60.t32.t14 t60.t32.t15))
% 0.72/0.93  (step t60.t32.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t60.t32.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t60.t32.t16 t60.t32.t17))
% 0.72/0.93  (step t60.t32 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t60.t33 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t60.t31 t60.t32))
% 0.72/0.93  (step t60.t34 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t60.t30 t60.t33))
% 0.72/0.93  (step t60.t35 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t60.t27 t60.t34 a5))
% 0.72/0.93  (step t60.t36 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t60.t7 t60.t12 t60.t21 a7 t60.t26 t60.t35 a4 a3 a2))
% 0.72/0.93  (step t60.t37 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t60.t36))
% 0.72/0.93  (step t60.t38 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t60.t36))
% 0.72/0.93  (step t60.t39 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t60.t37 t60.t38))
% 0.72/0.93  (step t60.t40 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t60.t6 t60.t39))
% 0.72/0.93  (step t60.t41 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t60.t42 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.93  (anchor :step t60.t43 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t60.t43.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (anchor :step t60.t43.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.93  (step t60.t43.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t60.t43.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.93  (step t60.t43.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.93  (step t60.t43.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t60.t43.t2.t2 t60.t43.t2.t3))
% 0.72/0.93  (step t60.t43.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t60.t43.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t60.t43.t2.t4 t60.t43.t2.t5))
% 0.72/0.93  (step t60.t43.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.93  (step t60.t43.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.93  (step t60.t43.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t60.t43.t2 t60.t43.t3))
% 0.72/0.93  (step t60.t43.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t60.t43.t4))
% 0.72/0.93  (step t60.t43.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.93  (step t60.t43.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t60.t43.t5 t60.t43.t6))
% 0.72/0.93  (step t60.t43 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.93  (step t60.t44 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.93  (step t60.t45 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t60.t43 t60.t44))
% 0.72/0.93  (step t60.t46 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t60.t42 t60.t45))
% 0.72/0.93  (step t60.t47 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t60.t41 t60.t46))
% 0.72/0.93  (step t60.t48 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t60.t40 t60.t47))
% 0.72/0.93  (step t60.t49 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t60.t5 t60.t48 a10))
% 0.72/0.93  (step t60.t50 (cl (and (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t60.t4 t60.t49 t60.t12 t60.t21 a7 t60.t26 t60.t35 a4 a3 a2))
% 0.72/0.93  (step t60.t51 (cl (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))))) :rule and :premises (t60.t50))
% 0.72/0.93  (step t60.t52 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t60.t53 (cl (= (@ tptp.mand P) (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P))) :rule cong :premises (t60.t51 t60.t52))
% 0.72/0.93  (step t60.t54 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t60.t55 (cl (= (@ (@ tptp.mand P) Q) (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q))) :rule cong :premises (t60.t53 t60.t54))
% 0.72/0.93  (step t60.t56 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t60.t57 (cl (= (@ (@ (@ tptp.mand P) Q) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) :rule cong :premises (t60.t55 t60.t56))
% 0.72/0.93  (step t60 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t61 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))))) :rule cong :premises (t59 t60))
% 0.72/0.93  (step t62 (cl (= tptp.iand tptp.iand)) :rule refl)
% 0.72/0.93  (anchor :step t63 :args ((P (-> $$unsorted Bool)) (:= P P) (Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t63.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t63.t2 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t63.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t63.t4 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))))) :rule all_simplify)
% 0.72/0.93  (step t63.t5 (cl (= Q Q)) :rule refl)
% 0.72/0.93  (step t63.t6 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q))) :rule cong :premises (t63.t4 t63.t5))
% 0.72/0.93  (step t63.t7 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ P U) (@ Y U))) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule all_simplify)
% 0.72/0.93  (step t63.t8 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))))) :rule trans :premises (t63.t6 t63.t7))
% 0.72/0.93  (step t63.t9 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t63.t10 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0))) :rule cong :premises (t63.t8 t63.t9))
% 0.72/0.93  (step t63.t11 (cl (= (@ (lambda ((U $$unsorted)) (and (@ P U) (@ Q U))) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t63.t12 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) :rule trans :premises (t63.t10 t63.t11))
% 0.72/0.93  (step t63 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t64 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U))) P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule cong :premises (t62 t63))
% 0.72/0.93  (step t65 (cl (= (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))))) :rule trans :premises (t61 t64))
% 0.72/0.93  (step t66 (cl (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0))))) :rule resolution :premises (t58 t65 a11))
% 0.72/0.93  (step t67 (cl (not (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) (not (= tptp.ifalse (@ tptp.inot tptp.itrue))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule equiv_pos2)
% 0.72/0.93  (step t68 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.93  (step t69 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U))))) (not (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.93  (step t70 (cl (not (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) (not (= tptp.itrue (lambda ((W $$unsorted)) true))) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule equiv_pos2)
% 0.72/0.93  (step t71 (cl (= tptp.itrue tptp.itrue)) :rule refl)
% 0.72/0.93  (step t72 (cl (= (lambda ((W $$unsorted)) true) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule all_simplify)
% 0.72/0.93  (step t73 (cl (= (= tptp.itrue (lambda ((W $$unsorted)) true)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t71 t72))
% 0.72/0.93  (step t74 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule resolution :premises (t70 t73 a9))
% 0.72/0.93  (step t75 (cl (not (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) (not (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule equiv_pos2)
% 0.72/0.93  (step t76 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.93  (anchor :step t77 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t77.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t77.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t77.t3 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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))))) (not (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) (not (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule and_neg)
% 0.72/0.93  (step t77.t4 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.93  (step t77.t5 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.93  (anchor :step t77.t6 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.93  (step t77.t6.t1 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t77.t6.t2 (cl (= X X)) :rule refl)
% 0.72/0.93  (step t77.t6.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.93  (step t77.t6 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.93  (step t77.t7 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t77.t5 t77.t6))
% 0.72/0.93  (step t77.t8 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t77.t4 t77.t7 a6))
% 0.72/0.93  (step t77.t9 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.93  (step t77.t10 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t77.t11 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t77.t11.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t77.t11.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t77.t11.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t77.t11.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))))) (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)))))) :rule and_neg)
% 0.72/0.93  (step t77.t11.t5 (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)))))) :rule resolution :premises (t77.t11.t4 a4 a3 a2))
% 0.72/0.93  (step t77.t11.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t77.t11.t5))
% 0.72/0.93  (step t77.t11.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t77.t11.t5))
% 0.72/0.93  (step t77.t11.t8 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t77.t11.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t77.t11.t7 t77.t11.t8))
% 0.72/0.93  (step t77.t11.t10 (cl (= (@ tptp.mor (@ tptp.mnot U)) (@ (lambda ((X (-> $$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 (t77.t11.t6 t77.t11.t9))
% 0.72/0.93  (step t77.t11.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t77.t11.t12 (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 $$unsorted)) (not (@ X U))) U)) V))) :rule cong :premises (t77.t11.t10 t77.t11.t11))
% 0.72/0.93  (step t77.t11.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t77.t11.t14 (cl (= (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0) (@ (@ (@ (lambda ((X (-> $$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 (t77.t11.t12 t77.t11.t13))
% 0.72/0.93  (step t77.t11 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0)))) :rule bind)
% 0.72/0.93  (step t77.t12 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (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 (t77.t10 t77.t11))
% 0.72/0.93  (step t77.t13 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.93  (anchor :step t77.t14 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.93  (step t77.t14.t1 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t77.t14.t2 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t77.t14.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t77.t14.t4 (cl (= (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule refl)
% 0.72/0.93  (step t77.t14.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.93  (step t77.t14.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 $$unsorted)) (not (@ U U)))))) :rule cong :premises (t77.t14.t4 t77.t14.t5))
% 0.72/0.93  (step t77.t14.t7 (cl (= (@ (lambda ((X (-> $$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)
% 0.72/0.93  (anchor :step t77.t14.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.93  (step t77.t14.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.93  (step t77.t14.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.93  (step t77.t14.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.93  (step t77.t14.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.93  (step t77.t14.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t77.t14.t8.t3 t77.t14.t8.t4))
% 0.72/0.93  (step t77.t14.t8 (cl (= (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule bind)
% 0.72/0.93  (step t77.t14.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (lambda ((U $$unsorted)) (not (@ U U)))) (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t77.t14.t7 t77.t14.t8))
% 0.72/0.93  (step t77.t14.t10 (cl (= (@ (lambda ((X (-> $$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 (t77.t14.t6 t77.t14.t9))
% 0.72/0.93  (step t77.t14.t11 (cl (= V V)) :rule refl)
% 0.72/0.93  (step t77.t14.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 $$unsorted)) (or (not (@ U U)) (@ Y U))) V))) :rule cong :premises (t77.t14.t10 t77.t14.t11))
% 0.72/0.93  (step t77.t14.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.93  (step t77.t14.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 (t77.t14.t12 t77.t14.t13))
% 0.72/0.93  (step t77.t14.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.93  (step t77.t14.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 (t77.t14.t14 t77.t14.t15))
% 0.72/0.93  (step t77.t14.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.93  (step t77.t14.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$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 (t77.t14.t16 t77.t14.t17))
% 0.72/0.93  (step t77.t14 (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 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule bind)
% 0.72/0.93  (step t77.t15 (cl (= (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t77.t13 t77.t14))
% 0.72/0.93  (step t77.t16 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t77.t12 t77.t15))
% 0.72/0.93  (step t77.t17 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t77.t9 t77.t16 a5))
% 0.72/0.93  (step t77.t18 (cl (and (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t77.t3 a7 t77.t8 t77.t17 a4 a3 a2))
% 0.72/0.93  (step t77.t19 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t77.t18))
% 0.72/0.93  (step t77.t20 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule and :premises (t77.t18))
% 0.72/0.93  (step t77.t21 (cl (= P P)) :rule refl)
% 0.72/0.93  (step t77.t22 (cl (= (@ tptp.mbox_s4 P) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P))) :rule cong :premises (t77.t20 t77.t21))
% 0.72/0.93  (step t77.t23 (cl (= (@ tptp.mnot (@ tptp.mbox_s4 P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)))) :rule cong :premises (t77.t19 t77.t22))
% 0.72/0.94  (step t77.t24 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t77.t25 (cl (= (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) :rule cong :premises (t77.t23 t77.t24))
% 0.72/0.94  (step t77 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)))) :rule bind)
% 0.72/0.94  (step t78 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))))) :rule cong :premises (t76 t77))
% 0.72/0.94  (step t79 (cl (= tptp.inot tptp.inot)) :rule refl)
% 0.72/0.94  (anchor :step t80 :args ((P (-> $$unsorted Bool)) (:= P P) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.94  (step t80.t1 (cl (= P P)) :rule refl)
% 0.72/0.94  (step t80.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t80.t3 (cl (= (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule refl)
% 0.72/0.94  (step t80.t4 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.94  (step t80.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t80.t3 t80.t4))
% 0.72/0.94  (step t80.t6 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))))) :rule all_simplify)
% 0.72/0.94  (anchor :step t80.t7 :args ((U $$unsorted) (:= U U)))
% 0.72/0.94  (step t80.t7.t1 (cl (= U U)) :rule refl)
% 0.72/0.94  (step t80.t7.t2 (cl (= (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.94  (step t80.t7.t3 (cl (= (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y)))))) :rule cong :premises (t80.t7.t2))
% 0.72/0.94  (step t80.t7 (cl (= (lambda ((U $$unsorted)) (not (@ (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) U))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.94  (step t80.t8 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (lambda ((X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t80.t6 t80.t7))
% 0.72/0.94  (step t80.t9 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))))) :rule trans :premises (t80.t5 t80.t8))
% 0.72/0.94  (step t80.t10 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t80.t11 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0))) :rule cong :premises (t80.t9 t80.t10))
% 0.72/0.94  (step t80.t12 (cl (= (@ (lambda ((U $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel U) Y)) (@ P Y))))) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule all_simplify)
% 0.72/0.94  (step t80.t13 (cl (= (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) :rule trans :premises (t80.t11 t80.t12))
% 0.72/0.94  (step t80 (cl (= (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0)) (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule bind)
% 0.72/0.94  (step t81 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) (@ (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))) P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule cong :premises (t79 t80))
% 0.72/0.94  (step t82 (cl (= (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule trans :premises (t78 t81))
% 0.72/0.94  (step t83 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule resolution :premises (t75 t82 a8))
% 0.72/0.94  (step t84 (cl (not (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) (not (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule equiv_pos2)
% 0.72/0.94  (step t85 (cl (= tptp.mbox_s4 tptp.mbox_s4)) :rule refl)
% 0.72/0.94  (anchor :step t86 :args ((P (-> $$unsorted Bool)) (:= P P) (X $$unsorted) (:= X X)))
% 0.72/0.94  (step t86.t1 (cl (= P P)) :rule refl)
% 0.72/0.94  (step t86.t2 (cl (= X X)) :rule refl)
% 0.72/0.94  (step t86.t3 (cl (= (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) :rule all_simplify)
% 0.72/0.94  (step t86 (cl (= (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y)))) (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule bind)
% 0.72/0.94  (step t87 (cl (= (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))))) :rule cong :premises (t85 t86))
% 0.72/0.94  (step t88 (cl (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y)))))) :rule resolution :premises (t84 t87 a6))
% 0.72/0.94  (step t89 (cl (not (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) (not (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0)))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule equiv_pos2)
% 0.72/0.94  (step t90 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.94  (anchor :step t91 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.94  (step t91.t1 (cl (= U U)) :rule refl)
% 0.72/0.94  (step t91.t2 (cl (= V V)) :rule refl)
% 0.72/0.94  (step t91.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t91.t4 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U))))) (not (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule and_neg)
% 0.72/0.94  (step t91.t5 (cl (and (= tptp.mand (lambda ((X (-> $$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 $$unsorted)) (not (@ X U)))))) :rule resolution :premises (t91.t4 a4 a3 a2))
% 0.72/0.94  (step t91.t6 (cl (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))))) :rule and :premises (t91.t5))
% 0.72/0.94  (step t91.t7 (cl (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))))) :rule and :premises (t91.t5))
% 0.72/0.94  (step t91.t8 (cl (= U U)) :rule refl)
% 0.72/0.94  (step t91.t9 (cl (= (@ tptp.mnot U) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U))) :rule cong :premises (t91.t7 t91.t8))
% 0.72/0.94  (step t91.t10 (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 $$unsorted)) (not (@ X U))) U)))) :rule cong :premises (t91.t6 t91.t9))
% 0.72/0.94  (step t91.t11 (cl (= V V)) :rule refl)
% 0.72/0.94  (step t91.t12 (cl (= (@ (@ tptp.mor (@ tptp.mnot U)) V) (@ (@ (lambda ((X (-> $$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 (t91.t10 t91.t11))
% 0.72/0.94  (step t91.t13 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t91.t14 (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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))) :rule cong :premises (t91.t12 t91.t13))
% 0.72/0.94  (step t91 (cl (= (lambda ((U (-> $$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)
% 0.72/0.94  (step t92 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$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 $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0))))) :rule cong :premises (t90 t91))
% 0.72/0.94  (step t93 (cl (= tptp.mimplies tptp.mimplies)) :rule refl)
% 0.72/0.94  (anchor :step t94 :args ((U (-> $$unsorted Bool)) (:= U U) (V (-> $$unsorted Bool)) (:= V V) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.94  (step t94.t1 (cl (= U U)) :rule refl)
% 0.72/0.94  (step t94.t2 (cl (= V V)) :rule refl)
% 0.72/0.94  (step t94.t3 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t94.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)
% 0.72/0.94  (step t94.t5 (cl (= (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U) (lambda ((U $$unsorted)) (not (@ U U))))) :rule all_simplify)
% 0.72/0.94  (step t94.t6 (cl (= (@ (lambda ((X (-> $$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 (t94.t4 t94.t5))
% 0.72/0.94  (step t94.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 $$unsorted)) (not (@ U U))) U) (@ Y U))))) :rule all_simplify)
% 0.72/0.94  (anchor :step t94.t8 :args ((Y (-> $$unsorted Bool)) (:= Y Y) (U $$unsorted) (:= U U)))
% 0.72/0.94  (step t94.t8.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.94  (step t94.t8.t2 (cl (= U U)) :rule refl)
% 0.72/0.94  (step t94.t8.t3 (cl (= (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (not (@ U U)))) :rule all_simplify)
% 0.72/0.94  (step t94.t8.t4 (cl (= (@ Y U) (@ Y U))) :rule refl)
% 0.72/0.94  (step t94.t8.t5 (cl (= (or (@ (lambda ((U $$unsorted)) (not (@ U U))) U) (@ Y U)) (or (not (@ U U)) (@ Y U)))) :rule cong :premises (t94.t8.t3 t94.t8.t4))
% 0.72/0.94  (step t94.t8 (cl (= (lambda ((Y (-> $$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)
% 0.72/0.94  (step t94.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 (t94.t7 t94.t8))
% 0.72/0.94  (step t94.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 $$unsorted)) (or (not (@ U U)) (@ Y U))))) :rule trans :premises (t94.t6 t94.t9))
% 0.72/0.94  (step t94.t11 (cl (= V V)) :rule refl)
% 0.72/0.94  (step t94.t12 (cl (= (@ (@ (lambda ((X (-> $$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 (t94.t10 t94.t11))
% 0.72/0.94  (step t94.t13 (cl (= (@ (lambda ((Y (-> $$unsorted Bool)) (U $$unsorted)) (or (not (@ U U)) (@ Y U))) V) (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule all_simplify)
% 0.72/0.94  (step t94.t14 (cl (= (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))))) :rule trans :premises (t94.t12 t94.t13))
% 0.72/0.94  (step t94.t15 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t94.t16 (cl (= (@ (@ (@ (lambda ((X (-> $$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 $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0))) :rule cong :premises (t94.t14 t94.t15))
% 0.72/0.94  (step t94.t17 (cl (= (@ (lambda ((U $$unsorted)) (or (not (@ U U)) (@ V U))) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule all_simplify)
% 0.72/0.94  (step t94.t18 (cl (= (@ (@ (@ (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U))) (@ (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U))) U)) V) __flatten_var_0) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))) :rule trans :premises (t94.t16 t94.t17))
% 0.72/0.94  (step t94 (cl (= (lambda ((U (-> $$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)
% 0.72/0.94  (step t95 (cl (= (= tptp.mimplies (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.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule cong :premises (t93 t94))
% 0.72/0.94  (step t96 (cl (= (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))) (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0)))))) :rule trans :premises (t92 t95))
% 0.72/0.94  (step t97 (cl (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (@ U __flatten_var_0)) (@ V __flatten_var_0))))) :rule resolution :premises (t89 t96 a5))
% 0.72/0.94  (step t98 (cl (and (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t69 t74 t83 a7 t88 t97 a4 a3 a2))
% 0.72/0.94  (step t99 (cl (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) :rule and :premises (t98))
% 0.72/0.94  (step t100 (cl (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) :rule and :premises (t98))
% 0.72/0.94  (step t101 (cl (= (@ tptp.inot tptp.itrue) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)))) :rule cong :premises (t99 t100))
% 0.72/0.94  (step t102 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))))) :rule cong :premises (t68 t101))
% 0.72/0.94  (step t103 (cl (= tptp.ifalse tptp.ifalse)) :rule refl)
% 0.72/0.94  (step t104 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))))) :rule all_simplify)
% 0.72/0.94  (anchor :step t105 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.94  (step t105.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (anchor :step t105.t2 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.94  (step t105.t2.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.94  (step t105.t2.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.94  (step t105.t2.t3 (cl (= (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y) true)) :rule all_simplify)
% 0.72/0.94  (step t105.t2.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true))) :rule cong :premises (t105.t2.t2 t105.t2.t3))
% 0.72/0.94  (step t105.t2.t5 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) true) true)) :rule all_simplify)
% 0.72/0.94  (step t105.t2.t6 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)) true)) :rule trans :premises (t105.t2.t4 t105.t2.t5))
% 0.72/0.94  (step t105.t2 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) (forall ((Y $$unsorted)) true))) :rule bind)
% 0.72/0.94  (step t105.t3 (cl (= (forall ((Y $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.94  (step t105.t4 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))) true)) :rule trans :premises (t105.t2 t105.t3))
% 0.72/0.94  (step t105.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) (not true))) :rule cong :premises (t105.t4))
% 0.72/0.94  (step t105.t6 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.94  (step t105.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y)))) false)) :rule trans :premises (t105.t5 t105.t6))
% 0.72/0.94  (step t105 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((__flatten_var_0 $$unsorted)) false))) :rule bind)
% 0.72/0.94  (step t106 (cl (= (lambda ((__flatten_var_0 $$unsorted)) false) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule all_simplify)
% 0.72/0.94  (step t107 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((BOUND_VARIABLE_922 $$unsorted)) true) Y))))) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t105 t106))
% 0.72/0.94  (step t108 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule trans :premises (t104 t107))
% 0.72/0.94  (step t109 (cl (= (= tptp.ifalse (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))) (lambda ((BOUND_VARIABLE_922 $$unsorted)) true))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule cong :premises (t103 t108))
% 0.72/0.94  (step t110 (cl (= (= tptp.ifalse (@ tptp.inot tptp.itrue)) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)))) :rule trans :premises (t102 t109))
% 0.72/0.94  (step t111 (cl (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false))) :rule resolution :premises (t67 t110 a10))
% 0.72/0.94  (step t112 (cl (and (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))) (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (@ Phi W))))) (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (not (forall ((W $$unsorted)) (not (@ Phi W)))))) (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))) (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (or (and (or (not (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200)))) (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (or (not (forall ((BOUND_VARIABLE_1210 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1210) BOUND_VARIABLE_1210)) (@ Q BOUND_VARIABLE_1210)))) (forall ((BOUND_VARIABLE_1200 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1200) BOUND_VARIABLE_1200)) (@ P BOUND_VARIABLE_1200))))) (forall ((Y $$unsorted)) (not (@ (@ tptp.irel __flatten_var_0) Y))))))) (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))))))) (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (or (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (@ P __flatten_var_0) (@ Q __flatten_var_0)))) (= tptp.ifalse (lambda ((BOUND_VARIABLE_2829 $$unsorted)) false)) (= tptp.itrue (lambda ((BOUND_VARIABLE_922 $$unsorted)) true)) (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))) (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel X) Y)) (@ P Y))))) (= tptp.mimplies (lambda ((U (-> $$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)))))) :rule resolution :premises (t2 a20 t7 t12 a17 t21 t30 t39 t48 t57 t66 t111 t74 t83 a7 t88 t97 a4 a3 a2))
% 0.72/0.94  (step t113 (cl (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))))) :rule and :premises (t112))
% 0.72/0.94  (step t114 (cl (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule and :premises (t112))
% 0.72/0.94  (step t115 (cl (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)))) :rule and :premises (t112))
% 0.72/0.94  (step t116 (cl (= tptp.p tptp.p)) :rule refl)
% 0.72/0.94  (step t117 (cl (= (@ tptp.iatom tptp.p) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p))) :rule cong :premises (t115 t116))
% 0.72/0.94  (step t118 (cl (= (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)))) :rule cong :premises (t114 t117))
% 0.72/0.94  (step t119 (cl (= (@ (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ tptp.iatom tptp.p)) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)))) :rule cong :premises (t118 t117))
% 0.72/0.94  (step t120 (cl (= (@ tptp.ivalid (@ (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ tptp.iatom tptp.p))) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p))))) :rule cong :premises (t113 t119))
% 0.72/0.94  (step t121 (cl (= (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ tptp.iatom tptp.p)))) (not (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)))))) :rule cong :premises (t120))
% 0.72/0.94  (step t122 (cl (= (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))))) :rule refl)
% 0.72/0.94  (step t123 (cl (= (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))))) :rule refl)
% 0.72/0.94  (step t124 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p) (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)))) :rule all_simplify)
% 0.72/0.94  (step t125 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0))))) :rule cong :premises (t123 t124))
% 0.72/0.94  (step t126 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))))))) :rule all_simplify)
% 0.72/0.94  (anchor :step t127 :args ((Q (-> $$unsorted Bool)) (:= Q Q) (__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.94  (step t127.t1 (cl (= Q Q)) :rule refl)
% 0.72/0.94  (step t127.t2 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (anchor :step t127.t3 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.94  (step t127.t3.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.94  (step t127.t3.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.94  (step t127.t3.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y) (@ tptp.p Y))) :rule all_simplify)
% 0.72/0.94  (step t127.t3.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) :rule cong :premises (t127.t3.t2 t127.t3.t3))
% 0.72/0.94  (step t127.t3 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) :rule bind)
% 0.72/0.94  (step t127.t4 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule cong :premises (t127.t3))
% 0.72/0.94  (step t127.t5 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y))))) :rule refl)
% 0.72/0.94  (step t127.t6 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule cong :premises (t127.t4 t127.t5))
% 0.72/0.94  (step t127.t7 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))))) :rule refl)
% 0.72/0.94  (step t127.t8 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule cong :premises (t127.t7 t127.t3))
% 0.72/0.94  (step t127.t9 (cl (= (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y))))) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))))) :rule cong :premises (t127.t6 t127.t8))
% 0.72/0.94  (step t127 (cl (= (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))))) :rule bind)
% 0.72/0.94  (step t128 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0))) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))))) :rule trans :premises (t126 t127))
% 0.72/0.94  (step t129 (cl (= (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))))) :rule trans :premises (t125 t128))
% 0.72/0.94  (step t130 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0))))) :rule cong :premises (t129 t124))
% 0.72/0.94  (step t131 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))))) :rule all_simplify)
% 0.72/0.94  (anchor :step t132 :args ((__flatten_var_0 $$unsorted) (:= __flatten_var_0 __flatten_var_0)))
% 0.72/0.94  (step t132.t1 (cl (= __flatten_var_0 __flatten_var_0)) :rule refl)
% 0.72/0.94  (step t132.t2 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule refl)
% 0.72/0.94  (anchor :step t132.t3 :args ((Y $$unsorted) (:= Y Y)))
% 0.72/0.94  (step t132.t3.t1 (cl (= Y Y)) :rule refl)
% 0.72/0.94  (step t132.t3.t2 (cl (= (not (@ (@ tptp.irel __flatten_var_0) Y)) (not (@ (@ tptp.irel __flatten_var_0) Y)))) :rule refl)
% 0.72/0.94  (step t132.t3.t3 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y) (@ tptp.p Y))) :rule all_simplify)
% 0.72/0.94  (step t132.t3.t4 (cl (= (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) :rule cong :premises (t132.t3.t2 t132.t3.t3))
% 0.72/0.94  (step t132.t3 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) :rule bind)
% 0.72/0.94  (step t132.t4 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule cong :premises (t132.t2 t132.t3))
% 0.72/0.94  (step t132.t5 (cl (= (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule cong :premises (t132.t3))
% 0.72/0.94  (step t132.t6 (cl (= (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) :rule refl)
% 0.72/0.94  (step t132.t7 (cl (= (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule cong :premises (t132.t5 t132.t6))
% 0.72/0.94  (step t132.t8 (cl (= (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))))) :rule cong :premises (t132.t4 t132.t7))
% 0.72/0.94  (step t132.t9 (cl (= (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule all_simplify)
% 0.72/0.94  (step t132.t10 (cl (= (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) :rule trans :premises (t132.t8 t132.t9))
% 0.72/0.94  (step t132 (cl (= (lambda ((__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0)) Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))))) :rule bind)
% 0.72/0.94  (step t133 (cl (= (@ (lambda ((Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) (lambda ((__flatten_var_0 $$unsorted)) (@ tptp.p __flatten_var_0))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))))) :rule trans :premises (t131 t132))
% 0.72/0.94  (step t134 (cl (= (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))))) :rule trans :premises (t130 t133))
% 0.72/0.94  (step t135 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p))) (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))))) :rule cong :premises (t122 t134))
% 0.72/0.94  (step t136 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) (forall ((W $$unsorted)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) W)))) :rule all_simplify)
% 0.72/0.94  (anchor :step t137 :args ((W $$unsorted) (:= W W)))
% 0.72/0.94  (step t137.t1 (cl (= W W)) :rule refl)
% 0.72/0.94  (step t137.t2 (cl (= (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) W) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y)))))) :rule all_simplify)
% 0.72/0.94  (step t137 (cl (= (forall ((W $$unsorted)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) W)) (forall ((W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y))))))) :rule bind)
% 0.72/0.94  (step t138 (cl (= (forall ((W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y))))) (forall ((W $$unsorted)) true))) :rule all_simplify)
% 0.72/0.94  (step t139 (cl (= (forall ((W $$unsorted)) true) true)) :rule all_simplify)
% 0.72/0.94  (step t140 (cl (= (forall ((W $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel W) Y)) (@ tptp.p Y))))) true)) :rule trans :premises (t138 t139))
% 0.72/0.94  (step t141 (cl (= (forall ((W $$unsorted)) (@ (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y))))) W)) true)) :rule trans :premises (t137 t140))
% 0.72/0.94  (step t142 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (lambda ((__flatten_var_0 $$unsorted)) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ tptp.p Y)))))) true)) :rule trans :premises (t136 t141))
% 0.72/0.94  (step t143 (cl (= (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p))) true)) :rule trans :premises (t135 t142))
% 0.72/0.94  (step t144 (cl (= (not (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)))) (not true))) :rule cong :premises (t143))
% 0.72/0.94  (step t145 (cl (= (not true) false)) :rule all_simplify)
% 0.72/0.94  (step t146 (cl (= (not (@ (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W))) (@ (@ (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (and (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (or (not (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ Q Y)))) (forall ((Y $$unsorted)) (or (not (@ (@ tptp.irel __flatten_var_0) Y)) (@ P Y)))))) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)) (@ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0)) tptp.p)))) false)) :rule trans :premises (t144 t145))
% 0.72/0.94  (step t147 (cl (= (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ tptp.iatom tptp.p)) (@ tptp.iatom tptp.p)))) false)) :rule trans :premises (t121 t146))
% 0.72/0.94  (step t148 (cl false) :rule resolution :premises (t1 t147 a21))
% 0.72/0.94  (step t149 (cl (not false)) :rule false)
% 0.72/0.94  (step t150 (cl) :rule resolution :premises (t148 t149))
% 0.72/0.94  
% 0.72/0.94  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.0LkT4eVYLE/cvc5---1.0.5_741.smt2
% 0.72/0.94  % cvc5---1.0.5 exiting
% 0.72/0.94  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------